Bidimensional regression and order relations: evaluating sketch maps with various spatial knowledge and distortions

Sketch maps are the external representations of people's cognition of the geographical environment. Previous research on extracting invariant information from sketch maps has proposed various spatial relation methods, encompassing both qualitative and quantitative relations. However, sketch maps can encode varieties of spatial knowledge and distortions. This paper summarizes the frequently occurring distortions in urban sketch maps, such as shape, scale, and position distortions. Building on our previous work, we analyzed the differences caused by various distortions on bidimensional regression and order relations (Point Algebra and coarse Interval Algebra), and summarized the characteristics of these methods. We evaluated the methods on a total of 30 sketch maps derived from landmark knowledge, route knowledge, and survey knowledge, and provided recommendations on the use of methods for different types of sketch maps. Furthermore, the experiment demonstrated that combining bidimensional regression and order relations allows for a better assessment of the sketch map accuracy. We believe that an in-depth analysis of various types of sketch maps and distortions can provide new insights for sketch map alignment.