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72
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 213 (34 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...
Qualitative Spatial Representation and Reasoning: An Overview
 FUNDAMENTA INFORMATICAE
, 2001
"... The paper is a overview of the major qualitative spatial representation and reasoning techniques. We survey the main aspects of the representation of qualitative knowledge including ontological aspects, topology, distance, orientation and shape. We also consider qualitative spatial reasoning inclu ..."
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Cited by 183 (17 self)
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The paper is a overview of the major qualitative spatial representation and reasoning techniques. We survey the main aspects of the representation of qualitative knowledge including ontological aspects, topology, distance, orientation and shape. We also consider qualitative spatial reasoning including reasoning about spatial change. Finally there is a discussion of theoretical results and a glimpse of future work. The paper is a revised and condensed version of [33, 34].
A Stochastic Grammar of Images
 Foundations and Trends in Computer Graphics and Vision
, 2006
"... This exploratory paper quests for a stochastic and context sensitive grammar of images. The grammar should achieve the following four objectives and thus serves as a unified framework of representation, learning, and recognition for a large number of object categories. (i) The grammar represents bot ..."
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Cited by 84 (20 self)
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This exploratory paper quests for a stochastic and context sensitive grammar of images. The grammar should achieve the following four objectives and thus serves as a unified framework of representation, learning, and recognition for a large number of object categories. (i) The grammar represents both the hierarchical decompositions from scenes, to objects, parts, primitives and pixels by terminal and nonterminal nodes and the contexts for spatial and functional relations by horizontal links between the nodes. It formulates each object category as the set of all possible valid configurations produced by the grammar. (ii) The grammar is embodied in a simple And–Or graph representation where each Ornode points to alternative subconfigurations and an Andnode is decomposed into a number of components. This representation supports recursive topdown/bottomup procedures for image parsing under the Bayesian framework and make it convenient to scale
Shapes, Shocks, and Deformations I: The Components of TwoDimensional Shape and the ReactionDiffusion Space
 International Journal of Computer Vision
, 1994
"... We undertake to develop a general theory of twodimensional 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. Th ..."
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Cited by 63 (5 self)
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We undertake to develop a general theory of twodimensional 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 HamiltonJacobi theory. These principles are based on the work of Sethian [82, 86], the OsherSethian 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 GageHamiltonGrayson [32, 37]. The result is a characterization of th...
Feature Centrality and Conceptual Coherence
 Cognitive Science
, 1998
"... This paper has two objectives. First, we will argue that the mutability of conceptual fea tures can be represented as a single, multiplevalued dimension. We will show that the fea tures of a concept can be reliably ordered with respect to the degree to which people are willing to transform the fe ..."
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Cited by 63 (6 self)
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This paper has two objectives. First, we will argue that the mutability of conceptual fea tures can be represented as a single, multiplevalued dimension. We will show that the fea tures of a concept can be reliably ordered with respect to the degree to which people are willing to transform the feature while retaining the integrity of a representation; i.e., that a number of conceptual tasks, all of which require people to transform conceptual features, produce similar orderings. Following Medin and Shoben (1988), these tasks have in common that they ask people to consider an object that is missing a feature but is otherwise intact (e.g., a real chair without a seat)
Recovering shape by purposive viewpoint adjustment
 International Journal of Computer Vision
, 1994
"... We present an approach for recovering surface shape from the occluding contour using an active (i.e., moving) observer. It is based onarelation between the geometries of a surface inascene and its occluding contour: If the viewing direction of the observer is along a principal direction for a surfac ..."
