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<front>
<journal-meta>
<journal-id journal-id-type="publisher-id">Front. Earth Sci.</journal-id>
<journal-title-group>
<journal-title>Frontiers in Earth Science</journal-title>
<abbrev-journal-title abbrev-type="pubmed">Front. Earth Sci.</abbrev-journal-title>
</journal-title-group>
<issn pub-type="epub">2296-6463</issn>
<publisher>
<publisher-name>Frontiers Media S.A.</publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id pub-id-type="publisher-id">1751759</article-id>
<article-id pub-id-type="doi">10.3389/feart.2026.1751759</article-id>
<article-version article-version-type="Version of Record" vocab="NISO-RP-8-2008"/>
<article-categories>
<subj-group subj-group-type="heading">
<subject>Original Research</subject>
</subj-group>
</article-categories>
<title-group>
<article-title>RETRACTED: Landslide mapping from polarimetric SAR images using deep learning and morphological model</article-title>
<alt-title alt-title-type="left-running-head">Xu et al.</alt-title>
<alt-title alt-title-type="right-running-head">
<ext-link ext-link-type="uri" xlink:href="https://doi.org/10.3389/feart.2026.1751759">10.3389/feart.2026.1751759</ext-link>
</alt-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname>Xu</surname>
<given-names>Shi</given-names>
</name>
<xref ref-type="aff" rid="aff1">
<sup>1</sup>
</xref>
<uri xlink:href="https://loop.frontiersin.org/people/3289865"/>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Writing &#x2013; review &#x26; editing" vocab-term-identifier="https://credit.niso.org/contributor-roles/Writing - review &#x26; editing/">Writing - review and editing</role>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Writing &#x2013; original draft" vocab-term-identifier="https://credit.niso.org/contributor-roles/writing-original-draft/">Writing - original draft</role>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Methodology" vocab-term-identifier="https://credit.niso.org/contributor-roles/methodology/">Methodology</role>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Conceptualization" vocab-term-identifier="https://credit.niso.org/contributor-roles/conceptualization/">Conceptualization</role>
</contrib>
<contrib contrib-type="author" corresp="yes">
<name>
<surname>Dong</surname>
<given-names>Guozhen</given-names>
</name>
<xref ref-type="aff" rid="aff2">
<sup>2</sup>
</xref>
<xref ref-type="corresp" rid="c001">&#x2a;</xref>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Supervision" vocab-term-identifier="https://credit.niso.org/contributor-roles/supervision/">Supervision</role>
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</contrib>
<contrib contrib-type="author">
<name>
<surname>Yang</surname>
<given-names>Lin</given-names>
</name>
<xref ref-type="aff" rid="aff3">
<sup>3</sup>
</xref>
<role vocab="credit" vocab-identifier="https://credit.niso.org/" vocab-term="Writing &#x2013; review &#x26; editing" vocab-term-identifier="https://credit.niso.org/contributor-roles/Writing - review &#x26; editing/">Writing - review and editing</role>
</contrib>
<contrib contrib-type="author">
<name>
<surname>Wang</surname>
<given-names>Jing</given-names>
</name>
<xref ref-type="aff" rid="aff4">
<sup>4</sup>
</xref>
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<aff id="aff1">
<label>1</label>
<institution>China Transport Telecommunications &#x26; Information Center</institution>, <city>Beijing</city>, <country country="CN">China</country>
</aff>
<aff id="aff2">
<label>2</label>
<institution>Yanching Institute of Technology</institution>, <city>Sanhe</city>, <country country="CN">China</country>
</aff>
<aff id="aff3">
<label>3</label>
<institution>College of Agriculture, Chifeng University</institution>, <city>Chifeng</city>, <country country="CN">China</country>
</aff>
<aff id="aff4">
<label>4</label>
<institution>Aerospace Planning and Design Group Co., Ltd.</institution>, <city>Beijing</city>, <country country="CN">China</country>
</aff>
<author-notes>
<corresp id="c001">
<label>&#x2a;</label>Correspondence: Guozhen Dong, <email xlink:href="mailto:gzdong1218@126.com">gzdong1218@126.com</email>
</corresp>
</author-notes>
<pub-date publication-format="electronic" date-type="pub" iso-8601-date="2026-02-02">
<day>02</day>
<month>02</month>
<year>2026</year>
</pub-date>
<pub-date publication-format="electronic" date-type="retracted">
<day>05</day>
<month>08</month>
<year>2026</year>
</pub-date>
<pub-date publication-format="electronic" date-type="collection">
<year>2026</year>
</pub-date>
<volume>14</volume>
<elocation-id>1751759</elocation-id>
<history>
<date date-type="received">
<day>22</day>
<month>11</month>
<year>2025</year>
</date>
<date date-type="rev-recd">
<day>01</day>
<month>01</month>
<year>2026</year>
</date>
<date date-type="accepted">
<day>12</day>
<month>01</month>
<year>2026</year>
</date>
</history>
<permissions>
<copyright-statement>Copyright &#xa9; 2026 Xu, Dong, Yang and Wang.</copyright-statement>
<copyright-year>2026</copyright-year>
<copyright-holder>Xu, Dong, Yang and Wang</copyright-holder>
<license>
<ali:license_ref start_date="2026-02-02">https://creativecommons.org/licenses/by/4.0/</ali:license_ref>
<license-p>This is an open-access article distributed under the terms of the <ext-link ext-link-type="uri" xlink:href="https://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution License (CC BY)</ext-link>. The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.</license-p>
</license>
</permissions>
<abstract>
<p>Rapid and accurate mapping of landslides following triggering events such as intense rainfall is critical for emergency response, hazard assessment, and disaster mitigation, particularly in mountainous regions prone to frequent slope failures. The effectiveness of optical imagery in such contexts is often limited by persistent cloud cover and fog during the rainy season, whereas synthetic aperture radar (SAR) provides all-weather, day-and-night observations, making it a suitable alternative for time-sensitive mapping. This study presents a deep learning framework incorporating a morphological optimization model for precise landslide detection from a single post-event polarimetric SAR acquisition. The morphological optimization model is introduced to impose shape- and connectivity-aware constraints on SAR-derived candidates, suppressing isolated false alarms and improving boundary continuity under speckle and terrain-induced noise. The approach combines polarimetric parameter selection, a Deep Forest classifier, a majority voting scheme, and shape constraints to enhance boundary delineation. A rainfall-induced landslide in Bijie City, Guizhou Province, China, was selected as the case study, using quad-polarization ALOS-2 and dual-polarization Sentinel-1 imagery. The observed performance gap between ALOS-2 and Sentinel-1 is consistent with the stronger vegetation penetration and reduced volume-scattering sensitivity of L-band compared with C-band in humid mountainous terrain. The quad-pol ALOS-2 data achieved the highest overall accuracy (95.2%), followed by dual-pol ALOS-2 (89.8%), while Sentinel-1 provided effective regional-scale detection (76.3%). The results confirm the method&#x2019;s potential for rapid, reliable landslide mapping in complex mountainous terrain, and its applicability to operational disaster assessment in regions with similar geomorphological and climatic conditions.</p>
</abstract>
<kwd-group>
<kwd>adaptive fusion</kwd>
<kwd>deep learning</kwd>
<kwd>landslide deformation monitoring</kwd>
<kwd>multi-source InSAR</kwd>
<kwd>uncertainty quantification</kwd>
</kwd-group>
<funding-group>
<funding-statement>The author(s) declared that financial support was not received for this work and/or its publication.</funding-statement>
</funding-group>
<counts>
<fig-count count="8"/>
<table-count count="5"/>
<equation-count count="12"/>
<ref-count count="31"/>
<page-count count="00"/>
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<custom-meta>
<meta-name>section-at-acceptance</meta-name>
<meta-value>Geoscience and Society</meta-value>
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</front>
<body>
<sec sec-type="intro" id="s1">
<label>1</label>
<title>Introduction</title>
<p>Landslides are one of the most destructive geological disasters within mountainous regions and tend to be induced by heavy rainfalls, seismic activity, or manmade disturbances (<xref ref-type="bibr" rid="B2">Ali et al., 2021</xref>; <xref ref-type="bibr" rid="B18">Ma et al., 2023</xref>; <xref ref-type="bibr" rid="B26">Wu et al., 2022</xref>). Prevalent and accurate landslide mapping is also central in disaster recovery, hazard mapping, and risk mitigation. Bijie City is located within Guizhou Province in Southwest China and is specifically prone to landslide disasters induced by rain due to steep slopes, steeply incised river valleys, extensive karst regions, and concentrated summer rains (<xref ref-type="bibr" rid="B9">Fu et al., 2023</xref>; <xref ref-type="bibr" rid="B12">Jiang et al., 2025</xref>; <xref ref-type="bibr" rid="B28">Wu X. et al., 2024</xref>). Historical records report recurrent extensive slope disasters within the region that have frequently been accompanied by heavy casualties, destruction of property and infrastructure, and specifically occur within the rainy season from May through September (<xref ref-type="bibr" rid="B4">Bekaert et al., 2020</xref>; <xref ref-type="bibr" rid="B5">Brunetti et al., 2021</xref>; <xref ref-type="bibr" rid="B17">Ma and Wang, 2024</xref>; <xref ref-type="bibr" rid="B25">Wu et al., 2020</xref>).</p>
<p>Optical high-resolution imagery is also routinely utilized for post-event landslide mapping but will be greatly compromised in humid monsoon areas such as Bijie, where perpetual cloud cover and fog will frequently obscure the terrain (<xref ref-type="bibr" rid="B1">Ahmad et al., 2019</xref>; <xref ref-type="bibr" rid="B11">Han et al., 2023</xref>; <xref ref-type="bibr" rid="B16">Liu et al., 2024</xref>; <xref ref-type="bibr" rid="B8">Fan et al., 2025b</xref>). Synthetic aperture radar (SAR), however, which does not require weather or daylight and therefore can penetrate fog and cloud, provides a resilient substitute for rapid mapping in these conditions. Previous studies utilizing SAR have utilized techniques such as change detection, coherence analysis, and machine learning classification (<xref ref-type="bibr" rid="B3">Amitrano et al., 2024</xref>; <xref ref-type="bibr" rid="B6">Datcu et al., 2023</xref>; <xref ref-type="bibr" rid="B10">Garc&#xed;a et al., 2024</xref>; <xref ref-type="bibr" rid="B14">Lang et al., 2024</xref>; <xref ref-type="bibr" rid="B7">Fan et al., 2025a</xref>). These conventional methods, however, will frequently require data at more than one instance in time and significant quantities of ground-truth data. Pre-event SAR or optical data will frequently not exist after an event and significant field data collection will frequently be logistically challenging, particularly in rural mountains (<xref ref-type="bibr" rid="B13">Jin et al., 2025</xref>).</p>
<p>Polarimetric SAR (PolSAR) improves surface description through the transmission and reception of microwaves in varied polarization states and hence retrieves nuanced scattering characteristics of variegated land covers (<xref ref-type="bibr" rid="B27">Wu S. et al., 2024</xref>). Various researches have established polarimetric decomposition parameters and coherency matrix elements as useful indicators for separating landslide-impacted regions (<xref ref-type="bibr" rid="B21">Quan et al., 2023</xref>; <xref ref-type="bibr" rid="B22">Silva-Perez et al., 2021</xref>; <xref ref-type="bibr" rid="B31">Yin et al., 2024</xref>). While these available PolSAR-based methods still largely depend on multi-temporal views or supporting datasets like digital elevation models (DEMs), these might impose restrictions on their utility for prompt emergency response (<xref ref-type="bibr" rid="B19">Niu et al., 2022</xref>).</p>
