Unlike standard surveillance cameras, fisheye cameras are equipped with a wide-angle lens. This facilitates wide-area coverage, but leads to various challenges that we discuss in Section 3. Front-facing fisheye cameras have found applications in autonomous navigation, primarily for pedestrian and obstacle detection, and have been widely researched (Cordts et al., 2016; Yogamani et al., 2019; Ye et al., 2020; Liao et al., 2023). Down-facing fisheye cameras, mounted above the scene of interest, have recently emerged as an alternative to standard side-mounted surveillance cameras due to the wide-area coverage and reduced occlusions. While in outdoor scenarios this is very much limited by the ability to mount such cameras above the scene (e.g., lamp posts), in indoor scenarios the mounting is relatively straightforward (e.g., suspension from the ceiling).

People detection in images from standard surveillance cameras has rich literature spanning at least two decades, from classical methods applying SVM classification to Histogram of Oriented Gradients (HOG) features (Dalal and Triggs, 2005) or using AdaBoost classifier with Aggregate Channel Features (ACF) (Dollár et al., 2014) to more recent deep-learning methods such as YOLO (Redmon et al., 2016), SSD (Liu et al., 2016) and R-CNN (Girshick, 2015; Ren et al., 2015). However, such methods directly applied to top-view fisheye images perform poorly due to a dramatic range of viewpoints in the same image (people under the camera are seen from above, but those farther away are seen from a side perspective) and arbitrary body orientations (e.g., standing people appear radially in images and can be seen “upside-down”) as shown in Figure 2. Furthermore, although more subtle, lens distortions cause body-shape deformations, especially close to fisheye-image periphery, which also penalizes person-detection performance. We discuss these issues in more detail in Section 3.

In the last decade, person-detection methods have been developed specifically for top-view fisheye images. Early attempts focused on model-based feature extraction and various adaptations to account for fisheye geometry. In perhaps the first work, background subtraction was combined with a probabilistic body-appearance model and followed by Kernel Ridge Regression (Saito et al., 2011). Chiang and Wang (2014) rotated each fisheye image in small angular steps and applied SVM to HOG features extracted from the top-center part of the image to detect people. Krams and Kiryati (2017) applied standard ACF classifier to dewarped features extracted from a fisheye image. Demirkus et al. (2017) also used ACF to learn different-size models dependent on the distance from image center.

The most recent methods are CNN-based end-to-end algorithms. Seidel et al. (2018) applied YOLO to dewarped versions of overlapping windows extracted from a fisheye image, but tested the algorithm on a private dataset only. Tamura et al. (2019) introduced a rotation-invariant version of YOLO, that was trained on rotated images from COCO 2017 (Lin et al., 2014), however the inference stage assumed that bounding boxes are aligned with the image radius thus not allowing for arbitrary body orientations. Li et al. (2019) rotated each fisheye image in 15° steps and applied YOLOv3 (Redmon and Farhadi, 2018) to the top-center part of the image where people usually appear upright, followed by post-processing to remove multiple detections of the same person. They also proposed an extension in which the algorithm is applied only to changed areas, as determined by background subtraction, rather than to the whole image. Minh et al. (2021) proposed an anchor-free CNN that allows bounding-box rotation and speeds up the inference. Chiang et al. (2021) proposed to unwrap patches from a fisheye image using simple fisheye-lens model in order to compose a perspective image for inference by YOLO, followed by post-processing to remove duplicate detections. Wei et al. (2022) applied a CNN with deformable convolution kernels to account for geometric distortions in top-view fisheye images, however tested the approach only on their own dataset. Finally, Tamura and Yoshinaga (2023) extended their earlier work by training on rectilinear datasets while leveraging ground-truth segmentations to fit bounding boxes more tightly around human bodies. Since deep-learning algorithms require extensive training data, a number of top-view fisheye-image datasets aimed at people detection have been published; we discuss the most commonly-used ones in Section 4.

