Sketching by hand is the most primitive and natural way for people to communicate. Sketches may be drawn on paper or on smart devices (e.g., with drawing tools on mobile phones and tablets, the CogSketch application, etc.) to extract spatial objects through image recognition technology. Hand-drawn sketches range from simple “stick” drawings to complex blueprints, and serve to bring to mind the memory of a spatial scene. The sketch used in this study is a hand-drawn map. As the name implies, hand-drawn sketches (or maps) do not use professional observation equipment or mapping technology, and only memory will serve to deliver information (e.g., road network structure, landmark position, familiarity with the shape of the surface area and position, etc.) to draw on paper or intelligent display devices, finally obtaining a visual cognitive map. This is a personalized recognition of the space environment. Space scenes are reflected in the human brain (Zheng And Xue’er, 2022).

Hand-drawn sketches are easily and rapidly obtained, yet at the same time also expose the shortcomings of color simplification, being mostly black and white images that do not contain color and texture information. Furthermore, because of people’s cognitive distortion and schematization, hand-drawn sketching is highly abstract and exaggerated, such that the measurement information in hand-drawn sketching is largely invalid and contains no reference to geographic coordinates, as do standard directions and coordinates.

Figure 1 shows two examples of simple hand-drawn sketches. Both are largely drawn with simple black lines and simply marked ground objects. For example, the numbers in the left picture represent the corresponding dormitory building numbers, and the building name is abbreviated to the picture on the right. In hand-drawn sketching, people tend to abstract unnecessary details and aggregate a few objects that are typically more obscure or difficult to achieve by hand. In particular, road segments are one of the spatial objects that people habitually converge. According to investigations of hand-drawn sketching by Jia and Schwering (Wang and Schwering, 2009; Wang and Schwering, 2015), even with a high degree of aggregation and less professional and metric information, hand-drawn sketching contains many relatively invariable spatial relations, such as the relative position, size, orientation, and order of spatial objects. Similarly, according to Jan et al. (Jan et al., 2017), different person’s cognition of the same spatial scene has 90% consistency in terms of the expression of spatial information. Therefore, regardless of the degree of distortion of a person’s spatial cognition, the qualitative spatial relationship between spatial objects remains largely unchanged.

Therefore, in the matching research of hand-drawn sketching, in order to match the hand-drawn map and vector map in this way, it is necessary to make full use of the qualitative spatial relations between the acquired spatial objects and make use of the constraints of single spatial relations or multiple spatial relations to match the hand-drawn map and the vector map.

Spatial objects are an objective reflection of space entities in human cognition. In this paper, space objects can be divided into roads, rivers, lakes, and other objects, and the shapes of entities can be divided into points, lines, and planes. A point is a spatial object that represents spatial location or location information, has no spatial scale, and is considered a 0-dimensional object. The locations of towns, shops, landmarks, by edges. Can be represented by points. Lines are represented by points connected sequentially, have no width, and are considered 1-dimensional objects. Rivers, roads, routes, etc. Can be represented by polylines or curves. A plane is a closed region belonging to a 2-dimensional object. Lakes, reservoirs, administrative areas, construction areas, green areas, and so on can be expressed by planes.

In this study, points, lines, and planes are taken as the basic objects of space,namely: S p a c e   o b j e c t = P o i n t , l i n e , p l a n e (1)

Recalling that points form lines and lines in turn form surfaces, relevant spatial data information can therefore be obtained from points. The hierarchical structure of the spatial objects is shown in Figure 2.

Interventionary studies involving animals or humans, and other studies that require ethical approval, must list the authority that provided approval and the corresponding ethical approval code.

Yingxinyang (Ying, 2003) analyzed spatial relations among spatial objects, including measurement relations (e.g., size, area, distance, angle, etc.), order relations (direction), and a variety of topological relations among points, lines, and planes. Considering the overall characteristics of hand-drawn sketches compared to the characteristics of the typical spatial object, hand-drawn sketches contain neither precise geometric features nor detailed semantic expressions. Therefore, prioritizing the topology relationship of spatial relations is invariant for hand-drawn sketches and vector maps. Spatial relations will become expressed through hand-drawn sketches by matching similarity measurements and matching the research focus of the vector map.

