## 3 Method
### Information Decay Based on Gestalt Cognitive Principles  
Due to the presence of a large number of artificial buildings in vector data, which exhibit strong distribution patterns and morphological similarities, directly summing up the spatial distribution information of these objects often generates a significant amount of redundant information. The Gestalt cognitive principles indicate that the proximity, similarity, and regularity of spatial objects all influence the outcome of spatial cognition [29; 30; 31; 32]. Furthermore, artificial building objects that possess such characteristics of proximity, similarity, and regularity are also the research targets of spatial clustering, merging operators, and generalization operators [33]. These operators aim to abstract regularly distributed individual element groups into a single entity for cognition or computation, thereby reducing the cost of cognition and processing. Therefore, the measurement of map spatial information should also take this feature into account. To address the above-mentioned spatial distribution characteristics, this paper introduces similarity metrics and visually constrained growth theory to eliminate redundant similarity information in the spatial distribution network structure. The theory of visually constrained growth of redundant information posits that human eyes do not simply accumulate and recognize repeatedly occurring patterns of information, but instead possess associative learning characteristics [25]. This associative cognition allows for the recognition of spatially similar patterns by associating them, thereby reducing the cost of visual cognition. As shown in the Figure 6, the information represented by the small blue squares along the diagonal of the ink screen is not merely the sum of individual black square information. In the research of [PERSON] et al. (1954), it is pointed out that the total entropy of a pattern is the sum of the entropy of non-repeating patterns and the entropy related to repeating patterns [34]. The entropy of repeating patterns is less than the cumulative sum of the entropy of individual repeating patterns. In the study by [PERSON] et al., the relationship be  
Figure 6: Schematic diagram of visual repetition patterns. tween visually repeating redundant information is discussed in detail, and a computational method for visually repeating information is provided [25]:  
\[y=\log(1+n)x, \tag{6}\]  
Due to subjective reasons in urban planning and construction, building objects exhibit a regularity in spatial distribution, characterized by similar geometric shapes, appropriate spatial distances, and relatively consistent spatial arrangement directions [35]. When all three conditions are met, area objects often exhibit a regular distribution pattern with distinct characteristics. As shown in Figure 7, the blue buildings on the left side, with similar spatial arrangement directions, geometric shapes, and close spatial distances, are generally easy for map users to summarize and recognize during visual cognition, thus expressing less spatial information. In contrast, the yellow buildings in Figure 7 on the right side exhibit greater spatial distribution information due to inconsistent spatial arrangement directions and geometric shapes. In the field of cartography, more detailed studies have been conducted on such arrangement patterns, such as linear arrangement and spatial clustering patterns based on similarity. Based on the above analysis, this study integrates Gestalt cognitive principles and the information theory of visually constrained growth to weaken the redundant information of area objects with similar spatial arrangements, aiming to obtain spatial information measurement results that are more aligned with visual cognition. Firstly, this method uses the area object as the basic computational unit and determines the consistency of spatial arrangement directions by calculating the spatial directional similarity between the area object and its first-order neighboring objects in the Voronoi diagram.