Person re-identification is a key component of people counting and by itself is a vast research area of critical importance for visual surveillance. While a detailed review of methods proposed for standard surveillance cameras is beyond the scope of this paper, below we briefly summarize key challenges and types of methods proposed.

Traditional person ReID is concerned with retrieving a person of interest across multiple cameras with non-overlapping FOVs. In closed-world person ReID, typically a single visual modality is used (e.g., RGB), person detections (bounding boxes) are assumed known and reliable, and the query person appears in the gallery set. There exist many methods developed in this context but they, in general, include three components: feature representation, metric learning and ranking optimization. Open-world person ReID attempts to address real-world challenges, such as multiple data modalities (e.g., RGB, depth, text), end-to-end ReID without pre-computed person detections (direct ReID from images/videos), semi-supervised or unsupervised learning with limited/unavailable annotations, dealing with noisy annotations, or open-set ReID when correct match is missing from the gallery. Two recent surveys by Ye et al. (2022) and by Zhang et al. (2024) discuss dozens of methods proposed and include experimental comparisons.

However, person ReID methods developed for rectilinear cameras perform poorly on top-view fisheye images, although re-training on fisheye data somewhat improves performance (Cokbas et al., 2022). In addition to arbitrary body orientations (e.g., “upside-down”), dramatic viewpoint differences (e.g., from above in one camera view, but from side-perspective in another camera view) and lens-distortions (more significant when a person appears at image periphery), another challenge for person ReID is body-scale difference between cameras. Traditional person ReID was developed for cameras with non-overlapping FOVs. Since each camera is oriented toward its own area of interest, people appearing in areas monitored by different cameras will often appear at a reasonably-similar size. This is not the case for fisheye ReID considered here. Since the overhead fisheye cameras have overlapping FOVs and since ReID is performed on images captured at the same time instant, a person might be under one camera but far away from another camera. In addition to different viewpoints, there will be a dramatic difference in person-image size and geometric distortion (person under a camera will be very large and seen from above, while person far away will be tiny and geometrically-distorted). For a detailed discussion and examples, please see Cokbas (2023) and Cokbas et al. (2023).

Very few methods have been proposed to date for person ReID using overhead fisheye cameras. The earliest work by Barman et al. (2018) considers only matching people who are located at a similar distance from each camera, thus assuring similar body size (and, potentially, similar viewpoint). Another work by Blott et al. (2019) uses tracking to extract three distinct viewpoints (back, side, front) that are subsequently jointly matched between cameras, which is similar in spirit to multiple-shot person ReID developed for standard cameras by Bazzani et al. (2010). However, this approach requires reliable tracking and visibility of each person from three very different angles—neither can be guaranteed. Both works report results only on private datasets. Another work somehwat related to person ReID is on tracking people in overhead fisheye views by Wang and Chiang (2023). The authors use their own person detection method (Chiang et al., 2021) and then apply a variant of DeepSORT for tracking.

Many recent approaches use RAPiD (Rotation-Aware People Detection) (Duan et al., 2020) as a benchmark for performance evaluation. RAPiD is a CNN based on YOLOv3 (Redmon and Farhadi, 2018) adapted to accommodate bounding-box rotation and trained using the original YOLOv3 loss function augmented with a novel periodic loss for angle regression. RAPiD handles unusual body viewpoints by training on a variety of fisheye images and its source code is publicly available¹. Table 2 compares performance of four recent algorithms against RAPiD. All algorithms were pre-trained on COCO 2017 (Lin et al., 2014) and then fine-tuned and tested on MW-R, HABBOF and CEPDOF via cross-dataset validation. Specificallly, two datasets were used for training and the third one was used for testing, and then the roles were swapped. This resulted in three sets of performance measures that were averaged and are shown in Table 2. The two versions of RAPiD differ in training/testing image resolutions to allow comparison with other methods. Even at the lower resolution, RAPiD significantly outperforms other methods in all performance metrics. However, ARPD by Minh et al. (2021) offers much faster inference than RAPiD at the cost of accuracy.

