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 relates 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.

Research on Similarity Measurements of 3D Models Based on Skeleton Trees

“…Yang et al [57] proposed a novel 2D object matching method based on a hierarchical skeleton capturing the object's topology and geometry, where determining similarity considers both single skeletons and skeleton pairs. Yasseen et al [58] developed a 2D shape matching method, which can perform a part-to-part matching analysis between two objects' visual protruding parts to measure the distance between them. Yang et al [59] mentioned a new shape matching method based on the interesting point detector and high-order graph matching.…”

View selection for sketch-based 3D model retrieval using visual part shape description

“…This paper is an extended study of what was originally proposed in [38] where we elaborate more on the shape descriptor introduced in [37] and augmented in [38], and highlight some setbacks in the query dataset. Furthermore, we present a thorough analysis of the 2D projected silhouettes of 3D objects, and study the influence of the number of representative views and the impact of the view selection criteria on the retrieval performances.…”

“…It is notable that there is a small range of 2D shape descriptors tested in sketch-based 3D object retrieval compared to the much larger number of available choices. The 2D shape descriptor that we employ in this paper uses a skeleton to represent shapes by visual parts and their spacial relationships [37].…”

“…For the sake of completeness, we give an overview of the CAT-based shape description method. However, a detailed description of our 2D shape matching method CAT-DTW and its performance evaluation on Kimia-99 and Kimia-216 2D shape datasets [32] can be found in [37].…”

“…In our previous work [38], we show how shape matching by part correspondence allows an extent of variability between the natures of matched objects. We employ a part-based 2D shape descriptor introduced in [37] that uses a chordal axis transform method [28] (CAT) to define and dynamic time warping (DTW) to match. On an abstract level, the CAT-DTW descriptor starts by a skeleton based segmentation of the silhouette of the 2D shapes.…”