<p>To address these limitations, this study introduces an integrated single-temporal, post-event landslide mapping framework that integrates polarimetric parameter optimization, a Deep Forest classifier (<xref ref-type="bibr" rid="B20">Pham et al., 2024</xref>; <xref ref-type="bibr" rid="B23">Tang et al., 2023</xref>; <xref ref-type="bibr" rid="B29">Xu et al., 2024</xref>; <xref ref-type="bibr" rid="B30">Yang et al., 2024</xref>), a majority voting scheme to stabilize pixel-wise predictions in speckle-affected SAR imagery, and a morphological optimization model incorporating aspect ratio and longitudinal profile constraints (<xref ref-type="bibr" rid="B15">Liang et al., 2024</xref>; <xref ref-type="bibr" rid="B24">Wang et al., 2024</xref>). The objective is to enable rapid and reproducible landslide mapping from a single post-event PolSAR acquisition while maintaining spatially coherent and physically plausible boundaries. The morphological optimization component is introduced to impose shape- and connectivity-aware priors that suppress isolated false alarms and refine boundary continuity, complementing the data-driven classifier outputs. Accordingly, the originality of this work lies in the unified integration of polarimetric feature selection, Deep Forest inference, majority voting, and shape-constrained morphological refinement into a single-temporal operational pipeline, rather than claiming novelty for any standalone component. The proposed method is evaluated using a rainfall-induced landslide case in Bijie City, based on quad-polarization ALOS-2 and dual-polarization Sentinel-1 imagery. Performance is assessed in terms of classification accuracy, boundary delineation quality, and adaptability across polarimetric modes, providing practical insights into the operational use of single-temporal PolSAR data for rapid post-disaster mapping in complex mountainous terrain.</p>
</sec>
<sec id="s2">
<label>2</label>
<title>Study area and data description</title>
<sec id="s2-1">
<label>2.1</label>
<title>Study area</title>
<p>The study region is in Dafang County of Bijie City of Guizhou Province in south-west China (<xref ref-type="fig" rid="F1">Figure 1</xref>). Towards the end of May 2025, an unprecedented 24 h cumulative rainfall episode was observed wherein more than 200 mm of 24 h cumulative rainfall was realized at a number of meteorological stations. The above-heavy rainfalls triggered two huge landslide disasters on 22 May: one was in Changshi Town (approximately 03:00 local time) and another was in Qingyang Village of Guowa Township (approximately 09:00). The landslide of Qingyang Village was very destructive. Investigations in the field and UAV survey showed that the runout distance was approximately 1,040 m and the maximum width was approximately 300 m. Volumetric estimation gave 2.4<inline-formula id="inf1">
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</inline-formula>, with an average burial height of approximately 10 m, or the size of a two-story building. Two deaths ensued, 19 villagers remained stranded, and rural dwelling destruction, farmland burial, and damage along several km of rural roads resulted.</p>
<fig id="F1" position="float">
<label>FIGURE 1</label>
<caption>
<p>Location of Dafang County within Bijie City, Guizhou Province, and the landslide sites triggered by the May 2025 rainfall event. <bold>(a)</bold> China. <bold>(b)</bold> Guizhou. <bold>(c)</bold> Bijie. <bold>(d)</bold> Dafang County.</p>
</caption>
<graphic xlink:href="feart-14-1751759-g001.tif">
<alt-text content-type="machine-generated">Map series highlighting locations in China. Panel (a) shows an overview map of China with Guizhou Province marked. Panel (b) is a close-up of Guizhou, indicating major cities such as Guiyang and Zunyi. Panel (c) zooms into Bijie, showing its surrounding areas, while Panel (d) focuses on Dafang County, providing greater detail of the region.</alt-text>
</graphic>
</fig>
<p>Dafang County is in a mountainous karst environment, with elevations between approximately 900 m in valley floors to over 2,350 m on ridge tops, and relative relief over 1,400 m in sections. Slopes that are likely to fail through landslide generally have over 25<inline-formula id="inf3">
<mml:math id="m3">
<mml:mrow>
<mml:mo>&#xb0;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> gradient. Subtropical humid monsoon climate is present in the area, with mean annual rainfall of approximately 1,200 mm, with over 70% of this concentrated during May to September. The interaction of steepness, fractured bedrock of limestone, large weathered mantle soils, and seasonally concentrated high-rainfall totals generates extremely high risk of rainfall-induced slope failures, especially in locations where high-density rural settlement and networks of roads are concentrated within slope toes.</p>
</sec>
<sec id="s2-2">
<label>2.2</label>
<title>Data description</title>
<p>The performance of the constructed landslide mapping framework was evaluated based on post-event polarimetric synthetic aperture radar (SAR) data acquired via the L-band <italic>Advanced Land Observing Satellite-2</italic> (ALOS-2) and the C-band <italic>Sentinel-1</italic> missions (<xref ref-type="table" rid="T1">Table 1</xref>). The ALOS-2 imagery was obtained in Stripmap (SM) mode with full quad-polarization channels (HH, HV, VH, VV), an incidence angle range of <inline-formula id="inf4">
<mml:math id="m4">
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<mml:mn>32.3</mml:mn>
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</inline-formula>, and a ground pixel spacing of <inline-formula id="inf6">
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</inline-formula> m. Sentinel-1 data were collected in Interferometric Wide (IW) swath mode with dual-polarization channels (VV, VH), covering an incidence angle range of <inline-formula id="inf7">
<mml:math id="m7">
<mml:mrow>
<mml:mn>41.7</mml:mn>
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</inline-formula> and a ground pixel spacing of <inline-formula id="inf9">
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<mml:mo>&#xd7;</mml:mo>
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</inline-formula> m. These two data sets were acquired in ascending orbits within a couple of days of the 22 May 2025 Dafang County landslide and, consequently, successfully reduced surficial changes that were unrelated to the event. Ascending-orbit acquisitions were selected to maintain a consistent viewing geometry and illumination direction across sensors, thereby reducing variability in backscattering responses caused by terrain-facing effects in steep mountainous areas. Although descending or combined ascending&#x2013;descending observations could further enhance robustness, this study focuses on a single-orbit configuration to ensure methodological consistency and reproducibility for rapid post-event mapping. Google Earth high-resolution optical imagery was additionally used to visualize real-world landslide appearances and to support qualitative interpretation of SAR-based results. A 30 m resolution Shuttle Radar Topography Mission (SRTM) digital elevation model (DEM) was used for geometric correction and topography and validation analysis.</p>
<table-wrap id="T1" position="float">
<label>TABLE 1</label>
<caption>
<p>Post-event polarimetric SAR datasets used for the Dafang County landslide case study.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left">Parameter</th>
<th align="center">Sentinel-1 (IW)</th>
<th align="center">ALOS-2 (SM)</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">Acquisition date</td>
<td align="center">25 May 2025</td>
<td align="center">28 May 2025</td>
</tr>
<tr>
<td align="left">Wavelength</td>
<td align="center">C-band</td>
<td align="center">L-band</td>
</tr>
<tr>
<td align="left">Polarization mode</td>
<td align="center">VV, VH</td>
<td align="center">HH, HV, VH, VV</td>
</tr>
<tr>
<td align="left">Incidence angle range <inline-formula id="inf10">
<mml:math id="m10">
<mml:mrow>
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</td>
<td align="center">41.7&#x2013;46.1</td>
<td align="center">32.3&#x2013;35.3</td>
</tr>
<tr>
<td align="left">Pixel spacing (m)</td>
<td align="center">
<inline-formula id="inf11">
<mml:math id="m11">
<mml:mrow>
<mml:mn>2.32</mml:mn>
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</td>
</tr>
<tr>
<td align="left">Orbit direction</td>
<td align="center">Ascending</td>
<td align="center">Ascending</td>
</tr>
<tr>
<td align="left">Acquisition mode</td>
<td align="center">Interferometric wide (IW)</td>
<td align="center">Stripmap (SM)</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
</sec>
<sec sec-type="methods" id="s3">
<label>3</label>
<title>Methodology</title>
<p>The proposed framework integrates polarimetric synthetic aperture radar (PolSAR) data with advanced classification and geometric refinement techniques to achieve accurate post-event landslide mapping (<xref ref-type="fig" rid="F2">Figure 2</xref>). PolSAR-derived parameters are first extracted and used as input to a Deep Forest (DF) classifier, which performs supervised land cover classification. The initial classification results are then processed using a majority voting (MV) scheme to enhance label consistency and reduce local misclassification. Finally, a morphological optimization model is applied, incorporating aspect ratio and longitudinal profile constraints, to refine the spatial extent and boundary geometry of the detected landslide. The morphological optimization module is introduced to impose shape- and connectivity-aware priors of landslide bodies, thereby suppressing isolated false alarms and improving boundary continuity under speckle and terrain-induced ambiguity.</p>
<fig id="F2" position="float">
<label>FIGURE 2</label>
<caption>
<p>Workflow of the proposed landslide mapping framework, combining polarimetric parameter extraction, Deep Forest classification, majority voting refinement, and morphological optimization.</p>
</caption>
<graphic xlink:href="feart-14-1751759-g002.tif">
<alt-text content-type="machine-generated">Flowchart depicting a four-step process: 1. Polarimetric SAR Data Processing includes Single-look Polarimetric SAR, Speckle Filtering, and Data Geocoding. 2. Deep Learning Algorithm involves Training and Testing Set, Machine Learning, Deep Forest Algorithm, Feature Extraction, and Neural Network Training. 3. Majority Voting Mechanism consists of Majority Voting, Solve Misclassification, and Result Optimization. 4. A Morphological Optimization Model to Extract Landslide Boundary includes A Morphological Optimization Method, Extract the Landslide Boundary, and Accuracy Evaluation.</alt-text>
</graphic>
</fig>
<sec id="s3-1">
<label>3.1</label>
<title>Polarimetric SAR-derived products</title>
<sec id="s3-1-1">
<label>3.1.1</label>
<title>Coherency <inline-formula id="inf13">
<mml:math id="m13">
<mml:mrow>
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<mml:mrow>
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</inline-formula> matrix</title>
<p>Different land-cover types exhibit distinct scattering mechanisms in polarimetric SAR observations. These differences can be characterized through the <inline-formula id="inf14">
<mml:math id="m14">
<mml:mrow>
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<mml:mo>&#xd7;</mml:mo>
<mml:mn>3</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula> coherency matrix <inline-formula id="inf15">
<mml:math id="m15">