We would like to point out that although the test datasets consist of top-view fisheye images, challenges vary (Table 1). While in MW-R and HABBOF people are either standing or walking, CEPDOF is more challenging with many unusual poses, severe occlusions and low-light conditions. Figures 3A–F show sample detections produced by RAPiD under various challenges. Except for extreme cases (people on the screen, low light), RAPiD performs exceedingly well. This is confirmed by AP₅₀ which exceeds 93%, and Precision, Recall and F-score that are over 0.9. However, all three datasets were recorded using high-quality cameras in “staged” scenarios (controlled environment, subjects instructed to behave in a certain way). Would these algorithms perform equally well “in the wild”, that is in uncontrolled real-life situations?

Table 3 shows performance of four of these algorithms² on the WEPDTOF dataset collected from YouTube, that includes real-life challenges as detailed in Section 4. In addition to AP₅₀, similarly to the MS COCO challenge (Lin et al., 2014), we report this metric for small, medium and large bounding boxes denoted as AP50S, AP50M, and AP50L, respectively. Clearly, RAPiD outperforms other algorithms in terms of AP₅₀ but is outperformed by AA and AB in terms of Precision and F-score. This is largely due to the fact that AA and AB compute bounding-box predictions from overlapped crops of a rotated image and combine these results in a post-processing step. Thus, they analyze a person's appearance multiple times, each at a slightly-different rotation angle, which boosts the confidence score of the bounding box for that person but hugely increases the complexity (Table 2).

Note that all metrics in Table 3 are significantly lower than those in Table 2 due to challenges captured in WEPDTOF. When visually evaluating these results by playing video with superimposed detections, we observed that some bounding boxes produced by RAPiD appear intermittently (they disappear for a frame or two but then reappear again) thus contributing to the reduced performance. Visual examples of misses (false negatives) in two challenging sequences from WEPDTOF are shown in Figures 3G, H.

To address the intermittent behavior of detections and improve performance, some form of temporal coherence of detections should be incorporated into the people-detection algorithm since people are either static or move incrementally in space-time. In this context, we developed three extensions of RAPiD (Tezcan et al., 2022) each leveraging temporal information differently, that we briefly summarize below. The source code for these algorithms is publicly available³.

If a people-detection algorithm, such as those discussed in Section 5, is perfectly accurate, then counting people is as simple as counting bounding boxes. However, certain errors in people detection may still result in a correct people count, for example when a false positive and false negative occur in the same image. These two errors cancel each other, so an accurate metric for people counting should ignore such scenarios. Furthermore, we are interested in how far off is an estimated count from a true count. In this section, we use the following metrics to evaluate performance of people-counting algorithms:

where η_i and η^i are the true and estimated people counts in frame number i, M is the total number of frames and 1(ε) is an indicator function, that is 1(ε) equals 1 if ε is true and 0 otherwise. While the Mean Absolute Error (MAE) is a commonly-used metric, it is not meaningful when comparing algorithms at different occupancy levels (e.g., 80 people vs. 8 people). This is addressed by the Mean Absolute Error per person (MAE_pp) which divides MAE by the average occupancy over M frames. The X-Accuracy (Acc_X) quantifies people-counting performance as “accuracy with slack of X”. For X = 0 this definition reverts to the traditional definition of accuracy, but for larger values of X it tolerates the departure of η^i from η_i by up to X. For example, Acc₅ gives the percentage of frames in which the estimated count is within 5 of the true count.

To evaluate performance of various algorithms, we recorded data over 3 days in a large classroom (Figure 2C) equipped with three cameras. On day 1 there were 11 high-occupancy periods (lectures) with up to 87 occupants (Figure 2F), on day 2 there were four such periods with up to 65 occupants, while on day 3 the classroom was mostly empty with maximum occupancy of 9 for a short period of time. We annotated all frames in terms of the number of people in the classroom, but not in terms of bounding boxes.

