Signature of a shape based on its pixel coverage representation

Abstract

© Springer International Publishing Switzerland 2016. Distance from the boundary of a shape to its centroid, a.k.a. signature of a shape, is a frequently used shape descriptor. Commonly, the observed shape results from a crisp (binary) segmentation of an image. The loss of information associated with binarization leads to a significant decrease in accuracy and precision of the signature, as well as its reduced invariance w.r.t. translation and rotation. Coverage information enables better estimation of edge position within a pixel. In this paper, we propose an iterative method for computing the signature of a shape utilizing its pixel coverage representation. The proposed method iteratively improves the accuracy of the computed signature, starting from a good initial estimate. A statistical study indicates considerable improvements in both accuracy and precision, compared to a crisp approach and a previously proposed approach based on averaging signatures over α-cuts of a fuzzy representation. We observe improved performance of the proposed descriptor in the presence of noise and reduced variation under translation and rotation.