A Moment-Based Shape Similarity Measurement for Areal Entities in Geographical Vector Data

Kaichun Zhou,Liang Fan,Zhongliang Fu,Zhiqiang Yu

doi:10.3390/ijgi7060208

Abstract

Shape similarity measurement model is often used to solve shape-matching problems in geospatial data matching. It is widely used in geospatial data integration, conflation, updating and quality assessment. Many shape similarity measurements apply only to simple polygons. However, areal entities can be represented either by simple polygons, holed polygons or multipolygons in geospatial data. This paper proposes a new shape similarity measurement model that can be used for all kinds of polygons. In this method, convex hulls of polygons are used to extract boundary features of entities and local moment invariants are calculated to extract overall shape features of entities. Combined with convex hull and local moment invariants, polygons can be represented by convex hull moment invariant curves. Then, a shape descriptor is obtained by applying fast Fourier transform to convex hull moment invariant curves, and shape similarity between areal entities is measured by the shape descriptor. Through similarity measurement experiments of different lakes in multiple representations and matching experiments between two urban area datasets, results showed that the method could distinguish areal entities even if they are represented by different kinds of polygons.

Highlights

With the influences of data acquisition errors, map generalization, different application purposes and people’s explanatory differences, there are inconsistencies in the expression of real-world objects in different geospatial data [1,2,3]
It can be found that the shape of every convex hull moment invariant curve is similar to the centroid distance curve
In order to eliminate the dependence of starting point on convex hull and get shape descriptors, we introduce the method of fast Fourier transform to extract features on convex hull moment invariant curves

Summary

Introduction

With the influences of data acquisition errors, map generalization, different application purposes and people’s explanatory differences, there are inconsistencies in the expression of real-world objects in different geospatial data [1,2,3]. In the field of traditional image processing, the moment description method has a wide range of applications in image matching, retrieval and identification [22] This method can extract invariant shape features under the transformation of translation, rotation, and scaling, and can describe global shape features of overall areas which means it can describe all kinds of polygons [23]. This region-based shape description method is more suitable for areal entities than methods based on shape contour description. The moment description method in the field of image processing is introduced to extract invariant moments of areal entities in vector data.

Areal Entities in Geographical Vector Data

Moments for Vector Polygons

Shape Description Model for Areal Entities

Local Moment Invariants of Complex Polygons

Convex Hull Moment Invariant Curves

Feature Similarity Calculation

F2 F3 F4 F5 F6 F7

Method Described in Correct

Conclusions