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</inline-formula>, computed from the target vector <inline-formula id="inf16">
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</inline-formula> as (see <xref ref-type="disp-formula" rid="e1">Equations 1</xref>&#x2013;<xref ref-type="disp-formula" rid="e3">3</xref>):<disp-formula id="e1">
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<mml:mrow>
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</mml:mfenced>
<mml:mo>&#x3d;</mml:mo>
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<mml:mrow>
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<mml:mtext> </mml:mtext>
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<mml:mo>,</mml:mo>
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<label>(1)</label>
</disp-formula>
<disp-formula id="e2">
<mml:math id="m18">
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<mml:mi>T</mml:mi>
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<mml:mrow>
<mml:mn>3</mml:mn>
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</mml:mfenced>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
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</mml:mfrac>
<mml:mfenced open="[" close="]">
<mml:mrow>
<mml:mtable class="matrix">
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<mml:mtd columnalign="center">
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<mml:mo>&#x2b;</mml:mo>
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<mml:mo stretchy="false">&#x27e9;</mml:mo>
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<mml:mtd columnalign="center">
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<mml:mo>&#x2b;</mml:mo>
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<mml:mtd columnalign="center">
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<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(2)</label>
</disp-formula>where the target vector is defined as:<disp-formula id="e3">
<mml:math id="m19">
<mml:mrow>
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<mml:mrow>
<mml:mn>1</mml:mn>
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<mml:mrow>
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<mml:mn>2</mml:mn>
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</mml:msqrt>
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</mml:mfrac>
<mml:mfenced open="[" close="]">
<mml:mrow>
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<mml:mi>H</mml:mi>
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<mml:mo>&#x2b;</mml:mo>
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<mml:mrow>
<mml:mi>H</mml:mi>
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<mml:mo>&#x2212;</mml:mo>
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<mml:mrow>
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<mml:mtd columnalign="center">
<mml:mn>2</mml:mn>
<mml:msub>
<mml:mrow>
<mml:mi>S</mml:mi>
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<mml:mrow>
<mml:mi>H</mml:mi>
<mml:mi>V</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
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</mml:mrow>
</mml:math>
<label>(3)</label>
</disp-formula>and <inline-formula id="inf17">
<mml:math id="m20">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>S</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>X</mml:mi>
<mml:mi>Y</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> denotes the complex scattering coefficient for transmitted polarization <inline-formula id="inf18">
<mml:math id="m21">
<mml:mrow>
<mml:mi>X</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> and received polarization <inline-formula id="inf19">
<mml:math id="m22">
<mml:mrow>
<mml:mi>Y</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>. The diagonal elements of <inline-formula id="inf20">
<mml:math id="m23">
<mml:mrow>
<mml:mo stretchy="false">[</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>3</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mo stretchy="false">]</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> are real and positive, while the off-diagonal elements are complex-valued. Prior to classification, the magnitude of the off-diagonal terms is extracted, converted to a logarithmic scale (dB), and filtered using a non-local means filter with an <inline-formula id="inf21">
<mml:math id="m24">
<mml:mrow>
<mml:mn>11</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:mn>11</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula> search window and <inline-formula id="inf22">
<mml:math id="m25">
<mml:mrow>
<mml:mn>5</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:mn>5</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula> patch size to suppress speckle. The resulting geocoded <inline-formula id="inf23">
<mml:math id="m26">
<mml:mrow>
<mml:mo stretchy="false">[</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>3</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mo stretchy="false">]</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> products have a spatial posting of <inline-formula id="inf24">
<mml:math id="m27">
<mml:mrow>
<mml:mn>5.13</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:mn>5.13</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula> m.</p>
</sec>
<sec id="s3-1-2">
<label>3.1.2</label>
<title>Polarimetric decomposition</title>
<p>Landslide-affected surfaces are generally dominated by bare soil and rock exposures, whose scattering properties can often be modeled as surface scattering. For smooth surfaces where the surface roughness parameter satisfies <inline-formula id="inf25">
<mml:math id="m28">
<mml:mrow>
<mml:mi>k</mml:mi>
<mml:mi>s</mml:mi>
<mml:mo>&#x3c;</mml:mo>
<mml:mn>0.3</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula> (with <inline-formula id="inf26">
<mml:math id="m29">
<mml:mrow>
<mml:mi>k</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> denoting the radar wavenumber and <inline-formula id="inf27">
<mml:math id="m30">
<mml:mrow>
<mml:mi>s</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> the RMS height), the Bragg model provides an adequate description of the scattering mechanism. For rougher landslide surfaces, however, the X-Bragg model is adopted, which extends the applicability to <inline-formula id="inf28">
<mml:math id="m31">
<mml:mrow>
<mml:mi>k</mml:mi>
<mml:mi>s</mml:mi>
<mml:mo>&#x3c;</mml:mo>
<mml:mn>1.0</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula> (see <xref ref-type="disp-formula" rid="e4">Equation 4</xref>):<disp-formula id="e4">
<mml:math id="m32">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mfenced open="[" close="]">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>3</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
<mml:mrow>
<mml:mtext>x</mml:mtext>
<mml:mo>-</mml:mo>
<mml:mtext>Bragg</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfenced open="[" close="]">
<mml:mrow>
<mml:mtable class="matrix">
<mml:mtr>
<mml:mtd columnalign="center">
<mml:mn>1</mml:mn>
</mml:mtd>
<mml:mtd columnalign="center">
<mml:msup>
<mml:mrow>
<mml:mi>&#x3b2;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x2a;</mml:mo>
</mml:mrow>
</mml:msup>
<mml:mtext>&#x2003;</mml:mtext>
<mml:mi mathvariant="normal">s</mml:mi>
<mml:mi mathvariant="normal">i</mml:mi>
<mml:mi mathvariant="normal">n</mml:mi>
<mml:mi mathvariant="normal">c</mml:mi>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mi>&#x3b4;</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mtd>
<mml:mtd columnalign="center">
<mml:mn>0</mml:mn>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd columnalign="center">
<mml:mi>&#x3b2;</mml:mi>
<mml:mtext>&#x2003;</mml:mtext>
<mml:mi mathvariant="normal">s</mml:mi>
<mml:mi mathvariant="normal">i</mml:mi>
<mml:mi mathvariant="normal">n</mml:mi>
<mml:mi mathvariant="normal">c</mml:mi>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mi>&#x3b4;</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mtd>
<mml:mtd columnalign="center">
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mfrac>
<mml:mo stretchy="false">&#x7c;</mml:mo>
<mml:mi>&#x3b2;</mml:mi>
<mml:msup>
<mml:mrow>
<mml:mo stretchy="false">&#x7c;</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msup>
<mml:mfenced open="[" close="]">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2b;</mml:mo>
<mml:mi mathvariant="normal">s</mml:mi>
<mml:mi mathvariant="normal">i</mml:mi>
<mml:mi mathvariant="normal">n</mml:mi>
<mml:mi mathvariant="normal">c</mml:mi>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mn>4</mml:mn>
<mml:mi>&#x3b4;</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mfenced>
</mml:mtd>
<mml:mtd columnalign="center">
<mml:mn>0</mml:mn>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd columnalign="center">
<mml:mn>0</mml:mn>
</mml:mtd>
<mml:mtd columnalign="center">
<mml:mn>0</mml:mn>
</mml:mtd>
<mml:mtd columnalign="center">
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:mfrac>
<mml:mo stretchy="false">&#x7c;</mml:mo>
<mml:mi>&#x3b2;</mml:mi>
<mml:msup>
<mml:mrow>
<mml:mo stretchy="false">&#x7c;</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msup>
<mml:mfenced open="[" close="]">
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:mi mathvariant="normal">s</mml:mi>
<mml:mi mathvariant="normal">i</mml:mi>
<mml:mi mathvariant="normal">n</mml:mi>
<mml:mi mathvariant="normal">c</mml:mi>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mn>4</mml:mn>
<mml:mi>&#x3b4;</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:mfenced>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:mfenced>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(4)</label>
</disp-formula>where <inline-formula id="inf29">
<mml:math id="m33">
<mml:mrow>
<mml:mi>&#x3b2;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is the complex scattering coefficient, determined by the incidence angle <inline-formula id="inf30">
<mml:math id="m34">
<mml:mrow>
<mml:mi>&#x3b8;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> and the dielectric constant <inline-formula id="inf31">
<mml:math id="m35">
<mml:mrow>
<mml:mi>&#x3b5;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>, and <inline-formula id="inf32">
<mml:math id="m36">
<mml:mrow>
<mml:mi>&#x3b4;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is the orientation angle induced by the local slope, influencing both depolarization and cross-polarized scattering power. The X-Bragg model is applied only to pixels satisfying <inline-formula id="inf33">
<mml:math id="m37">
<mml:mrow>
<mml:msubsup>
<mml:mrow>
<mml:mi>&#x3c3;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>H</mml:mi>
<mml:mi>H</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:msubsup>
<mml:mo>&#x3c;</mml:mo>
<mml:msubsup>
<mml:mrow>
<mml:mi>&#x3c3;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>V</mml:mi>
<mml:mi>V</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:msubsup>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf34">
<mml:math id="m38">
<mml:mrow>
<mml:msubsup>
<mml:mrow>
<mml:mi>&#x3c3;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>V</mml:mi>
<mml:mi>H</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:msubsup>
<mml:mo>/</mml:mo>
<mml:msubsup>
<mml:mrow>
<mml:mi>&#x3c3;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>V</mml:mi>
<mml:mi>V</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:msubsup>
<mml:mo>&#x3c;</mml:mo>
<mml:mo>&#x2212;</mml:mo>
<mml:mn>11</mml:mn>
<mml:mspace width="0.3333em"/>
<mml:mtext>dB</mml:mtext>
</mml:mrow>
</mml:math>
</inline-formula>, thereby excluding vegetated areas and extremely rough surfaces <inline-formula id="inf35">
<mml:math id="m39">
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi>k</mml:mi>
<mml:mi>s</mml:mi>
<mml:mo>&#x3e;</mml:mo>
<mml:mn>3.0</mml:mn>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>. For the valid pixels, H/A/<inline-formula id="inf36">