As mentioned earlier, standardized extraction and classification of spatial objects in hand-drawn sketches comprise three main types of spatial objects: points, lines and planes. The spatial relations expressed by different spatial objects are varied, and the detailed classifications and expressions are as follows:

(1) Topological relationships of road segments. The spatial relationship of roads generally includes the topological relationship of road segments, the connections between adjacent road segments, and the spatial relationship of fork points. At present, road section topological relationship models constructed based on the above feature space include the DRA7 (Oliver Wallgrün et al., 2010), DRA24 (Moratz and Ragni, 2008), and DRA72 (Moratz and Ragni, 2008) models, and the expression precision is successively from low to high.

The above seven spatial relations include topological relations, azimuth relations and sequence relations, and refer to ways in which the spatial relations in the hand-drawn sketch can be obtained in a more comprehensive way.

Suppose a graph has two basic representations: an adjacency list and an adjacency matrix. These two basic representations can be used to represent both undirected and directed graphs. The expression G = V , E is generally used to represent a sparse graph (i.e., the number of edges is far less than the number of node squares), while the adjacency matrix is usually used to represent either a dense graph (i.e., the number of edges is close to the number of node squares), or to judge whether there are connecting edges between two given nodes.

A graph is a commonly used data structure in computers, and are considered to define many interesting computational problems. It can be assumed that the spatial relation obtained by hand-drawn sketching is the input graph, and the spatial relation in the vector map is the reference graph. Given an input graph and a target graph, the task of matching is to establish a one-to-one mapping relationship between all nodes in the input graph and nodes in the target graph.

Assume that R is the set of spatial relations, where N is the node, E is the edge of the graph, and I is the mapping function. The matching mapping function of the input graph ( G = N , E , I ) and target graph ( G ′ = ( N ′ , E ′ , I ′ ) φ : N → N ′ ∪ ⊥ is the matching relationship between the input node and the target node; if the input node N does not find a matching target node, it is expressed as N → ⊥ . The mapping function then maps the target node N ′ unidirectionally; that is, two different input nodes will not map to the same target node.

Figure 5 shows a hand-drawn sketch near the south gate of the informatics department and its topological relationship based on RCC8 and the vector of the same area and its topological relationship based on RCC8. Spatial objects and qualitative spatial relations in hand-drawn sketches and vector maps are, respectively, expressed by an adjacency matrix, with spatial objects as nodes and qualitative spatial relations as the weight of edges. The expression results are shown in Tables 1, 2. However, it is very difficult to realize the matching process of graphs using two independent adjacency matrices. The essence of graph matching is that any point in the hand-drawn sketch and any node in the vector map forms a point pair to be matched. Further, it is also judged whether the weight of the corresponding edge of any two point pairs to be matched is consistent. If so, the two-point pair is considered to be matched.

Notes: The node set of the input graph is expressed by: N = a 3 , a 5 , ⋅ ⋅ ⋅ , a 13 , c b 5 , ⋅ ⋅ ⋅ , c b 11 . The reference target node set is expressed by: N = B 1 , B 2 , ⋅ ⋅ ⋅ , B 10 , B 11 , M 1 , ⋅ ⋅ ⋅ , M 8 .

In Figure 5, it is assumed that there are potential matching point pairs ϕ ′ c b 8 = M 2 and ϕ ′ c b 7 = M 4 , where the spatial relation of the edge corresponding to c b 8 , c b 7 is represented by EC, and the spatial relation of the edge corresponding to M 2 , M 4 is also represented by EC. Therefore, I c b 8 , c b 7 = I M 2 , M 4 = E C satisfies the mapping relationship. On the other hand, if there are potential matching points for ϕ ′ c b 8 = M 2 and ϕ ′ c b 7 = M 9 , then I c b 8 , c b 7 = E C and I , M 2 , M 9 ≠ E C , and c b 8 , c b 7 and M 2 , M 9 are not matched. Therefore, the row and row of the improved adjacency matrix are composed of the node pairs of the input graph and the target graph, and the value in the cell indicates whether the weights of the corresponding edges of the matching point pair are the same: 1 indicates that the spatial relationship of the point pair is the same, and 0 indicates that it is not. The improved adjacency matrix formed by the spatial relationship in Figure 5 is shown in Table 3.