Table 5 shows the people-counting performance of RAPiD on this dataset for each of the three cameras. The much larger values of MAE on days 1 and 2 are due to high average occupancy on these two days. MAE_pp, on the other hand, is similar across all days confirming its relative independence of occupancy scenarios. Its value of about 0.4 suggests RAPiD commits an error of about 40% per person which is high. This mediocre performance is confirmed by the values of Acc_X. Cumulatively over 3 days, RAPiD produces exact counts in 46–55% of frames depending on the camera and only in 76–79% frames with count error of up to 10. Clearly, a single camera is incapable of accurate counting in this large a space.

Increasing the number of cameras to 2 creates a problem of potential overcounting since the same person may be captured by both cameras due to their wide fields of view (Figure 1). In order to make sure that each person is counted only once, person re-identification is needed.

We propose a general approach to person ReID using N-D score matrices. Such matrices can quantify similarity between identities using people locations, as proposed by Bone et al. (2021), or their appearance, as explored by Cokbas et al. (2023). We first consider a 3-camera setup (N = 3) of our test classroom shown in Figure 2C, however we note that, in general, cameras need not be collinear. In Figure 6, we graphically illustrate (Venn diagram) the general relationship between sets of person detections from three cameras. In this diagram, C₁, C₂, C₃ denote the sets of people detections in images simultaneously captured by cameras #1, #2 and #3, respectively. The Venn diagram allows us to compute the actual people count η as follows:

where |C| denotes the cardinality of set C. Clearly, |C₁|, |C₂|, |C₃| are people counts in respective camera views provided by a people-detection algorithm (e.g., RAPiD). The numbers of identities matched between two cameras, namely |C₁∩C₂|, |C₁∩C₃|, |C₂∩C₃|, are provided by a two-camera ReID algorithm, such as the one described in Section 6.4.1. However, we still need to identify the number of identities matched across all three cameras: |C₁∩C₂∩C₃|. This necessitates a 3-camera ReID algorithm.

As discussed in Section 6.4.1 and shown in Figure 5, person ReID between two cameras results in a 2-D score (distance) matrix D that is subject to a greedy search to match identities. With three cameras, this matrix would become 3-dimensional with each entry containing, for example, a measure of appearance similarity for a triplet of people detections (one detection from each camera view), or a distance metric computed from locations of this triplet. Rather than defining a new 3-camera distance metric, we adopt 2-camera metrics developed by Bone et al. (2021), apply them to 3 pairs of cameras and average the resulting scores as follows:

where S₁₂, S₁₃, S₂₃ are 2-D score matrices (like those in Figure 5), S₁₂₃ is a 3-D score matrix and i_K is the identity detected in view from camera #K. Clearly, S₁₂(i₁, i₂) quantifies the location mismatch for identities i₁ and i₂ from cameras #1 and #2, respectively, and S₁₂₃(i₁, i₂, i₃) represents the location mismatch for identities i₁, i₂, i₃, each from its respective camera.

An extension to N>3 is relatively straightforward but one must carefully consider various combinations of n out of N cameras, across which identities need to be matched. For example, for N = 4 cameras, re-identifications between 2, 3, or 4 camera views are needed in order to obtain the correct overall count. For N cameras, the total number of camera combinations to be considered is:

where the summation starts at n = 2 since re-identification requires at least two camera views. For N = 3, this amounts to four camera combinations which is consistent with four intersections in the Venn diagram in Figure 6. For N = 4, there are 11 camera combinations (6 two-camera combinations, 4 three-camera combination, and 1 four-camera combination), and for N = 5 there are 26 camera combinations, rapidly increasing with a growing number of cameras.

