In this paper, we identify some of the limitations of current-day shape matching techniques. We provide examples of how contour-based shape matching techniques cannot provide a good match for certain visually similar shapes. To overcome this limitation, we propose a perceptually motivated variant of the well-known shape context descriptor. We identify that the interior properties of the shape play an important role in object recognition and develop a descriptor that captures these interior properties. We show that our method can easily be augmented with any other shape matching algorithm. We also show from our experiments that the use of our descriptor can significantly improve the retrieval rates.
The Medial Axis Transform (MAT) and its variant, shock graphs, have been used by certain authors for matching shapes @cite_31 @cite_40 . The medial axis, or skeleton, is the locus of the centers of all maximally inscribed circles of the object. While the MAT captures the interior properties of the shape to a large extent, by definition, the generation of a skeleton depends on the boundary of the object. Therefore, the objects shown in Figure will all have vastly different skeletons. @cite_36 , proposed to model shapes using skelet al contexts. Their contexts are calculated at the skeleton endings and the bins are populated by the non-uniformly sampled points from the boundary. Relying on the skeleton, and the boundary points, makes their method susceptible to indentations in the contour. We show, in Section , how our method does not fall prey to such boundary perturbations.
@cite_36 @cite_40 @cite_31
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The medial axis transform (MAT) of a shape, better known as its skeleton, is frequently used in shape analysis and related areas. In this paper a new approach for determining the skeleton of an object is presented. The boundary is segmented at points of maximal positive curvature and a distance map from each of the segments is calculated. The skeleton is then located by applying simple rules to the zero sets of distance map differences. A framework is proposed for numerical approximation of distance maps that is consistent with the continuous case and hence does not suffer from digitization bias due to metrication errors of the implementation on the grid. Subpixel accuracy in distance map calculation is obtained by using gray-level information along the boundary of the shape in the numerical scheme. The accuracy of the resulting efficient skeletonization algorithm is demonstrated by several examples. Medial descriptions, such as shock graphs, have gained significant momentum in the shape-based object recognition community due to their invariance to translation, rotation, scale and articulation and their ability to cope with moderate amounts of within-class deformation. While they attempt to decompose a shape into a set of parts, this decomposition can suffer from ligature-induced instability. In particular, the addition of even a small part can have a dramatic impact on the representation in the vicinity of its attachment. We present an algorithm for identifying and representing the ligature structure, and restoring the non-ligature structures that remain. This leads to a bone graph, a new medial shape abstraction that captures a more intuitive notion of an objectpsilas parts than a skeleton or a shock graph, and offers improved stability and within-class deformation invariance. We demonstrate these advantages by comparing the use of bone graphs to shock graphs in a set of view-based object recognition and pose estimation trials. The paper describes an algorithm for generating an approximation of the medial axis transform (MAT) for planar objects with free form boundaries. The algorithm generates the MAT by a tracing technique that marches along the object boundary rather than the bisectors of the boundary entities. The level of approximation is controlled by the choice of the step size in the tracing procedure. Criteria based on distance and local curvature of boundary entities are used to identify the junction or branch points and the search for these branch points is more efficient than while tracing the bisectors. The algorithm works for multiply connected objects as well. Results of implementation are provided. Skeletonization algorithms typically decompose an object's silhouette into a set of symmetric parts, offering a powerful representation for shape categorization. However, having access to an object's silhouette assumes correct figure-ground segmentation, leading to a disconnect with the mainstream categorization community, which attempts to recognize objects from cluttered images. In this paper, we present a novel approach to recovering and grouping the symmetric parts of an object from a cluttered scene. We begin by using a multiresolution superpixel segmentation to generate medial point hypotheses, and use a learned affinity function to perceptually group nearby medial points likely to belong to the same medial branch. In the next stage, we learn higher granularity affinity functions to group the resulting medial branches likely to belong to the same object. The resulting framework yields a skelet al approximation that is free of many of the instabilities that occur with traditional skeletons. More importantly, it does not require a closed contour, enabling the application of skeleton-based categorization systems to more realistic imagery.