<mml:math id="m40">
<mml:mrow>
<mml:mi>&#x3b1;</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> decomposition parameters are computed, together with soil roughness and moisture estimates derived from the X-Bragg parameters <inline-formula id="inf37">
<mml:math id="m41">
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi>&#x3b2;</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>&#x3b4;</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>. The complete set of extracted polarimetric features is summarized in <xref ref-type="table" rid="T2">Table 2</xref>. For completeness, we also specify the feature vectors used for the dual-pol ALOS-2 and dual-pol Sentinel-1 experiments in the same table.</p>
<table-wrap id="T2" position="float">
<label>TABLE 2</label>
<caption>
<p>The set of input features for the classifier from quad-pol and dual-pol SAR data.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left">Data</th>
<th align="left">Features used in this study</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">Quad-pol (ALOS-2)</td>
<td align="left">Intensity (dB): <inline-formula id="inf38">
<mml:math id="m42">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>11</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>12</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>13</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>22</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>23</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>33</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>
</td>
</tr>
<tr>
<td align="left">Dual-pol (ALOS-2)</td>
<td align="left">Intensity (dB): <inline-formula id="inf39">
<mml:math id="m43">
<mml:mrow>
<mml:mi>V</mml:mi>
<mml:mi>V</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>V</mml:mi>
<mml:mi>H</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>; polarization ratio: <inline-formula id="inf40">
<mml:math id="m44">
<mml:mrow>
<mml:mi>V</mml:mi>
<mml:mi>H</mml:mi>
<mml:mo>/</mml:mo>
<mml:mi>V</mml:mi>
<mml:mi>V</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> (dB)</td>
</tr>
<tr>
<td align="left">Dual-pol (Sentinel-1, VV/VH)</td>
<td align="left">Intensity (dB): <inline-formula id="inf41">
<mml:math id="m45">
<mml:mrow>
<mml:mi>V</mml:mi>
<mml:mi>V</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi>V</mml:mi>
<mml:mi>H</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>; polarization ratio: <inline-formula id="inf42">
<mml:math id="m46">
<mml:mrow>
<mml:mi>V</mml:mi>
<mml:mi>H</mml:mi>
<mml:mo>/</mml:mo>
<mml:mi>V</mml:mi>
<mml:mi>V</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> (dB)</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
</sec>
<sec id="s3-2">
<label>3.2</label>
<title>Deep forest algorithm</title>
<p>Single-date radar acquisitions can be insufficient for reliable ground-object characterization due to the complex and nonlinear interactions between radar signals and surface properties. To enhance classification robustness under these conditions, the Deep Forest (DF) algorithm is adopted for landslide identification. DF is a non-neural deep learning framework particularly suited to small-to-moderate training datasets, where conventional deep neural networks may be prone to overfitting (see <xref ref-type="fig" rid="F3">Figure 3</xref>).</p>
<fig id="F3" position="float">
<label>FIGURE 3</label>
<caption>
<p>Schematic of the Deep Forest (DF) classifier structure used in this study, illustrating feature partitioning, ensemble learning with RF and CRTF, and final prediction aggregation.</p>
</caption>
<graphic xlink:href="feart-14-1751759-g003.tif">
<alt-text content-type="machine-generated">Flowchart illustrating a system of multi-grained scanning and cascade forests. The left section shows input dimensions processed by random forests and completely-random tree forests. The right section depicts a cascade forest structure with levels labeled as \(I_A\), \(I_B\), \(I_C\), \(N_A\), and \(N_C\), leading to a final output.</alt-text>
</graphic>
</fig>
<p>In this study, the DF classifier is fed with a 13-dimensional polarimetric feature vector (<xref ref-type="table" rid="T2">Table 2</xref>). A sliding-window sampling of length three is applied to generate five 5-dimensional feature subsets. Each subset is used to train two types of ensemble learners: a Random Forest (RF) and a Completely Random Tree Forest (CRTF), producing multiple mapping models <inline-formula id="inf43">
<mml:math id="m47">
<mml:mrow>
<mml:mo stretchy="false">{</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>d</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
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</mml:msub>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi>x</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>d</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>2</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
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</mml:mrow>
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<mml:mrow>
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<mml:mrow>
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<mml:mrow>
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</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mo stretchy="false">}</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>. The final DF prediction is obtained by averaging the outputs of the <inline-formula id="inf44">
<mml:math id="m48">
<mml:mrow>
<mml:mi>n</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> mapping models (see <xref ref-type="disp-formula" rid="e5">Equation 5</xref>):<disp-formula id="e5">
<mml:math id="m49">
<mml:mrow>
<mml:msubsup>
<mml:mrow>
<mml:mover accent="true">
<mml:mrow>
<mml:mi>f</mml:mi>
<mml:mo>&#xa0;</mml:mo>
</mml:mrow>
<mml:mo stretchy="false">&#x302;</mml:mo>
</mml:mover>
</mml:mrow>
<mml:mrow>
<mml:mtext>rf</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mi>n</mml:mi>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:msubsup>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mi>x</mml:mi>
</mml:mrow>
</mml:mfenced>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mi>n</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mstyle displaystyle="true">
<mml:munderover>
<mml:mrow>
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</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
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<mml:mn>1</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mi>n</mml:mi>
</mml:mrow>
</mml:munderover>
</mml:mstyle>
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<mml:mrow>
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<mml:mrow>
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</mml:mrow>
</mml:mfenced>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(5)</label>
</disp-formula>where <inline-formula id="inf45">
<mml:math id="m50">
<mml:mrow>
<mml:msubsup>
<mml:mrow>
<mml:mover accent="true">
<mml:mrow>
<mml:mi>f</mml:mi>
<mml:mo>&#xa0;</mml:mo>
</mml:mrow>
<mml:mo stretchy="false">&#x302;</mml:mo>
</mml:mover>
</mml:mrow>
<mml:mrow>
<mml:mtext>rf</mml:mtext>
</mml:mrow>
<mml:mrow>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi>n</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:msubsup>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi>x</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> denotes the aggregated DF output and <inline-formula id="inf46">
<mml:math id="m51">
<mml:mrow>
<mml:mi>n</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is the total number of mapping models. To ensure full reproducibility, the DF configuration is explicitly documented as follows: each cascade layer contains one RF and one CRTF, both using 500 trees; the maximum tree depth is set to None (fully grown); the feature sampling strategy follows the default sqrt rule; and the internal validation uses 5-fold cross-validation. The cascade grows until the validation improvement is below 0.001 for 2 consecutive layers, resulting in 3 cascade layers in this study. All experiments were conducted on a single workstation with a standard CPU environment, and the average inference time per scene is within minutes, supporting rapid post-event deployment. For comparison, four benchmark classifiers&#x2014;RF, Artificial Neural Network (ANN), K-Nearest Neighbor (KNN), and Support Vector Classification (SVC)&#x2014;were implemented using the same polarimetric feature set. Comparative experiments demonstrate that DF consistently outperforms the benchmark methods, especially in mountainous terrain characterized by mixed scattering mechanisms.</p>
</sec>
<sec id="s3-3">
<label>3.3</label>
<title>Majority voting mechanism</title>
<p>While the DF classifier applied to polarimetric SAR features is effective in detecting clusters of landslide pixels, surrounding terrain elements with similar polarimetric signatures can lead to misclassifications and the presence of isolated holes within the detected landslide mask. To mitigate these issues, the output from the X-Bragg polarimetric decomposition is incorporated as a supplementary data layer, and a Majority Voting (MV) scheme is implemented to refine the delineation of landslide boundaries (see <xref ref-type="fig" rid="F4">Figure 4</xref>).</p>
<fig id="F4" position="float">
<label>FIGURE 4</label>
<caption>
<p>Illustration of the Majority Voting (MV) refinement strategy, combining DF classification results with X-Bragg polarimetric decomposition to improve boundary consistency and reduce misclassification.</p>
</caption>
<graphic xlink:href="feart-14-1751759-g004.tif">
<alt-text content-type="machine-generated">Three 15x15 grids depict the progression of data processing through the DF algorithm, polarimetric decomposition, and majority voting. Each grid contains values of zero and one with specific colored cells indicating changes or inputs in orange, blue, yellow, red, and green as data moves between phases denoted by arrows.</alt-text>
</graphic>
</fig>
<p>For reproducibility, the MV refinement is formulated as follows. Let <inline-formula id="inf47">
<mml:math id="m52">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>M</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>DF</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi>p</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mo>&#x2208;</mml:mo>
<mml:mrow>
<mml:mo stretchy="false">{</mml:mo>
<mml:mrow>
<mml:mn>0,1</mml:mn>
</mml:mrow>
<mml:mo stretchy="false">}</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf48">
<mml:math id="m53">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>M</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>PD</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi>p</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mo>&#x2208;</mml:mo>
<mml:mrow>
<mml:mo stretchy="false">{</mml:mo>
<mml:mrow>
<mml:mn>0,1</mml:mn>
</mml:mrow>
<mml:mo stretchy="false">}</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> denote the binary landslide masks at pixel <inline-formula id="inf49">
<mml:math id="m54">
<mml:mrow>
<mml:mi>p</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> predicted by the DF classifier and by the polarimetric-decomposition-based detection (PD), respectively. The refined mask <inline-formula id="inf50">
<mml:math id="m55">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>M</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>MV</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi>p</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> is defined as (see <xref ref-type="disp-formula" rid="e6">Equation 6</xref>)<disp-formula id="e6">
<mml:math id="m56">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>M</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>MV</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mi>p</mml:mi>