Figure 6 shows the construction process of the improved adjacency matrix, including the analysis of its features, removal of the point pairs that do not have matching values, and making of the adjacency matrix sparse, so as to obtain further matching point pair combinations. Where Tables 1, 2 are the matrices corresponding to the marked portions in Figure 6.

The characteristics of the improved adjacency matrix are as follows:

(1) If the spatial relation of the hand-drawn sketch is orthogonal, then all the compatibility matrices are also orthogonal.

Glover proposed an algorithm based on local neighborhood search to achieve a global optimal search, the tabu search (TS) algorithm, which is considered as the best simulation of human brain activities and aims to solve typical optimization problems. The TS algorithm is based on two important basic theories: local search and tabu criterion. As a local search algorithm, the TS algorithm selects the optimal scheme for the current searched neighborhood in each iteration. In the TS algorithm, tabu criteria and a tabu table are introduced to avoid repeated searches, and then amnesty criteria are adopted to release the high-quality scheme of the tabu, thus the final global optimization is guaranteed. The TS algorithm is considered to have the closest functionality to human brain activity among the current intelligent optimization algorithms. By marking the local optimal solution and then iterating the search, tabu objects can be avoided as far as possible in the search process. However, through the amnesty criterion, tabu objects can be searched in a circular manner in order to realize the search for a global optimal solution. The basic search steps of the TS algorithm are as follows:

(1) Set the initial solution X 0 and clear the tabu list L T a b u .

In this study, the traditional tabu search algorithm is improved from the two aspects of the selection of the optimal initial solution and the setting of the adaptive value function, so as to make the TS algorithm more suitable for the process of graph matching, improve the matching efficiency, and obtain the optimal matching results. The two main steps used are described as follows:

(1) Select the initial solution. In order to avoid the low efficiency of the algorithm caused by improper selection of the initial solution, this study first randomly generated a group of initial solutions, then executed a complete matching process to obtain a group of effective solutions under the initial solution, and took the effective solution as the optimal initial solution for the formal matching process.

Using the TS process, in this study the adjacency matrix of the hand-drawn sketch and vector map was first obtained as the original input matching data. According to the construction principle of the improved adjacency matrix, the corresponding improved adjacency matrix containing spatial relationship consistency information was constructed as the “checkerboard” of the tabu search. For the initial solution of the tabu search, a set of initial solutions were generated randomly for the first time, and an optimal solution under the initial solution was obtained according to the following steps of the tabu search, and the modified optimal solution was taken as the initial solution of the second matching process. The steps for the tabu search used in this study are as follows:

(1) The tabu list was emptied. The initialized tabu length L was the number of objects in the hand-drawn sketch, that is, the number of iterations of the tabu solution in the tabu list. The tabu length of the tabu solution in each iteration was correspondingly reduced by 1 and released from the tabu list until reaching 0. The tabu frequency was F, the number of objects in the hand-drawn sketch was multiplied by the number of objects in the vector map, that is, the number of tabu solutions appearing in the tabu list. When the tabu solution entered the tabu list, the number of tabu solutions entering the list was recorded. If this number was greater than F, it was considered to be a solution with a low matching result and would not be released again.

The specific matching method flow is shown in Figure 7.

