We have been developing a theory for the generic representation of 2-D shape, where structural descriptions are derived from the shocks (singularities) of a curve evolution process, acting on bounding contours. We now apply the theory to the problem of shape matching. The shocks are organized into a directed, acyclic shock graph, and complexity is managed by attending to the most significant (central) shape components first. The space of all such graphs is highly structured and can be characterized by the rules of a shock graph grammar. The grammar permits a reduction of a shock graph to a unique rooted shock tree. We introduce a novel tree matching algorithm which finds the best set of corresponding nodes between two shock trees in polynomial time. Using a diverse database of shapes, we demonstrate our system's performance under articulation, occlusion, and changes in viewpoint. Keywords: shape representation; shape matching; shock graph; shock graph grammar; subgraph isomorphism. 1 I...

We explore a new approach to shape recognition based on a virtually in nite family of binary features (\queries") of the image data, designed to accommodate prior in-formation about shape invariance and regularity. Each query corresponds to a spatial arrangement ofseveral local topographic codes (\tags") which are in themselves too primitive and common to be informative about shape. All the discriminating power derives from relative angles and distances among the tags. The important attributes of the queries are (i) a natural partial ordering corresponding to increasing structure and complexity � (ii) semi-invariance, meaning that most shapes of a given class will answer the same way totwo queries which are successive in the ordering � and (iii) stability, since the queries are not based on distinguished points and substructures. No classi er based on the full feature set can be evaluated and it is impossible to determine a priori which arrangements are informative. Our approach istoselect informative features and build tree classi ers at the same time by inductive learning. In e ect, each tree provides an approximation to the full posterior where the features

In this paper, we show how relative 3D reconstruction from point correspondences of multiple uncalibrated images can be achieved through reference points. The original contributions with respect to related works in the field are mainly a direct global method for relative 3D reconstruction, and a geometrical method to select a correct set of reference points among all image points. Experimental results from both simulated and real image sequences are presented, and robustness of the method and reconstruction precision of the results are discussed. Key words: relative reconstruction, projective geometry, uncalibration, geometric interpretation 1 Introduction 1.1 Relative positioning From a single image, no depth can be computed without a priori information. Even more, no invariant can be computed from a general set of points as shown by Burns, Weiss and Riseman (1990). This problem becomes feasible using multiple images. The process is composed of two major steps. First, image feature...

We propose an affine framework for perspective views, captured by a single extremely simple equation based on a viewer-centered invariant we call relative affine structure. Via a number of corollaries of our main results we show that our framework unifies previous work -- including Euclidean, projective and affine -- in a natural and simple way, and introduces new, extremely simple, algorithms for the tasks of reconstruction from multiple views, recognition by alignment, and certain image coding applications.

We survey the main ideas behind recent research in model-based object recognition. The survey covers representations for models and images and the methods used to match them. Perceptual organization, the use of invariants, indexing schemes, and match verification are also reviewed. We conclude that there is still much room for improvement in the scope, robustness, and efficiency of object recognition methods. We identify what we believe are the ways improvements will be achieved. ii Contents 1. Introduction .................................................................................................................................... 1 2. Representation ................................................................................................................................ 3 2.1 What makes a good shape representation? ............................................................................ 3 2.2 The choice of coordinate system ..........................................

A number of recent papers have argued that invariants do not exist for three dimensional point sets in general position [3, 4, 13]. This has often been misinterpreted to mean that invariants cannot be computed for any three dimensional structure. This paper proves by example that although the general statement is true, invariants do exist for structured three dimensional point sets. Projective invariants are derived for two classes of object: the first is for points that lie on the vertices of polyhedra, and the second for objects that are projectively equivalent to ones possessing a bilateral symmetry. The motivations for computing such invariants are twofold: firstly they can be used for recognition; secondly they can be used to compute projective structure. Examples of invariants computed from real images are given. 1 Introduction Exploiting structure modulo a projectivity has recently been shown to simplify a number of vision tasks such as model based recognition [1, 7, 10, 11, 1...

Recent work on the visual interpretation of traffic scenes is described which relies heavily on a priori knowledge of the scene and position of the camera, and expectations about the shapes of vehicles and their likely movements in the scene. Knowledge is represented in the computer as explicit 3D geometrical models, dynamic filters, and descriptions of behaviour. Model-based vision, based on reasoning with analog models, avoids many of the classical problems in visual perception: recognition is robust against changes in the image of shape, size, colour and illumination. The 3D understanding of the scene which results also deals naturally with occlusion, and allows the behaviour of vehicles to be interpreted. The experiments with machine vision raise questions about the part played by perceptual context for object recognition in natural vision, and the neural mechanisms which might serve such a role. Vision in constrained scenes - 2 - GDS 8/3/92 1. INTRODUCTION High-level vision i...

We introduce a new surface representation for recognizing curved objects. Our approach begins by representing an object by a discrete mesh of points built from range data or from a geometric model of the object. The mesh is computed from the data by deforming a standard shaped mesh, for example, an ellipsoid, until it fits the surface of the object. We define local regularity constraints that the mesh must satisfy. We then define a canonical mapping between the mesh describing the object and a standard spherical mesh. A surface curvature index that is pose-invariant is stored at every node of the mesh. We use this object representation for recognition by comparing the spherical model of a reference object with the model extracted from a new observed scene. We show how the similarity between reference model and observed data can be evaluated and we show how the pose of the reference object in the observed scene can be easily computed using this representation. We present results on real range images which show that this approach to modelling and recognizing three-dimensional objects has three main advantages: First, it is applicable to complex curved surfaces that cannot be handled by conventional techniques. Second, it reduces the recognition problem to the computation of similarity between spherical distributions; in particular, the recognition algorithm does not require any combinatorial search. Finally, even though it is based on a spherical mapping, the approach can handle occlusions and partial views.

The recognition community has long avoided bridging the representational gap between traditional, low-level image features and generic models. Instead, the gap has been artificially eliminated by either bringing the image closer to the models, using simple scenes containing idealized, textureless objects, or by bringing the models closer to the images, using 3-D CAD model templates or 2-D appearance model templates. In this paper, we attempt to bridge the representational gap for the domain of model acquisition. Specifically, we address the problem of automatically acquiring a generic 2-D view-based class model from a set of images, each containing an exemplar object belonging to that class. We introduce a novel graph-theoretical formulation of the problem, and demonstrate the approach on real imagery.

We describe a model based recognition system, called LEWIS, for the identification of planar objects based on a projectively invariant representation of shape. The advantages of this shape description include simple model acquisition (direct from images), no need for camera calibration or object pose computation, and the use of index functions. We describe the feature construction and recognition algorithms in detail and provide an analysis of the combinatorial advantages of using index functions. Index functions are used to select models from a model base and are constructed from projective invariants based on algebraic curves and a canonical projective coordinate frame. Examples are given of object recognition from images of real scenes, with extensive object libraries. Successful recognition is demonstrated despite partial occlusion by unmodelled objects, and realistic lighting conditions. 1 Introduction 1.1 Overview In the context of this paper, recognition is defined as the prob...