Towards Measuring Shape Similarity of Polygons Based on Multiscale Features and Grid Context Descriptors

Hongchao Fan,Zhiyao Zhao,Wenwen Li

doi:10.3390/ijgi10050279

Abstract

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.

Highlights

As a metric for distinguishing polygonal geometric features, shape similarity measurement is widely used to match, retrieve, and classify polygons [1]
Calculating a reliable shape similarity measurement result which is consistent with human judgment is a basic stage for completely and accurately unravelling valuable spatial information
A contour diffusion method based on the multiscale feature is proposed to combine external and internal contour features

Summary

Introduction

As a metric for distinguishing polygonal geometric features, shape similarity measurement is widely used to match, retrieve, and classify polygons [1]. Scholars have made efforts to retrieve similar polygons to explore building distribution patterns [2] and match corresponding entities [3] for enriching geo-data and mining spatial information hidden in vector datasets. Calculating a reliable shape similarity measurement result which is consistent with human judgment is a basic stage for completely and accurately unravelling valuable spatial information. For the map generalization task, the completeness and accuracy of its results relies on whether the similar shape judgement is consistent with visual perception [4]. We can qualitatively determine the difference of polygons as objects in observation regarding visual perception. Polygons are mathematically represented by a series of coefficients or indicators that are invariant to translation, rotation, and scale to derive a similarity measurement for comparing the polygons

Methods

Results

Discussion

Conclusion