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Cited by 55 (8 self)
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We present an approach for recovering surface shape from the occluding contour using an active (i.e., moving) observer. It is based onarelation between the geometries of a surface inascene and its occluding contour: If the viewing direction of the observer is along a principal direction for a surface point whose projection is on the contour, surface shape (i.e., curvature) at the surfacepoint can be recovered from the contour. Unlike previous approaches for recovering shape from the occluding contour, we use an observer that purposefully changes viewpoint in order to achieve a wellde ned geometric relationship with respect to a 3D shape prior to its recognition. We show that there is a simple and e cient viewing strategy that allows the observer to align the viewing direction with one of the two principal directions for a point on the surface. Experimental results demonstrate that our method can be easily implemented and can provide reliable shape information. 1
Modelling Topological and Metrical Properties in Physical Processes.
 eds), Proceedings 1st International Conference on the Principles of Knowledge Representation and Reasoning
, 1989
"... Developing suitable representations for formalising nontrivial domain knowledge has always been central to AI. Within Naive Physics ie. the task of encoding experiential knowledge of the world, few formal theories have appeared that exhibit formal elegance, conciseness and generality to cover ..."
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Cited by 51 (6 self)
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Developing suitable representations for formalising nontrivial domain knowledge has always been central to AI. Within Naive Physics ie. the task of encoding experiential knowledge of the world, few formal theories have appeared that exhibit formal elegance, conciseness and generality to cover a wide variety of modelling problems. We outline a first order formalism being developed that meets these criteria. The formalism is particularly attractive in that it provides the user with the means to model either spatial and/or temporal information as required. The power of the formalism is illustrated by modelling the process of phagocytosis of the amoeba, together with an outline of how many properties of physical entities and relations between them can be modelled within a unitary framework. 1.0 Introduction The importance of representation within a formal framework has always been a central topic for discussion within AI. This has been particularly noticeable since Hayes'...
SymmetryCurvature Duality
 Computer Vision, Graphics, and Image processing
, 1987
"... Several studies have shown the importance of two very different descriptors for shape: symmetry structure and curvature extrema. The main theorem proved by this paper, i.e. the SymmetryCurvature Duality Theorem, states that there is an important relationship between symmetry and curvature extrema: ..."
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Cited by 33 (2 self)
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Several studies have shown the importance of two very different descriptors for shape: symmetry structure and curvature extrema. The main theorem proved by this paper, i.e. the SymmetryCurvature Duality Theorem, states that there is an important relationship between symmetry and curvature extrema: If we say that curvature extrema are of two opposite types, either maxima or minima, then the theorem states: Any segment of a smooth planar curve, bounded by two consecutive curvature extrema of the same type, has a unique symmetry axis, and the axis terminates at the curvature extremum of the opposite type. The theorem is initially proved using Brady’s SLS as the symmetry analysis. However, the theorem is then generalized for any differential symmetry analysis. In order to prove the theorem, a number of results are established concerning the symmetry structure of Hoffman’s and Richards ’ codons. All results are obtained first by observing that any codon is a string of two, three, or four spirals, and then by reducing the theory of codons to that of spirals. We show that the SLS of a codon is either (1) an SAT, which is a
Perspective Projection: The Wrong Imaging Model
, 1995
"... : Perspective projection is generally accepted as the ideal model of image formation. Many recent algorithms, and many recent judgements about the relative merits of different algorithms, depend on this assumption. However, perspective projection represents only the front half of the viewing sphere ..."
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Cited by 33 (2 self)
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: Perspective projection is generally accepted as the ideal model of image formation. Many recent algorithms, and many recent judgements about the relative merits of different algorithms, depend on this assumption. However, perspective projection represents only the front half of the viewing sphere and it distorts the shape and intensity of objects unless they lie near the optical axis. It is only one of several projections used in lens design and it does not accurately model the behavior of many real lenses. It works well only for narrowangle images. This paper surveys the properties of several alternative models of image formation. A model based on stereographic projection of the viewing sphere is shown to be a better generalpurpose imaging model than perspective projection. The new model can represent wider fields of view and more closely approximates real wideangle lenses. It preserves a suitable range of shape properties, including local symmetries. It approximates narrowangl...
Looking for trouble: using causal semantics to direct focus of attention
 In Proc. 4th Int’l Conf. on Computer Vision
, 1993
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