</mml:mrow>
</mml:mfenced>
<mml:mo>&#x3d;</mml:mo>
<mml:mfenced open="{" close="">
<mml:mrow>
<mml:mtable class="cases">
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<mml:mo>,</mml:mo>
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</mml:mtd>
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<mml:msub>
<mml:mrow>
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</mml:mrow>
<mml:mrow>
<mml:mtext>DF</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mi>p</mml:mi>
</mml:mrow>
</mml:mfenced>
<mml:mo>&#x3d;</mml:mo>
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<mml:mo>&#x2227;</mml:mo>
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<mml:msub>
<mml:mrow>
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<mml:mrow>
<mml:mtext>PD</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mi>p</mml:mi>
</mml:mrow>
</mml:mfenced>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>,</mml:mo>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd columnalign="left">
<mml:mn>1</mml:mn>
<mml:mo>,</mml:mo>
<mml:mspace width="1em"/>
</mml:mtd>
<mml:mtd columnalign="left">
<mml:msub>
<mml:mrow>
<mml:mi>M</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>DF</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mi>p</mml:mi>
</mml:mrow>
</mml:mfenced>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
<mml:mspace width="0.3333em"/>
<mml:mo>&#x2227;</mml:mo>
<mml:mspace width="0.3333em"/>
<mml:msub>
<mml:mrow>
<mml:mi>M</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>PD</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mi>p</mml:mi>
</mml:mrow>
</mml:mfenced>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>0</mml:mn>
<mml:mo>,</mml:mo>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd columnalign="left">
<mml:mn>1</mml:mn>
<mml:mo>,</mml:mo>
<mml:mspace width="1em"/>
</mml:mtd>
<mml:mtd columnalign="left">
<mml:msub>
<mml:mrow>
<mml:mi>M</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>DF</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mi>p</mml:mi>
</mml:mrow>
</mml:mfenced>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>0</mml:mn>
<mml:mspace width="0.3333em"/>
<mml:mo>&#x2227;</mml:mo>
<mml:mspace width="0.3333em"/>
<mml:msub>
<mml:mrow>
<mml:mi>M</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>PD</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mi>p</mml:mi>
</mml:mrow>
</mml:mfenced>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
<mml:mspace width="0.3333em"/>
<mml:mo>&#x2227;</mml:mo>
<mml:mspace width="0.3333em"/>
<mml:mi mathvariant="normal">&#x3a6;</mml:mi>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:mi>p</mml:mi>
</mml:mrow>
</mml:mfenced>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
<mml:mo>,</mml:mo>
</mml:mtd>
</mml:mtr>
<mml:mtr>
<mml:mtd columnalign="left">
<mml:mn>0</mml:mn>
<mml:mo>,</mml:mo>
<mml:mspace width="1em"/>
</mml:mtd>
<mml:mtd columnalign="left">
<mml:mtext>otherwise,</mml:mtext>
</mml:mtd>
</mml:mtr>
</mml:mtable>
</mml:mrow>
</mml:mfenced>
</mml:mrow>
</mml:math>
<label>(6)</label>
</disp-formula>where <inline-formula id="inf51">
<mml:math id="m57">
<mml:mrow>
<mml:mi mathvariant="normal">&#x3a6;</mml:mi>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi>p</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> is a statistical consistency test based on the scattering-power range of the coherency matrix components. Specifically, let <inline-formula id="inf52">
<mml:math id="m58">
<mml:mrow>
<mml:mi mathvariant="bold">t</mml:mi>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi>p</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:msup>
<mml:mrow>
<mml:mrow>
<mml:mo stretchy="false">[</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>11</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi>p</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>22</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi>p</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mo>,</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>33</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi>p</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mo stretchy="false">]</mml:mo>
</mml:mrow>
</mml:mrow>
<mml:mrow>
<mml:mo>&#x22a4;</mml:mo>
</mml:mrow>
</mml:msup>
</mml:mrow>
</mml:math>
</inline-formula> (in dB), and let <inline-formula id="inf53">
<mml:math id="m59">
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi mathvariant="bold-italic">&#x3bc;</mml:mi>
<mml:mo>,</mml:mo>
<mml:mi mathvariant="bold-italic">&#x3c3;</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> be the mean and standard deviation computed from DF-confirmed landslide pixels. We set <inline-formula id="inf54">
<mml:math id="m60">
<mml:mrow>
<mml:mi mathvariant="normal">&#x3a6;</mml:mi>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi>p</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula> if <inline-formula id="inf55">
<mml:math id="m61">
<mml:mrow>
<mml:mo stretchy="false">&#x7c;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>t</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi>p</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3bc;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo stretchy="false">&#x7c;</mml:mo>
<mml:mo>&#x2264;</mml:mo>
<mml:mn>2</mml:mn>
<mml:msub>
<mml:mrow>
<mml:mi>&#x3c3;</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>j</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> holds for <inline-formula id="inf56">
<mml:math id="m62">
<mml:mrow>
<mml:mi>j</mml:mi>
<mml:mo>&#x2208;</mml:mo>
<mml:mrow>
<mml:mo stretchy="false">{</mml:mo>
<mml:mrow>
<mml:mn>1,2,3</mml:mn>
</mml:mrow>
<mml:mo stretchy="false">}</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>; otherwise <inline-formula id="inf57">
<mml:math id="m63">
<mml:mrow>
<mml:mi mathvariant="normal">&#x3a6;</mml:mi>
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi>p</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>.</p>
<p>For a given input patch (e.g., <inline-formula id="inf58">
<mml:math id="m64">
<mml:mrow>
<mml:mn>15</mml:mn>
<mml:mo>&#xd7;</mml:mo>
<mml:mn>15</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula> pixels) where landslide pixels are labeled as class 1 and non-landslide pixels as class 0, the MV procedure evaluates three cases: 1. Pixels identified as landslides by both the DF classifier and polarimetric decomposition are retained as class 1 (red). 2. Pixels detected only by the DF classifier are retained as class 1 (blue). 3. Pixels detected only by polarimetric decomposition are retained as class 1 (green) if the scattering power of all <inline-formula id="inf59">
<mml:math id="m65">
<mml:mrow>
<mml:mo stretchy="false">[</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>T</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>3</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mo stretchy="false">]</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> matrix components falls within the statistical range of known landslide pixels; otherwise, they are reclassified as class 0 (yellow). By integrating complementary information from supervised classification and statistical decomposition, the MV approach enhances the spatial continuity of mapped landslides and reduces false positives, particularly along boundary regions.</p>
</sec>
<sec id="s3-4">
<label>3.4</label>
<title>Morphological optimization model</title>
<p>Morphological optimization is employed to refine the initial classification results by leveraging the geometric characteristics commonly observed in landslides, including their aspect ratio and longitudinal shape. This step is motivated by the fact that pixel-wise classifiers may produce fragmented masks or spurious blobs in rugged terrain; enforcing empirically supported geometric regularities helps improve spatial coherence and interpretability of mapped landslide outlines. The aspect ratio <inline-formula id="inf60">
<mml:math id="m66">
<mml:mrow>
<mml:mi>Q</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is defined as the ratio of the landslide length <inline-formula id="inf61">
<mml:math id="m67">
<mml:mrow>
<mml:mi>L</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> to its maximum width <inline-formula id="inf62">
<mml:math id="m68">
<mml:mrow>
<mml:mi>W</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> (see <xref ref-type="disp-formula" rid="e7">Equation 7</xref>):<disp-formula id="e7">
<mml:math id="m69">
<mml:mrow>
<mml:mi>Q</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mi>L</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>W</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(7)</label>
</disp-formula>where <inline-formula id="inf63">
<mml:math id="m70">
<mml:mrow>
<mml:mi>L</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is measured along the central flow axis from the head scarp to the distal toe, and <inline-formula id="inf64">
<mml:math id="m71">
<mml:mrow>
<mml:mi>W</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is the maximum cross-sectional width. To complement <inline-formula id="inf65">
<mml:math id="m72">
<mml:mrow>
<mml:mi>Q</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>, the longitudinal shape is characterized by the variation in landslide width along the central flow axis. Two indicators are introduced: 1. Relative width change <inline-formula id="inf66">
<mml:math id="m73">
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>R</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>chg</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>: describing the overall trend in width variation; 2. Relative width fluctuation <inline-formula id="inf67">
<mml:math id="m74">
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>R</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>flu</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>: quantifying local deviations from the fitted longitudinal profile. The two metrics are defined as (see <xref ref-type="disp-formula" rid="e8">Equations 8</xref>, <xref ref-type="disp-formula" rid="e9">9</xref>):<disp-formula id="e8">
<mml:math id="m75">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>R</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>chg</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>y</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>nor</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>y</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
<mml:mo>&#xd7;</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mi>Q</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mfenced open="(" close=")">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>y</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>nor</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>y</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfenced>
<mml:mo>&#xd7;</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mi>L</mml:mi>
<mml:mo>/</mml:mo>
<mml:mi>W</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(8)</label>
</disp-formula>
<disp-formula id="e9">
<mml:math id="m76">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>R</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>flu</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mi mathvariant="normal">R</mml:mi>
<mml:mi mathvariant="normal">M</mml:mi>
<mml:mi mathvariant="normal">S</mml:mi>
<mml:mi mathvariant="normal">E</mml:mi>
<mml:mo>&#xd7;</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mi>Q</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mi mathvariant="normal">R</mml:mi>
<mml:mi mathvariant="normal">M</mml:mi>
<mml:mi mathvariant="normal">S</mml:mi>
<mml:mi mathvariant="normal">E</mml:mi>
<mml:mo>&#xd7;</mml:mo>
<mml:mn>2</mml:mn>
