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111
Shock Graphs and Shape Matching
, 1998
"... We have been developing a theory for the generic representation of 2D 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 ..."
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Cited by 203 (32 self)
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We have been developing a theory for the generic representation of 2D 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...
Shape quantization and recognition with randomized trees
 Neural Computation
, 1997
"... 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 information about shape invariance and regularity. Each query corresponds to a spatial arrangement ofseveral local topographic code ..."
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Cited by 179 (17 self)
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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 information 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) semiinvariance, 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
Relative 3D Reconstruction Using Multiple Uncalibrated Images
, 1995
"... 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 geo ..."
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Cited by 90 (14 self)
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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...
Relative Affine Structure: Canonical Model for 3D from 2D Geometry and Applications
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1996
"... We propose an affine framework for perspective views, captured by a single extremely simple equation based on a viewercentered 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, projec ..."
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Cited by 59 (9 self)
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We propose an affine framework for perspective views, captured by a single extremely simple equation based on a viewercentered 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.
Visual interpretation of known objects in constrained scenes
 Phil. Trans. R. Soc. Lond. B
, 1992
"... 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 ..."
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Cited by 58 (12 self)
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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. Modelbased 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 Highlevel vision i...
Extracting Projective Structure from Single Perspective Views of 3D Point Sets
 Views of 3D Point Sets Proc. of 4:th ICCV
, 1993
"... 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 genera ..."
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Cited by 57 (11 self)
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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...
ModelBased Object Recognition  A Survey of Recent Research
, 1994
"... We survey the main ideas behind recent research in modelbased 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 ..."
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Cited by 55 (1 self)
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We survey the main ideas behind recent research in modelbased 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 ..........................................
Generic model abstraction from examples
 IEEE Trans. on Pattern Analysis and Machine Intelligence
"... The recognition community has long avoided bridging the representational gap between traditional, lowlevel 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 ob ..."
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Cited by 53 (8 self)
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The recognition community has long avoided bridging the representational gap between traditional, lowlevel 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 3D CAD model templates or 2D 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 2D viewbased class model from a set of images, each containing an exemplar object belonging to that class. We introduce a novel graphtheoretical formulation of the problem, and demonstrate the approach on real imagery.
Planar Object Recognition using Projective Shape Representation
 International Journal of Computer Vision
, 1995
"... 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 pos ..."
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Cited by 53 (9 self)
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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...
Representation and Recognition of FreeForm Surfaces
, 1992
"... 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 ..."
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Cited by 52 (6 self)
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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 poseinvariant 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 threedimensional 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.