Towards measuring shape similarity of polygons based on multiscale features and grid context descriptors

In spatial analysis applications, measuring the shape similarity of polygons is crucial for polygonal object retrieval and shape clustering. As a complex cognition process, measuring shape similarity should involve finding the difference between polygons, as objects in observation, in terms of visual perception and the differences of the regions, boundaries, and structures formed by the polygons from a mathematical point of view. In existing approaches, the shape similarity of polygons is calculated by only comparing their mathematical characteristics while not taking human perception into consideration. Aiming to solve this problem, we use the features of context and texture of polygons, since they are basic visual perception elements, to fit the cognition purpose. In this paper, we propose a contour diffusion method for the similarity measurement of polygons. By converting a polygon into a grid representation, the contour feature is represented as a multiscale statistic feature, and the region feature is transformed into condensed grid of context features. Instead of treating shape similarity as a distance between two representations of polygons, the proposed method observes similarity as a correlation between textures extracted by shape features. The experiments show that the accuracy of the proposed method is superior to that of the turning function and Fourier descriptor.