Clearly, score matrices S of up to N dimensions are needed for N-camera re-identification. One possibility is to generalize Equation (2) to N dimensions through the use of the well-known inclusion-exclusion principle by van Lint and Wilson (1992) as follows:

We would like to emphasize that this approach to N-camera person ReID is general and can be applied to both appearance- and location-based features. However, in the remainder of this section we focus on location-based matching due to its superior performance for overhead fisheye cameras (Cokbas et al., 2023) and low computational complexity. The computational complexity is a serious concern for large N since the number of camera combinations that need to be considered grows exponentially with a growing N (4).

The approach we proposed in the previous section is general and applies to both appearance- and location-based features. If applied to location-based features, it effectively performs identity matching based on locations in the 2-D image plane (pixel coordinates); identities are matched based on the proximity of detected and predicted locations in a given camera view. All the predicted locations are obtained by first inverse-mapping 2-D locations detected in one camera view to 3-D coordinates and then forward-mapping these 3-D coordinates to 2-D locations in the other camera view (bidirectional location mapping in Figure 5). This may result in location-error imbalance since the detected locations do not undergo any mapping, while the predicted locations are obtained via inverse-forward mapping that uses intrinsic and extrinsic parameter estimates⁴, unlikely to be perfectly accurate.

In order to avoid this location-error imbalance, we propose to perform identity matching in real-world coordinates, that is map person-detection locations in all camera views to 3-D coordinates. An explanation is required at this point. The inverse mapping from a 2-D location in a camera view to 3-D coordinates must be constrained due to scale ambiguity (the problem is underconstrained). In the scenario of indoor monitoring, considered here, with people positioned on a room's floor, this ambiguity can be removed by assuming average height of a person (168 cm). Then, the location of a person detection (center of the bounding box) in any camera view can be mapped to 3-D room coordinates such that the 3-D point is 84 cm above the floor (vertical center of human body of average height). The inverse mapping of all person-detection locations from N camera views to 3-D space results in a point “cloud”, or rather a 2-D point “spatter” on a plane parallel to and 84 cm above the floor. We propose to cluster the locations in this “spatter” to match identities.

We note that, ideally, the number of location clusters should correspond to the number of people in the room. Therefore, we cannot use a clustering algorithm such as K-means (Lloyd, 1982) since we do not know the value of K in advance. We adopt DBSCAN (Ester et al., 1996) since it requires no advance knowledge of the number of clusters. DBSCAN is a density-based clustering algorithm that has two parameters, ϵ and minPoints. In DBSCAN, first one picks a random point as the point of interest and finds all points that are within radius ϵ from it. All such points, including the point of interest, get assigned to the same cluster. This process is repeated; each point in the cluster is treated as the new point of interest, thus enlarging the cluster. One continues to spread out the cluster until there is no point within ϵ distance from any of the points in the cluster. Then, one picks another point from the dataset that has not been visited yet and repeats the process. For a group of points to be considered a cluster, there should be at least minPoints elements in the cluster. Also, if a certain data point has no other data points within ϵ radius, it is labeled as noise and gets discarded.

Similarly to DBSCAN, we propose clustering of the mapped real-world coordinates using two parameters: ϵ and maxPoints. While ϵ has the same role as in DBSCAN, maxPoints is used differently. In DBSCAN, the size of a cluster has a lower bound of minPoints with no upper bound. In our case, cluster size must be between 1 and maxPoints due to the nature of person re-identification and people counting that we are tackling. Each person should have their own cluster, where each point in the cluster corresponds to a detection of the same person in a different camera view. In re-identification across N cameras, some people can get detected in one camera view only due to occlusions or failed detections, potentially resulting in a single point in their cluster. On the other hand, a person can be detected in at most N camera views, so a cluster may have at most N points and so maxPoints = N.

In experiments reported in the next section, we use 3-D Euclidean distance as the distance measure between the mapped real-world locations. However, since all such locations occur on a plane, as discussed above, effectively this is a 2-D distance in real-world coordinates.

