Underlying recognition is an organization of objects and their parts into classes and hierarchies. A representation of parts for recognition requires that they be invariant to rigid transformations, robust in the presence of occlusions, stable with changes in viewing geometry, and be arranged in a hierarchy. These constraints are captured in a general framework using notions of a part-line and a partitioning scheme. A proposed general principle of "form from function" motivates a particular partitioning scheme involving two types of parts, neck-based and limb-based, whose psychophysical relevance was demonstrated in [39]. Neckbased parts arise from narrowings in shape, or the local minima in distance between two points on the boundary, while limb-based parts arise from a pair of negative curvature minima which have "co-circular" tangents. In this paper, we present computational support for the limb-based and neck-based parts by showing that they are invariant, robust, stable and yield...

We undertake to develop a general theory of two-dimensional shape by elucidating several principles which any such theory should meet. The principles are organized around two basic intuitions: first, if a boundary were changed only slightly, then, in general, its shape would change only slightly. This leads us to propose an operational theory of shape based on incremental contour deformations. The second intuition is that not all contours are shapes, but rather only those that can enclose "physical" material. A theory of contour deformation is derived from these principles, based on abstract conservation principles and Hamilton-Jacobi theory. These principles are based on the work of Sethian [82, 86], the Osher-Sethian level set formulation [65], the classical shock theory of Lax [53, 54], as well as curve evolution theory for a curve evolving as a function of the curvature and the relation to geometric smoothing of Gage-Hamilton-Grayson [32, 37]. The result is a characterization of th...

Blum's medial axes have great strengths, in principle, in intuitively describing object shape in terms of a quasi-hierarchy of figures. But it is well known that, derived from a boundary, they are damagingly sensitive to detail in that boundary. The development of notions of spatial scale has led to some definitions of multiscale medial axes different from the Blum medial axis that considerably overcame the weakness. Three major multiscale medial axes have been proposed: iteratively pruned trees of Voronoi edges (Ogniewicz, 1993; Szekely, 1996; Naf, 1996), shock loci of reaction-diffusion equations (Kimia et al., 1995; Siddiqi and Kimia, 1996), and height ridges of medialness (cores) (Fritsch et al., 1994; Morse et al., 1993; Pizer et al., 1998). These are different from the Blum medial axis, and each has different mathematical properties of generic branching and ending properties, singular transitions, and geometry of implied boundary, and they have different strengths and weaknesses for computing object descriptions from images or from object boundaries. These mathematical properties and computational abilities are laid out and compared and contrasted in this paper.

Accessing large image databases requires effective indexing in order to restrict the number of database items that have to be processed. Indexing based on shapes is particularly challenging owing to the difficulty of deriving a similarity measure that supports clustering of shapes conforming with human perceptual similarity. Most previous techniques are based on the extraction of salient shape features and their organization into multi-dimensional point access structures. However, these features are extracted by analyzing shapes at a single resolution scale, and are not able to provide a robust representation. In this paper, we present a technique which exploits multi-scale analysis of shapes, to derive a hierarchical shape representation in which shape details are progressively filtered out while shape characterizing elements are preserved. A graph structure is introduced to represent shape parts at different scales and a procedure is defined to merge graphs of different shapes. Given a query shape, the graph can be traversed to select, through a coarse to fine matching, those database shapes which share similar structural parts with the query. # 1999 Elsevier Science B.V. All rights reserved.

Part based representations allow for recognition that is robust in the presence of occlusion, movement, growth, and deletion of portions of an object. We propose a general "form from function" principle arising from the interactions of objects in their environment, which, together with properties of visual projection, gives rise to two kinds of parts: limb-based parts arise from a pair of negative curvature minima with evidence for "good continuation" of boundaries on one side; neck-based parts arise from narrowings in shape. We then test this hypothesis by requiring subjects to partition a variety of biological and nonsense 2D shapes into perceived components. We examine: 1) whether a subject determines components consistently across different trials of the same partitioning task, 2) whether there is evidence for consistency between subjects for the same partitioning task, and 3) how the perceived parts compare with the parts proposed by the "form from function" principle. The results...

We address the problem of obtaining natural (intuitive) descriptions of 3D shapes. We present one of the first attempts to address the description of 3D compound objects, where the parts are connected smoothly. The input we consider is either complete 3D data or range data from a single view. We suggest a volumetric graph representation of the object, where the nodes represent individual parts and the edges represent connectivity information. We suggest the use of properties of the parabolic curves for performing the part decomposition. We currently consider parts with tubular structure with a straight or curved axis. The graph description presents a structural description of the shape in terms of parts and their arrangement. We are also interested in the internal description of the parts. We study two well defined classes of shapes, namely Straight Homogeneous Generalized Cylinders, and Planar Right Constant GCs. We suggest the use of properties of the parabolic curves for recovering natural descriptions of these classes in terms of their cross sections and axes. 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.

The recognition of objects from their projected two-dimensional shapes is a challenging problem owing to the spectrum of possible variations reflected in the image domain, e.g., those caused by movement of parts, changes in viewing geometry, occlusion, etc. This motivates a need for quantitative as well as qualitative descriptions of shape in terms of structural relations between components; the latter remain largely invariant under the above changes. In this paper we confront the theoretical and practical difficulties of computing such a representation, based on the detection of shocks or singularities that arise as a shape is deformed, as organized in two stages. First, we develop subpixel local detectors for the detection of shocks and a classification of them into four types. Second, we show that shock patterns are not arbitrary, but obey the rules of a grammar which limits the possible shock combinations. In addition, shock patterns satisfy specific topological and geometric constraints. We develop this shock grammar and exploit the topological and geometric constraints to enforce global consistency: shock hypotheses that violate the grammar or are topologically or geometrically invalid are pruned, and survivors are organized into higher level structures. The result is a computational method for the detection, classification, and grouping of shocks. This leads to a description of shape as a hierarchical graph of shock groups. The graph is computed in the reaction-diffusion space, where diffusion plays a role of regularization to determine the significance of each shock-group. The representation is stable with rotations, scale changes, occlusion, movement of parts, noise and other variations, even at very low resolutions. We illustrate the suitability of this repres...

E#ective image retrieval by content from database requires that visual image properties are used instead of textual labels to recover pictorial data. Retrieval by image similarity given a template image is particularly challenging. The di#culty is to derive a similarity measure that combines shape, grey level patterns and texture in a way that closely conforms to human perception. In this paper a system is presented which supports retrieval by image similarity based on elastic template matching. The template can be both a 1D template modeling the contour of an object, and a 2D template modeling a part of an image with a significant grey level pattern. The retrieval process is obtained as a continuous interaction by which the original query of the user can be refined or changed on the basis of the results provided by the system. # 1999 Pattern Recognition Society. Published by Elsevier Science Ltd. All rights reserved.

In this paper, we present a technique for grouping line segments sinto convex sets, where the line segments are obtained by linking edges obtained from the Canny edge detector. The novelty of the approach istwofold: �rst we de�ne an e�cient approach for testing the global convexity criterion, and second, we develop an optimal search based on dynamic programming or grouping the line segments into convex sets. Furthermore, we use the convexity results as the initial conditions for a deformable contour for object tracking. We show results on real images, and present a speci�c domain where this type of grouping can be directly applied. 1