</mml:mrow>
<mml:mrow>
<mml:mi>L</mml:mi>
<mml:mo>/</mml:mo>
<mml:mi>W</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(9)</label>
</disp-formula>where <inline-formula id="inf68">
<mml:math id="m77">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>y</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>nor</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> denotes the normalized landslide length, <inline-formula id="inf69">
<mml:math id="m78">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>y</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf70">
<mml:math id="m79">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>y</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> are the intercepts with the vertical axis at the start and end of the profile, and <inline-formula id="inf71">
<mml:math id="m80">
<mml:mrow>
<mml:mi mathvariant="normal">R</mml:mi>
<mml:mi mathvariant="normal">M</mml:mi>
<mml:mi mathvariant="normal">S</mml:mi>
<mml:mi mathvariant="normal">E</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> (root mean square error) measures the deviation between observed widths and a linear fit to the representative widths <inline-formula id="inf72">
<mml:math id="m81">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>Q</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>fir</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula id="inf73">
<mml:math id="m82">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>Q</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>mid</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, and <inline-formula id="inf74">
<mml:math id="m83">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>Q</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>end</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>. By applying empirically determined thresholds to <inline-formula id="inf75">
<mml:math id="m84">
<mml:mrow>
<mml:mi>Q</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula id="inf76">
<mml:math id="m85">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>R</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>chg</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, and <inline-formula id="inf77">
<mml:math id="m86">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>R</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>flu</mml:mtext>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula>, the morphological optimization model removes implausible geometries, smooths irregular boundaries, and eliminates isolated misclassified patches. Following common geomorphological constraints for rainfall-induced runout landslides, we apply <inline-formula id="inf78">
<mml:math id="m87">
<mml:mrow>
<mml:mi>Q</mml:mi>
<mml:mo>&#x2208;</mml:mo>
<mml:mrow>
<mml:mo stretchy="false">[</mml:mo>
<mml:mrow>
<mml:mn>1.5</mml:mn>
<mml:mo>,</mml:mo>
<mml:mn>3.5</mml:mn>
</mml:mrow>
<mml:mo stretchy="false">]</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula id="inf79">
<mml:math id="m88">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>R</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>chg</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3e;</mml:mo>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>, and <inline-formula id="inf80">
<mml:math id="m89">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>R</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>flu</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3c;</mml:mo>
<mml:mn>0.2</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula> for the case study, consistent with the values reported in Section ?? This process produces morphologically coherent landslide outlines consistent with field-observed shapes.</p>
</sec>
</sec>
<sec id="s4">
<label>4</label>
<title>Results and analysis</title>
<sec id="s4-1">
<label>4.1</label>
<title>Accuracy assessment</title>
<p>To improve transparency and reproducibility, we explicitly define the evaluation metrics used throughout this study. For a given class, let <inline-formula id="inf81">
<mml:math id="m90">
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mi>P</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula id="inf82">
<mml:math id="m91">
<mml:mrow>
<mml:mi>F</mml:mi>
<mml:mi>P</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula id="inf83">
<mml:math id="m92">
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mi>N</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula>, and <inline-formula id="inf84">
<mml:math id="m93">
<mml:mrow>
<mml:mi>F</mml:mi>
<mml:mi>N</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> denote the numbers of true positives, false positives, true negatives, and false negatives, respectively. Precision <inline-formula id="inf85">
<mml:math id="m94">
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi>P</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>, recall <inline-formula id="inf86">
<mml:math id="m95">
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:mi>R</mml:mi>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>, and F1-score <inline-formula id="inf87">
<mml:math id="m96">
<mml:mrow>
<mml:mo stretchy="false">(</mml:mo>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>F</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mo stretchy="false">)</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula> are computed as (see <xref ref-type="disp-formula" rid="e10">Equations 10</xref>, <xref ref-type="disp-formula" rid="e11">11</xref>)<disp-formula id="e10">
<mml:math id="m97">
<mml:mrow>
<mml:mi>P</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mi>P</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mi>P</mml:mi>
<mml:mo>&#x2b;</mml:mo>
<mml:mi>F</mml:mi>
<mml:mi>P</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mo>,</mml:mo>
<mml:mspace width="2em"/>
<mml:mi>R</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mi>P</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:mi>P</mml:mi>
<mml:mo>&#x2b;</mml:mo>
<mml:mi>F</mml:mi>
<mml:mi>N</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mo>,</mml:mo>
<mml:mspace width="2em"/>
<mml:msub>
<mml:mrow>
<mml:mi>F</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:mn>2</mml:mn>
<mml:mi>P</mml:mi>
<mml:mi>R</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>P</mml:mi>
<mml:mo>&#x2b;</mml:mo>
<mml:mi>R</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mo>.</mml:mo>
</mml:mrow>
</mml:math>
<label>(10)</label>
</disp-formula>
</p>
<p>Overall accuracy (OA) is defined as<disp-formula id="e11">
<mml:math id="m98">
<mml:mrow>
<mml:mi mathvariant="normal">O</mml:mi>
<mml:mi mathvariant="normal">A</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mo>&#x2211;</mml:mo>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mi>T</mml:mi>
<mml:msub>
<mml:mrow>
<mml:mi>P</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mi>N</mml:mi>
</mml:mrow>
</mml:mfrac>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(11)</label>
</disp-formula>where <inline-formula id="inf88">
<mml:math id="m99">
<mml:mrow>
<mml:mi>T</mml:mi>
<mml:msub>
<mml:mrow>
<mml:mi>P</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the number of correctly classified pixels for class <inline-formula id="inf89">
<mml:math id="m100">
<mml:mrow>
<mml:mi>i</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> and <inline-formula id="inf90">
<mml:math id="m101">
<mml:mrow>
<mml:mi>N</mml:mi>
</mml:mrow>
</mml:math>
</inline-formula> is the total number of evaluated pixels. The Kappa coefficient is computed as (see <xref ref-type="disp-formula" rid="e12">Equation 12</xref>)<disp-formula id="e12">
<mml:math id="m102">
<mml:mrow>
<mml:mi>&#x3ba;</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mfrac>
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>p</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>o</mml:mi>
</mml:mrow>
</mml:msub>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>p</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>e</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
<mml:mrow>
<mml:mn>1</mml:mn>
<mml:mo>&#x2212;</mml:mo>
<mml:msub>
<mml:mrow>
<mml:mi>p</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>e</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:mfrac>
<mml:mo>,</mml:mo>
</mml:mrow>
</mml:math>
<label>(12)</label>
</disp-formula>where <inline-formula id="inf91">
<mml:math id="m103">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>p</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>o</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the observed agreement and <inline-formula id="inf92">
<mml:math id="m104">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>p</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mi>e</mml:mi>
</mml:mrow>
</mml:msub>
</mml:mrow>
</mml:math>
</inline-formula> is the expected agreement by chance derived from the marginal totals of the confusion matrix. Unless otherwise stated, all metrics reported in this section are computed pixel-wise by comparing rasterized reference labels and predicted maps, rather than polygon-intersection-based scoring.</p>
</sec>
<sec id="s4-2">
<label>4.2</label>
<title>Classification performance with quad-pol ALOS-2</title>
<p>Using the quad-polarization ALOS-2 imagery (HH, HV, VH, VV), the proposed Deep Forest (DF) classifier achieved high classification accuracy across the four land-cover classes&#x2014;landslide, building, vegetation, and water&#x2014;based on their distinct polarimetric backscatter responses. Out of the total 1,270 reference samples, 80% were used for training and 20% for independent validation. To support reproducibility, reference labels were derived from field and UAV interpretation and were rasterized to the evaluation grid consistent with the SAR products; the training and validation samples were separated to avoid spatial overlap between patches, following a region-based split for the study area.</p>
<p>
<xref ref-type="table" rid="T3">Table 3</xref> summarizes the per-class performance in terms of precision, recall, and F1-score, in addition to the overall accuracy (OA) and Kappa coefficient. The method attained an OA of 94.5% and a Kappa of 0.92, indicating strong agreement between predicted and reference labels. The landslide class achieved a recall of 0.93 and a precision of 0.94, reflecting the method&#x2019;s capability to capture most true landslide pixels while maintaining a low false-alarm rate. Vegetation and water classes were classified with F1-scores above 0.95, while buildings showed slightly lower precision (0.91) due to confusion with double-bounce returns from landslide deposits.</p>
<table-wrap id="T3" position="float">
<label>TABLE 3</label>
<caption>
<p>Classification metrics for quad-pol ALOS-2 data. Precision (P), recall (R), and F1-score are computed per class, with overall accuracy (OA) and Kappa shown for all classes combined.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left">Class</th>
<th align="center">P</th>
<th align="center">R</th>
<th align="center">F1</th>
<th align="center">Support</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">Landslide</td>
<td align="center">0.94</td>
<td align="center">0.93</td>
<td align="center">0.94</td>
<td align="center">320</td>
</tr>
<tr>
<td align="left">Building</td>
<td align="center">0.91</td>
<td align="center">0.90</td>
<td align="center">0.91</td>
<td align="center">300</td>
</tr>
<tr>
<td align="left">Vegetation</td>
<td align="center">0.96</td>
<td align="center">0.97</td>
<td align="center">0.96</td>
<td align="center">400</td>
</tr>
<tr>
<td align="left">Water</td>
<td align="center">0.98</td>
<td align="center">0.97</td>
<td align="center">0.98</td>
<td align="center">250</td>
</tr>
<tr>
<td align="left">OA/Kappa</td>
<td colspan="4" align="center">94.5%/0.92</td>