Assuming that the spatial objects and their spatial relation diagram of G s k e t c h = N s k e t c h , E s k e t c h in the hand-drawn sketch correspond to the reference vector map in Figure G m a p = N m a p , E m a p , the number of spatial objects in G s k e t c h is C o u n t N − s k e t c h , the number of spatial objects in G m a p is C o u n t N − m a p , and the spatial objects (nodes) in the hand-drawn sketch are recorded by C o u n t m a t c h _ s k e t c h , then the matching accuracy of the hand-drawn sketch can be expressed as: M a t c h a c c u r a c y = C o u n t m a t c h _ s k e t c h C o u n t N _ s k e t c h (3)

Standard deviation was used to identify the difference between the matching results. The larger the standard deviation, the larger the variance of the matching results and the greater the difference of the matching results. In this paper, matching experiments are carried on two spaces near the school gate and in the student dormitory area. Eight valid hand drawings are collected for experiment in each space. The n 1 , n 2 , ⋅ ⋅ ⋅ , n k is used to represent the set of k-frame hand-drawn sketches that successfully matching the number of space object collections in the same space, n i for the ith image matching success by the number of space objects, the standard deviation between the matching results of hand-drawn sketches in the same space can be expressed as follows: s m a t c h = n 1 − μ 2 + n 1 − μ 2 + ⋅ ⋅ ⋅ + n k − μ 2 k (4)

Assuming that for two projections of the same space, the same spatial objects and their spatial relations are present in each projection, and different qualitative expression models are used for the same spatial relationships, the purpose of the Mann–Whitney U test is to test the difference between different qualitative expression models under the same spatial relationship, and to judge whether there is a significant difference in matching results. According to cognitive research, people maintain 90% of the correct relationship between the drawn object and reality, thus the threshold of no significant difference given in this study is p=0.05. The specific process of the Mann–Whitney U test method in this study can be described as follows:

(1) Determine hypothesis H 0 and alternative hypothesis H 1 ;

If the values are the same, then the average value of each grade is calculated as follows:

(1) Calculate grades T A and T B , then calculate ranks R A and R B ;

To improve the credibility of the matching result in practical applications, we did not select only one constraint relation for matching and instead usually used two or more spatial relations as constraints for the matching process.

Before selecting two or more spatial relationships for matching, the characteristics of the experimental area were analyzed. For experimental area I, near the south gate of the university, the road network relationship is complex and the road structure is irregular. Therefore, the topological relationship of the road segments was the main constraint condition for matching. For experimental area II, the student dormitory area, which mainly expresses the relative position relationship of the dormitory group, the road is relatively regular. Therefore, the relative order relationship between ground features and road sections and the topological relationship between ground features and regional surface blocks were selected as the main constraint conditions for matching.

To apply multiple spatial relations in the matching process, this study adopted the hierarchical method for matching; that is, multiple spatial relations were matched in turn.

Based on road segment priority matching, the left-right symmetric model was first used to match the adjacent ground features of adjacent road segments, and the selection of the best matching ground features was helpful in refining the topological relationship of streets. Then, the DRA7 model was used to strengthen the topological relationship of the road segments, and the road segments with the highest matching rate were identified as the basis for the next matching. Finally, according to the selected optimal and correctly matched road segments, the linear sequence of ground features along the road segment or the cyclic sequence of ground features at the fork could be matched. In this step, the relative positioning of the ground features could be performed to find the relatively correctly matched ground features. Matching process based on road is shown in Figure 10. And matching rate based on road segment matching process is shown in Table 12.

Based on the matching between ground objects and regional surface blocks, the RCC11 model had a good matching rate for the topological relationship between ground objects and the regional surface under a single constraint relationship. Therefore, basic matching could be performed based on the RCC11 model. First, the ground object with the highest matching rate was identified as the basis for the next matching. Then, the RCC5 model was used to match the regional surface blocks. Finally, the linear sequence relationship between ground objects and road segments and the cyclic sequence relationship at fork points were used for matching.

The above matching process involved four kinds of spatial relations to match in turn as constraint conditions, and each step selected the spatial object correctly matched in the previous step as the basis. Based on the matching process of landmark and city block priority is shown in Figure 11. The matching rate and algorithm complexity were further used to evaluate the matching process, as shown in Table 13.