We evaluate the people-counting performance of both N-camera person ReID algorithms on the 3-day dataset captured by three cameras, that we introduced in Section 6.2. While in Table 5 we reported people-counting results using only camera #1 and in Table 6 using cameras #2 and #3, here we report results using all three cameras installed in the classroom.

We use location-based re-identification with the PPD distance metric to evaluate both N-camera algorithms. Note, that in the N-D score-matrix approach elements of S (PPD values) are expressed in pixels (i.e., the lower the score/distance, the more similar the identities). While the greedy algorithm (Figure 5) performs identity matching until no more matches are possible, some late matches may be unlikely if the corresponding element in S is large. To avoid such unlikely matches, we introduce a distance threshold λ (in pixels), and stop the matching once all remaining elements in S exceed λ. The N-camera location-clustering approach (Section 7.2) also has a tuning parameter ϵ, expressed in centimeters, that quantifies a threshold on distance in real-world coordinates.

In Figure 7, we show the people-counting performance of both N-camera algorithms (N = 3) when their respective tuning parameters vary. The N-D score-matrix approach yields the lowest MAE value for λ = 400 pixels, while the real-world location-clustering approach achieves the best performance for ϵ = 250 cm. We note that these values are relatively large considering the fact that we are working with 2,048 × 2,048-pixel images in a 22 × 8.5 m room. Very likely some identity matches are incorrect (as are some RAPiD detections) and yet the people count is quite accurate. However, since our dataset is labeled for people-counting only (no bounding boxes or identity labels), we cannot report ReID accuracy to verify this hypothesis.

While a low MAE is maintained by the N-D score-matrix approach for a wide range of λ values (from about 100 pixels to 1,000 pixels), a high-performance range for the real-world location clustering approach happens only for ϵ between about 200 and 300 cm. Outside of these ranges, MAE increases and especially rapidly for small parameter values. For example, small values of threshold ϵ allow little room for image-to-3-D mapping errors; imprecisely mapped locations get absorbed into incorrect clusters. The more accurate the mapping algorithm, the smaller the value of ϵ that can be used. In the extreme case of ϵ = 0 cm, there is no room for mapping errors. Unless same-identity locations from all cameras are mapped to the same 3-D location, they cannot form one cluster. Since error-free mappings are very unlikely, for ϵ = 0 cm very few identities can be matched, thus resulting in small η^iKL in Equation (1) and causing overcounting. As ϵ increases, the degree of overcounting gets reduced. At the other extreme, if ϵ is too large the mapped locations of different identities might fall into the same cluster thus potentially resulting in too many matches and leading to undercounting. Similar conclusions can be drawn for the impact of λ on performance of the N-D score-matrix algorithm.

In order to confirm our observations about overcounting and undercounting, Figure 8 shows the true occupancy during the 3-day test (red line) and occupancy estimated by the N-D score-matrix algorithm (blue line) for three values of λ: 100, 400 and 1,500 pixels. Notably, for λ = 100 pixels the algorithm significantly overcounts, while for λ = 1, 500 pixels it largely undercounts. However, for λ = 400 pixels, it closely follows the true people count. Figure 9 shows similar results for the real-world location-clustering algorithm and three values of ϵ: 50, 250, and 800 cm. Again, for ϵ = 50 cm the algorithm severely overcounts, for ϵ = 800 cm it largely undercounts, and for ϵ = 250 cm it is most accurate.

Table 7 quantifies performance of both algorithms in terms of MAE, MAE_pp, Acc_X for the tuning parameters that yielded the smallest cumulative MAE value (Figure 7), namely λ = 400 pixels and ϵ = 250 cm. For ease of comparison, included are also results for the 2-camera people-counting algorithms from Table 6 that employ greedy search of a 2-D score matrix populated by either PPD or CBD values. We note, that in terms of cumulative metrics the 3-camera score-matrix algorithm using the PPD metric slightly outperforms the same algorithm using 2 cameras. However, it performs equally well-compared to the 2-camera score-matrix algorithm with the CBD metric in terms of MAE and MAE_pp, and results are mixed in terms of Acc_X (slightly better for X = 5 and 10, and slightly worse for X = 0). As for the 3-camera real-world location-clustering algorithm, it does not perform as well; its cumulative MAE and MAE_pp values are higher by 0.07 and 0.04, respectively, than corresponding values for the 3-camera score-matrix algorithm, and the Acc_X values are lower by up to 1% point.