</tr>
</tbody>
</table>
</table-wrap>
<p>The confusion matrix in <xref ref-type="fig" rid="F5">Figure 5</xref> highlights the dominant misclassification patterns. Most errors arose from spectral overlap between landslide deposits and barren or sparsely vegetated slopes, particularly in sun-facing aspects where soil moisture was low. Incorporating the Majority Voting refinement reduced salt-and-pepper noise along class boundaries, improving spatial coherence. Subsequent morphological optimization further eliminated isolated false positives by enforcing geometric constraints (aspect ratio <inline-formula id="inf93">
<mml:math id="m105">
<mml:mrow>
<mml:mi>Q</mml:mi>
<mml:mo>&#x2208;</mml:mo>
<mml:mrow>
<mml:mo stretchy="false">[</mml:mo>
<mml:mrow>
<mml:mn>1.5</mml:mn>
<mml:mo>,</mml:mo>
<mml:mn>3.5</mml:mn>
</mml:mrow>
<mml:mo stretchy="false">]</mml:mo>
</mml:mrow>
</mml:mrow>
</mml:math>
</inline-formula> and positive relative width change <inline-formula id="inf94">
<mml:math id="m106">
<mml:mrow>
<mml:msub>
<mml:mrow>
<mml:mi>R</mml:mi>
</mml:mrow>
<mml:mrow>
<mml:mtext>chg</mml:mtext>
</mml:mrow>
</mml:msub>
<mml:mo>&#x3e;</mml:mo>
<mml:mn>0</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>), yielding a final boundary consistent with field observations. Qualitatively, the final delineated landslide polygon exhibited <inline-formula id="inf95">
<mml:math id="m107">
<mml:mrow>
<mml:mi>Q</mml:mi>
<mml:mo>&#x3d;</mml:mo>
<mml:mn>2.10</mml:mn>
</mml:mrow>
</mml:math>
</inline-formula>, <inline-formula id="inf96">
<mml:math id="m108">
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</inline-formula>, consistent with a widening transition&#x2013;deposition zone morphology (<xref ref-type="fig" rid="F6">Figure 6</xref>). This agreement between SAR-derived metrics and geomorphological expectations confirms the effectiveness of the proposed approach in extracting physically meaningful landslide boundaries.</p>
<fig id="F5" position="float">
<label>FIGURE 5</label>
<caption>
<p>Confusion matrix for quad-pol ALOS-2 classification results. Values are normalized by row to show per-class recall.</p>
</caption>
<graphic xlink:href="feart-14-1751759-g005.tif">
<alt-text content-type="machine-generated">Confusion matrix for four classes: Landslide, Building, Vegetation, and Water. Each row represents true labels and columns represent predicted labels. High accuracy is shown for Landslide (93%), Building (90%), Vegetation (93%), and Water (95%). Colorbar displays percentages from 0 to 100.</alt-text>
</graphic>
</fig>
<fig id="F6" position="float">
<label>FIGURE 6</label>
<caption>
<p>Final mapped boundary of the Dafang County landslide obtained from the proposed method, showing the agreement between SAR-based delineation and field-observed morphology. <bold>(a)</bold> DF algorithm. <bold>(b)</bold> X-Bragg model. <bold>(c)</bold> MV mechanism. <bold>(d)</bold> Morphological.</p>
</caption>
<graphic xlink:href="feart-14-1751759-g006.tif">
<alt-text content-type="machine-generated">Four-panel graphic comparing landslide detection methods. Panel (a) shows a colored map using DF algorithm with landslides in red. Panel (b) illustrates a black and white X-Bragg model. Panel (c) displays landslides in black using MV mechanism. Panel (d) outlines landslide boundaries in red using morphological analysis. Each panel has geographic coordinates.</alt-text>
</graphic>
</fig>
</sec>
<sec id="s4-3">
<label>4.3</label>
<title>Boundary refinement and morphological optimization effects</title>
<p>The initial output from the Deep Forest classifier, although achieving high overall accuracy, exhibited small-scale noise along object boundaries and occasional misclassification in mixed-pixel regions. These issues were most prominent in transition zones between landslide deposits and surrounding land-cover types, where polarimetric signatures partially overlapped.</p>
<p>To address these artifacts, a two-stage post-processing strategy was applied: 1. Majority Voting (MV) refinement: This step aggregated the class labels of neighboring pixels within a fixed spatial kernel, effectively smoothing isolated misclassified pixels and enhancing local consistency. Compared with the raw DF output, MV increased boundary completeness and reduced salt-and-pepper effects, particularly in sparsely vegetated or partially built-up areas. 2. Morphological optimization: A shape-based filtering was subsequently applied to the MV-refined map, imposing an aspect ratio constraint <inline-formula id="inf98">
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</inline-formula> were preferentially retained to ensure boundary smoothness. This stage removed small, irregular false positives&#x2014;often caused by road segments, bare soil patches, or shadowed slopes&#x2014;while preserving the elongated geometry of the true landslide body.</p>
<p>
<xref ref-type="table" rid="T4">Table 4</xref> quantifies the improvement across three shape descriptors&#x2014;<inline-formula id="inf101">
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</inline-formula>&#x2014;as well as the overall classification accuracy. The morphological optimization yielded a final landslide polygon with <inline-formula id="inf104">
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</mml:math>
</inline-formula>, closely matching geomorphological measurements from UAV surveys. Visually, <xref ref-type="fig" rid="F6">Figure 6</xref> illustrates the progressive improvement from the raw DF classification to the MV-refined and morphologically optimized results. The final map exhibits smoother, more coherent boundaries and better agreement with the field-surveyed outline, confirming that the combined refinement process not only improves pixel-level classification but also produces landslide geometries that are physically plausible and operationally useful.</p>
<table-wrap id="T4" position="float">
<label>TABLE 4</label>
<caption>
<p>Changes in classification and shape metrics after boundary refinement.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left">Stage</th>
<th align="center">OA (%)</th>
<th align="center">
<inline-formula id="inf107">
<mml:math id="m119">
<mml:mrow>
<mml:mi>Q</mml:mi>
</mml:mrow>
</mml:math>
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<th align="center">
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<mml:math id="m120">
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<th align="center">
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</inline-formula>
</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">Raw DF output</td>
<td align="center">93.2</td>
<td align="center">1.42</td>
<td align="center">0.31</td>
<td align="center">0.28</td>
</tr>
<tr>
<td align="left">MV refinement</td>
<td align="center">94.1</td>
<td align="center">1.85</td>
<td align="center">0.54</td>
<td align="center">0.22</td>
</tr>
<tr>
<td align="left">MV &#x2b; Morph. opt.</td>
<td align="center">
<bold>94.5</bold>
</td>
<td align="center">
<bold>2.10</bold>
</td>
<td align="center">
<bold>0.68</bold>
</td>
<td align="center">
<bold>0.16</bold>
</td>
</tr>
</tbody>
</table>
<table-wrap-foot>
<fn>
<p>Bold is the best results.</p>
</fn>
</table-wrap-foot>
</table-wrap>
</sec>
<sec id="s4-4">
<label>4.4</label>
<title>Field validation</title>
<p>To quantitatively assess the reliability of the SAR-derived landslide boundary, ground-truth data were collected through a field campaign combining UAV photogrammetry and high-precision GNSS surveying. The UAV orthophotos, acquired at a ground sampling distance (GSD) of 0.10 m, provided detailed morphological context, while GNSS survey points achieved a horizontal accuracy of <inline-formula id="inf110">
<mml:math id="m122">
<mml:mrow>
<mml:mo>&#xb1;</mml:mo>
</mml:mrow>
</mml:math>
</inline-formula>8 mm &#x2b; 1 ppm, ensuring precise georeferencing. The UAV-derived landslide extent was manually delineated by experienced interpreters and served as the reference boundary. <xref ref-type="fig" rid="F7">Figure 7</xref> overlays the SAR-based result (red) from the proposed method on the reference outline (blue). The spatial agreement between the two boundaries was evaluated using pixel-based accuracy metrics, yielding an overall accuracy (OA) of 94.5% and a Kappa coefficient of 0.92. The UAV-derived polygon was converted into raster reference labels by assigning pixels whose centers fall inside the polygon as landslide pixels, ensuring a consistent pixel-wise evaluation grid. These results confirm the high positional consistency between the remote-sensing-derived and field-mapped boundaries.</p>
<fig id="F7" position="float">
<label>FIGURE 7</label>
<caption>
<p>Comparison between the proposed SAR-based landslide boundary (red) and the UAV-interpreted reference boundary (blue) for the Dafang County landslide. <bold>(a)</bold> Deep Forest. <bold>(b)</bold> Masked Out. <bold>(c)</bold> Majority Voting. <bold>(d)</bold> Morphological.</p>
</caption>
<graphic xlink:href="feart-14-1751759-g007.tif">
<alt-text content-type="machine-generated">Comparison of landslide detection using different satellite polarizations. The top row shows color-coded land cover maps identifying landslides, buildings, vegetation, and lakes from ALOS-2 quad-pol, ALOS-2 dual-pol, and Sentinel-1 dual-pol. The second row displays corresponding grayscale Bragg model outputs. The third row highlights landslide detection in black. The bottom row compares landslide profiles and boundaries with specific measurements for each method.</alt-text>
</graphic>
</fig>
<p>A qualitative inspection revealed three primary sources of residual misclassification:<list list-type="bullet">
<list-item>
<p>Case A: Double-bounce scattering from building clusters. Structures located near the landslide toe produced strong double-bounce returns, which were occasionally confused with landslide deposits in the initial classification.</p>
</list-item>
<list-item>
<p>Case B: Road segments at the landslide margin. Portions of rural roads partially buried by debris exhibited scattering signatures similar to disturbed bare soil, leading to localized commission errors.</p>
</list-item>
<list-item>
<p>Case C: Mixed vegetation&#x2013;soil patches on steep head-scarp slopes. These areas were sometimes omitted in the initial DF output due to dominant vegetation returns, but were successfully recovered after morphological optimization.</p>
</list-item>
</list>
</p>
<p>Despite these localized discrepancies, the strong alignment between the SAR-derived and UAV-interpreted boundaries demonstrates that the proposed workflow is capable of producing operationally reliable landslide maps. This is particularly relevant for post-disaster situations where UAV deployment or extensive field surveys may not be feasible due to terrain inaccessibility or time constraints.</p>
</sec>
<sec id="s4-5">
<label>4.5</label>
<title>Comparison with dual-pol datasets</title>
<p>To evaluate the adaptability of the proposed workflow to more widely available SAR configurations, we compared its performance on quad-polarization (HH, HV, VH, VV) ALOS-2 data against dual-polarization (VV, VH) datasets from both ALOS-2 and Sentinel-1. The same training&#x2013;validation protocol and parameter settings were applied to ensure methodological consistency.</p>
<sec id="s4-5-1">
<label>4.5.1</label>
<title>ALOS-2 dual-pol</title>
<p>Using only VV and VH channels, the method achieved an overall accuracy of 91.0% and a Kappa coefficient of 0.87. While closely approaching the quad-pol performance, minor reductions in boundary precision were observed in areas with complex topography, where cross-polarimetric channels in the full quad-pol dataset provided additional scattering discrimination.</p>
</sec>
<sec id="s4-5-2">
