Abstract—This paper presents a novel framework for the recognition of objects based on their silhouettes. The main idea is to measure the distance between two shapes as the minimum extent of deformation necessary for one shape to match the other. Since the space of deformations is very high-dimensional, three steps are taken to make the search practical: 1) define an equivalence class for shapes based on shock-graph topology, 2) define an equivalence class for deformation paths based on shock-graph transitions, and 3) avoid complexity-increasing deformation paths by moving toward shock-graph degeneracy. Despite these steps, which tremendously reduce the search requirement, there still remain numerous deformation paths to consider. To that end, we employ an edit-distance algorithm for shock graphs that finds the optimal deformation path in polynomial time. The proposed approach gives intuitive correspondences for a variety of shapes and is robust in the presence of a wide range of visual transformations. The recognition rates on two distinct databases of 99 and 216 shapes each indicate highly successful within category matches (100 percent in top three matches), which render the framework potentially usable in a range of shape-based recognition applications. Index Terms—Shape deformation, shock graphs, graph matching, edit distance, shape matching, object recognition, dynamic programming. æ 1

For analyzing shapes of planar, closed curves, we propose di#erential geometric representations of curves using their direction functions and curvature functions. Shapes are represented as elements of infinite-dimensional spaces and their pairwise di#erences are quantified using the lengths of geodesics connecting them on these spaces. We use a Fourier basis to represent tangents to the shape spaces and then use a gradient-based shooting method to solve for the tangent that connects any two shapes via a geodesic.

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Abstract—We introduce a novel rich local descriptor of an image point, we call the (labeled) distance set, which is determined by the spatial arrangement of image features around that point. We describe a two-dimensional (2-D) visual object by the set of (labeled) distance sets associated with the feature points of that object. Based on a dissimilarity measure between (labeled) distance sets and a dissimilarity measure between sets of (labeled) distance sets, we address two problems that are often encountered in object recognition: object segmentation, for which we formulate a distance sets shape filter, and shape matching. The use of the shape filter is illustrated on printed and handwritten character recognition and detection of traffic signs in complex scenes. The shape comparison procedure is illustrated on handwritten character classification, COIL-20 database object recognition and MPEG-7 silhouette database retrieval. Index Terms—Character recognition, distance set, image database retrieval, MPEG-7, object recognition, segmentation, shape descriptor, shape filter, traffic sign recognition. I.

We present a novel approach that allows us to reliably compute many useful properties of a silhouette. Our approach assigns for every internal point of the silhouette a value reflecting the mean time required for a random walk beginning at the point to hit the boundaries. This function can be computed by solving Poisson’s equation, with the silhouette contours providing boundary conditions. We show how this function can be used to reliably extract various shape properties including part structure and rough skeleton, local orientation and aspect ratio of different parts, and convex and concave sections of the boundaries. In addition to this we discuss properties of the solution and show how to efficiently compute this solution using multigrid algorithms. We demonstrate the utility of the extracted properties by using them for shape classification and retrieval.

We introduce Hierarchical Procrustes Matching (HPM), a segment-based shape matching algorithm which avoids problems associated with purely global or local methods and performs well on benchmark shape retrieval tests. The simplicity of the shape representation leads to a powerful matching algorithm which incorporates intuitive ideas about the perceptual nature of shape while being computationally efficient. This includes the ability to match similar parts even when they occur at different scales or positions. While comparison of multiscale shape representations is typically based on specific features, HPM avoids the need to extract such features. The hierarchical structure of the algorithm captures the appealing notion that matching should proceed in a global to local direction. 1.

We develop a new framework for the quantitative analysis of shapes of planar curves. Shapes are modeled on elastic strings that can be bent, stretched or compressed at different rates along the curve. Shapes are treated as elements of a space obtained as the quotient of an infinite-dimensional Riemannian manifold of elastic curves by the action of a reparameterization group. The Riemannian metric encodes the elastic properties of the string and has the property that reparameterizations act by isometries. Geodesics in shape space are used to quantify shape dissimilarities, interpolate and extrapolate shapes, and align shapes according to their elastic properties. The shape spaces and metrics constructed offer a novel environment for the study of shape statistics and for the investigation and simulation of shape dynamics. 1.

Abstract. This paper describes a view-based method for recognizing 3D objects from 2D images. We employ an aspect-graph structure, where the aspects are not based on the singularities of visual mapping but are instead formed using a notion of similarity between views. Specifically, the viewing sphere is endowed with a metric of dis-similarity for each pair of views and the problem of aspect generation is viewed as a ”segmentation ” of the viewing sphere into homogeneous regions. The viewing sphere is sampled at regular (5 degree) intervals and an iterative procedure is used to combine views using the metric into aspects with a prototype representing each aspect, in a ”region-growing ” regime which stands in contrast to the usual ”edge detection ” styles to computing the aspect graph. The aspect growth is constrained such that two aspects of an object remain distinct under the given similarity metric. Once the database of 3D objects is organized as a set of aspects and prototypes for these aspects for each object, unknown views of database objects are compared with the prototypes and the results are ordered by similarity. We use two similarity metrics for shape, one based on curve matching and the other based on matching shock graphs, which for a database of 64 objects and unknown views of objects for the database give (90.3%, 74.2%, 59.7%) and (95.2%, 69.0%, 57.5%), respectively, for the top three matches; identification based on the top three matches is 98 % and 100%, respectively. The result of indexing unknown views of objects not in the database also produce intuitive matches. We also develop a hierarchical indexing scheme the goal of which is to prune unlikely objects at an early stage to improve the efficiency of indexing, resulting in savings of 35 % at the top level and of 55 % at the next level, cumulatively. 1.

We study shapes of planar arcs and closed contours modeled on elastic curves obtained by bending, stretching or compressing line segments non-uniformly along their extensions. Shapes are represented as elements of a quotient space of curves obtained by identifying those that differ by shape-preserving transformations. The elastic properties of the curves are encoded in Riemannian metrics on these spaces. Geodesics in shape spaces are used to quantify shape divergence and to develop morphing techniques. The shape spaces and metrics constructed are novel and offer an environment for the study of shape statistics. Elasticity leads to shape correspondences and deformations that are more natural and intuitive than those obtained in several existing models. Applications of shape geodesics to the definition and calculation of mean shapes and to the development of shape clustering techniques are also investigated.

Abstract. This paper gives an overview of shape dissimilarity measure properties, such as metric and robustness properties, and of retrieval performance measures. Fifteen shape similarity measures are shortly described and compared. Their retrieval results on the MPEG-7 Core Experiment CE-Shape-1 test set as reported in the literature and obtained by a reimplementation are compared and discussed. 1