Determining the Similarity Between Two Arbitrary 2-D Shapes and Its Application to Biological Objects

Petra Perner

doi:10.15344/2456-4451/2018/139

Abstract

Generalized shape models of objects are necessary to match and identify an object in an image. To acquire these kind of models special methods are necessary that allow to learn the similarity pair-wise similarity between shapes. They mainly concern is the establishment of point correspondences between two shapes and the detection of outlier. Known algorithm assume that the aligned shapes are quite similar in a way. But special problems arise if we have to align shapes that are very different, for example aligning concave to convex shapes. In such cases it is indispensable to take into account the order of the pointsets and to enforce legal sets of correspondences; otherwise the calculated distances are incorrect. We present our novel shape alignment algorithm which can also handle such cases. The algorithm establishes symmetric and legal one-to-one point correspondences between arbitrary shapes, represented as ordered sets of 2D-points and returns a distance measure which runs between 0 and 1.

Highlights

The analysis of shapes and shape variation is of great importance in a wide variety of disciplines
In 1917 D’Arcy Thompson [1] studied the field of geometrical shape analysis from a biological point of view. It is especially interesting for biologists since shape is one of the most concise features of an object class and may change over time due to growth or evolution
The establishment of point correspondences is only held in a nearest neighbor framework so they do not guarantee to produce legal sets of correspondences

Summary

Introduction

The analysis of shapes and shape variation is of great importance in a wide variety of disciplines. In 1917 D’Arcy Thompson [1] studied the field of geometrical shape analysis from a biological point of view. In digital image processing the statistical analysis of shape is a fundamental task in object recognition and classification It concern applications in a wide variety of fields, e.g. Special problems arise if we have to align shapes that are very different, for example aligning concave to convex shapes In these cases it is indispensable to take into account the order of the point-sets and to enforce legal sets of correspondences, otherwise the calculated distances are incorrect. The algorithm establishes symmetric and legal one-toone point correspondences between arbitrary shapes, represented as ordered sets of 2D-points and returns a distance measure which runs between 0 and 1

Related Work

Background

A L controls the maximal error of the approximation since

Evaluation of our alignment algorithm

Conclusions