<label>4.5.2</label>
<title>Sentinel-1 dual-pol</title>
<p>Sentinel-1 imagery yielded an overall accuracy of 84.3% (Kappa &#x3d; 0.79). Although the main landslide body was accurately captured, omission errors were more frequent in narrow source zones, and commission errors increased in dense built-up areas due to reduced polarimetric diversity and coarser spatial resolution.</p>
<p>To further improve transparency, confusion matrices for the ALOS-2 dual-pol and Sentinel-1 dual-pol experiments are provided in the revised manuscript, complementing the quad-pol confusion matrix shown in <xref ref-type="fig" rid="F5">Figure 5</xref>.</p>
</sec>
<sec id="s4-5-3">
<label>4.5.3</label>
<title>Summary and implications</title>
<p>
<xref ref-type="table" rid="T5">Table 5</xref> summarizes the classification metrics across datasets. The results confirm that quad-pol data provide the highest boundary precision, dual-pol ALOS-2 offers a competitive trade-off between accuracy and data availability, and Sentinel-1&#x2014;despite lower precision&#x2014;remains valuable for rapid reconnaissance due to its open access and high revisit frequency.</p>
<table-wrap id="T5" position="float">
<label>TABLE 5</label>
<caption>
<p>Classification accuracy of the proposed method across SAR datasets for the Dafang County landslide.</p>
</caption>
<table>
<thead valign="top">
<tr>
<th align="left">Dataset</th>
<th align="center">Polarization</th>
<th align="center">Overall accuracy (%)</th>
<th align="center">Kappa</th>
</tr>
</thead>
<tbody valign="top">
<tr>
<td align="left">ALOS-2</td>
<td align="center">Quad-pol (HH, HV, VH, VV)</td>
<td align="center">94.5</td>
<td align="center">0.92</td>
</tr>
<tr>
<td align="left">ALOS-2</td>
<td align="center">Dual-pol (VV, VH)</td>
<td align="center">91.0</td>
<td align="center">0.87</td>
</tr>
<tr>
<td align="left">Sentinel-1</td>
<td align="center">Dual-pol (VV, VH)</td>
<td align="center">84.3</td>
<td align="center">0.79</td>
</tr>
</tbody>
</table>
</table-wrap>
</sec>
<sec id="s4-5-4">
<label>4.5.4</label>
<title>Representative misclassification cases</title>
<p>
<xref ref-type="fig" rid="F8">Figure 8</xref> illustrates three typical sources of error: (A) building clusters with strong double-bounce scattering misclassified as landslide deposits; (B) partially buried rural roads at the landslide margin producing soil-like scattering signatures; (C) mixed vegetation&#x2013;soil surfaces on steep scarps that were initially omitted but partially recovered after morphological optimization. These examples highlight that reduced polarimetric diversity (dual-pol) and coarser resolution (Sentinel-1) increase the likelihood of confusion between landslide and non-landslide surfaces.</p>
<fig id="F8" position="float">
<label>FIGURE 8</label>
<caption>
<p>Examples of representative misclassification cases.</p>
</caption>
<graphic xlink:href="feart-14-1751759-g008.tif">
<alt-text content-type="machine-generated">Map showing a region with overlaid contours in different colors representing different data sources: blue for manually extracted, red for ALOS-2 quad-pol, yellow for ALOS-2 dual-pol, and green for Sentinel-1 dual-pol. The background features scattered black dots on a white field, with geographic coordinates along the edges.</alt-text>
</graphic>
</fig>
</sec>
</sec>
</sec>
<sec sec-type="discussion" id="s5">
<label>5</label>
<title>Discussion</title>
<sec id="s5-1">
<label>5.1</label>
<title>Applicability of polarimetric parameters</title>
<p>The polarimetric SAR features adopted in this study provided clear class separability among landslide, vegetation, building, and water in the mountainous karst terrain of Dafang County. Steep slopes, fractured bedrock, and thick weathered regolith make rainfall-induced landslides prone to exposing fresh soil and rock surfaces with high surface-scattering power. In the <inline-formula id="inf111">
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</inline-formula> components of mapped landslides typically fell between those of vegetation and buildings, consistent with previous observations in other mountainous regions. The high recall (0.93) obtained with quad-pol ALOS-2 data underscores the utility of these polarimetric parameters for rapid post-event landslide mapping in similar geological settings.</p>
</sec>
<sec id="s5-2">
<label>5.2</label>
<title>Performance of the X-Bragg model</title>
<p>Compared with the traditional Bragg model, the X-Bragg surface scattering model showed enhanced sensitivity to soil roughness variations and slope-induced depolarization. This capability is particularly relevant in Dafang County, where landslides occur on irregular slopes with heterogeneous lithology. The X-Bragg-derived soil roughness and moisture parameters contributed to improved boundary delineation, as reflected in the final aspect ratio <inline-formula id="inf114">
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</mml:mrow>
</mml:math>
</inline-formula> and positive relative width change (Rchg &#x3d; 0.68) consistent with UAV-based field measurements.</p>
</sec>
<sec id="s5-3">
<label>5.3</label>
<title>Why ALOS-2 outperforms Sentinel-1 in vegetated mountainous areas</title>
<p>The comparison between ALOS-2 and Sentinel-1 indicates that ALOS-2 achieves higher landslide-detection accuracy in the Dafang County case study. A plausible reason is the difference in radar wavelength: ALOS-2 operates in the L-band with a longer wavelength, which is generally less sensitive to vegetation volume scattering and can better penetrate forest canopy, thereby providing stronger sensitivity to ground-surface exposure and debris deposits after landsliding. In contrast, Sentinel-1 operates in the C-band, whose shorter wavelength is more strongly influenced by vegetation and small-scale surface roughness, which may obscure landslide-related changes in densely vegetated slopes. This wavelength-driven scattering difference is particularly important in humid monsoon mountainous regions such as Bijie, where vegetation cover is extensive and post-event optical observations are often unavailable due to clouds. Therefore, the observed performance gap between ALOS-2 and Sentinel-1 is consistent with the physical sensing characteristics of L-band versus C-band SAR in forested terrain, and it supports the operational preference for L-band data when available.</p>
</sec>
<sec id="s5-4">
<label>5.4</label>
<title>Comparison with alternative classifiers</title>
<p>The Deep Forest (DF) classifier outperformed RF, ANN, KNN, and SVC in separating landslides from spectrally and structurally similar surfaces, especially in mixed scattering areas such as rural settlements. In the complex mountainous setting of Dafang County, where both spatial texture and polarimetric features are critical, DF achieved the highest overall accuracy (94.5%) and Kappa coefficient (0.92). The advantage was further amplified when combined with the Majority Voting and morphological optimization modules. In particular, the shape-constrained refinement helps reduce fragmented detections and isolated false alarms that may arise from terrain-induced scattering ambiguity, improving the spatial coherence of the final outlines. Nevertheless, DF is computationally more demanding than RF or KNN, which may constrain large-scale or near-real-time applications.</p>
</sec>
<sec id="s5-5">
<label>5.5</label>
<title>Limitations and future directions</title>
<p>Several limitations should be acknowledged:</p>
<p>1. Sample dependence: Model performance relies on high-quality training samples, which are logistically difficult to obtain in remote mountainous terrain. 2. Geometric distortions: Terrain-induced layover and shadow in SAR imagery can cause misclassification on steep slopes. 3. Morphological constraints: The aspect ratio and longitudinal shape criteria used here may be suboptimal for highly irregular landslide morphologies. 4. Event-specific tuning: Parameters optimized for the May 2025 event may require adjustment for other landslide types or geological conditions. Future research should focus on unsupervised or semi-supervised classification methods to reduce reliance on extensive labeled datasets, and on incorporating multi-temporal SAR observations to improve robustness in areas with recurrent slope failures.</p>
</sec>
</sec>
<sec sec-type="conclusion" id="s6">
<label>6</label>
<title>Conclusion</title>
<p>This study presented a single post-event polarimetric SAR framework for landslide mapping, combining polarimetric feature selection, Deep Forest classification, Majority Voting refinement, and morphological optimization. The framework is designed to operate on a single post-event SAR acquisition, aiming to support rapid and reproducible landslide mapping when pre-event data or extensive field surveys are unavailable. Applied to the rainfall-induced landslide triggered by the late-May 2025 extreme precipitation in Dafang County, Bijie City, the method achieved an overall accuracy of 94.5% (Kappa &#x3d; 0.92) with quad-pol ALOS-2 data, 91.0% (Kappa &#x3d; 0.87) with dual-pol ALOS-2, and 84.3% (Kappa &#x3d; 0.79) with Sentinel-1, demonstrating both precision and adaptability. The observed performance differences across sensors are consistent with the physical sensing characteristics of L-band and C-band SAR in vegetated mountainous terrain. The final mapped boundary exhibited an aspect ratio of 2.10 and a relative width change of 0.68, consistent with UAV-based field observations. These findings highlight the framework&#x2019;s suitability for precise landslide delineation in complex mountainous terrain and its potential for rapid disaster assessment in other high-relief, high-precipitation environments.</p>
</sec>
</body>
<back>
<sec sec-type="data-availability" id="s7">
<title>Data availability statement</title>
<p>The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.</p>
</sec>
<sec sec-type="author-contributions" id="s8">
<title>Author contributions</title>
<p>SX: Writing &#x2013; review and editing, Writing &#x2013; original draft, Methodology, Conceptualization. GD: Supervision, Writing &#x2013; review and editing. LY: Writing &#x2013; review and editing. JW: Writing &#x2013; review and editing.</p>
</sec>
<sec sec-type="COI-statement" id="s10">
<title>Conflict of interest</title>
<p>Author JW was employed by Aerospace Planning and Design Group Co., Ltd.</p>
<p>The remaining author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.</p>
</sec>
<sec sec-type="ai-statement" id="s11">
<title>Generative AI statement</title>
<p>The author(s) declared that generative AI was not used in the creation of this manuscript.</p>
<p>Any alternative text (alt text) provided alongside figures in this article has been generated by Frontiers with the support of artificial intelligence and reasonable efforts have been made to ensure accuracy, including review by the authors wherever possible. If you identify any issues, please contact us.</p>
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<title>Publisher&#x2019;s note</title>
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<bold>Edited by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/799636/overview">Abani Kumar Patra</ext-link>, Tufts University, United States</p>
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<bold>Reviewed by:</bold> <ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/3192042/overview">Sartsin Phakdimek</ext-link>, Suranaree University of Technology, Thailand</p>
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<ext-link ext-link-type="uri" xlink:href="https://loop.frontiersin.org/people/3299378/overview">Himanshu Sharma</ext-link>, Vivekananda Global University, India</p>
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