With respect to different occupancy scenarios, the 3-camera score-matrix approach quite consistently outperforms other algorithms on days 1 and 2 (high average occupancy), but is outperformed by the 2-camera approaches on day 3 (mostly empty). Interestingly, on day 3 the single-camera results (Table 5) are even better than those for two cameras; for example, camera #1 mounted in the center of the classroom produces MAE and MAE_pp twice lower than those for the 2-camera algorithms. This is due to the fact that the few occupants on day 3 are located in classroom center which is effectively covered by camera #1. With no challenges (people are directly under the camera, no occlusions, no occupants at FOV periphery), people counting using one camera is erroneous only if people detection fails. However, when multiple cameras are needed for large-area coverage, additional errors may be introduced by person ReID. Clearly, under spatially-localized low occupancy, single-camera RAPiD may be sufficient. However, in large spaces with spatially-distributed high occupancy, a multi-camera people-counting system is essential.

The results in Table 7 may seem somewhat disappointing since the better 3-camera approach only slightly outperforms the best 2-camera approach and only in crowded scenarios. However, there is a reason for this. The 2-camera score-matrix (CBD) approach performs very well in this 187 m² test space producing cumulative MAE_pp of only 0.097 (9.7% error per person) vastly outperforming the 1-camera RAPiD performance (no re-identification) that produced a 0.373 cumulative MAE_pp (or 37.3% error per person) as shown in Table 5. As reported in Konrad et al. (2024), RAPiD applied to a single-camera video stream can deliver MAE_pp of 0.065 (6.5% error per person) up to about 75 m² (≈800 ft²) of a square-room area and 0.133 (or 13.3%) up to about 116 ft² (≈1,250 ft²). Considering that this is a 22 × 8.5 m space and that each of the cameras used by the 2-camera score-matrix approach (cameras #2 and #3 in Figure 2) roughly covers one half of the classroom (about 11 × 8.5 m space with 93.5 m² area), it is clear that little improvement can be expected from additional cameras in this case. However, the N-camera ReID algorithms proposed in this paper are expected to be highly beneficial in larger spaces in which two cameras would be insufficient. We believe that the proposed N-camera methodology would be very valuable in scaling up people-counting to much larger spaces such as convention halls, food courts, airport terminals, train/bus stations, etc.

Theoretically, a fisheye camera with FOV covering 360° in plane parallel to the sensor and at least 180° orthogonally should capture an area of any size. However, due to radial distortions of its lens and finite sensor resolution, details captured at FOV periphery are insufficient for reliable person detection (and re-identification). As discussed above, in our test scenario (Figure 2C) a single camera mounted 3.15 m above the floor can produce reliable detections up to about 8.7 × 8.7 m square area (≈75 m²). However, in a square area of 87 × 87 m, it is unlikely that 100 fisheye cameras used jointly by person ReID methods described in Sections 7.1 and 7.2 would produce reliable results using a location-based approach (PPD or CBD). As the physical distance between cameras increases, the bidirectional projection errors will grow due to errors in intrinsic and extrinsic parameters. Depending on the accuracy of these parameters, a very large area may need to be partitioned into sections, each monitored independently by a smaller group of cameras (e.g., 2 × 2 or 3 × 3). One could consider using the N-D score matrix approach with appearance features (instead of location), but a person captured by far apart cameras may appear dramatically smaller in one FOV than in the other posing very serious challenges for ReID. Again, small groups of nearby cameras would be more effective.