Shape matching by part alignment using extended chordal axis transform

Abstract

One of the main challenges in shape matching is overcoming intra-class variation where objects that are conceptually similar have significant geometric dissimilarity. The key to a solution around this problem is incorporating the structure of the object in the shape descriptor which can be described by a connectivity graph customarily extracted from its skeleton. In a slightly different perspective, the structure may also be viewed as the arrangement of protruding parts along its boundary. This arrangement does not only convey the protruding part׳s ordering along the anti clockwise direction, but also these parts on different levels of detail. In this paper, we propose a shape matching method that estimates the distance between two objects by conducting a part-to-part matching analysis between their visual protruding parts. We start by a skeleton-based segmentation of the shape inspired by the Chordal Axis Transform. Then, we extract the segments that represent the protruding parts in its silhouette on varied levels of detail. Each one of these parts is described by a feature vector. A shape is thus described by the feature vectors of its parts in addition to their angular and linear proximities to each other. Using dynamic programming, our algorithm finds a minimal cost correspondence between parts. Our experimental evaluations validate the proposition that part correspondence allows conceptual matching of precisely dissimilar shapes.