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87
Recognitionbycomponents: A theory of human image understanding
 Psychological Review
, 1987
"... The perceptual recognition of objects is conceptualized to be a process in which the image of the input is segmented at regions of deep concavity into an arrangement of simple geometric components, such as blocks, cylinders, wedges, and cones. The fundamental assumption of the proposed theory, recog ..."
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Cited by 723 (11 self)
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The perceptual recognition of objects is conceptualized to be a process in which the image of the input is segmented at regions of deep concavity into an arrangement of simple geometric components, such as blocks, cylinders, wedges, and cones. The fundamental assumption of the proposed theory, recognitionbycomponents (RBC), is that a modest set of generalizedcone components, called geons (N ^ 36), can be derived from contrasts of five readily detectable properties of edges in a twodimensional image: curvature, collinearity, symmetry, parallelism, and cotermmation. The detection of these properties is generally invariant over viewing position and image quality and consequently allows robust object perception when the image is projected from a novel viewpoint or is degraded. RBC thus provides a principled account of the heretofore undecided relation between the classic principles of perceptual organization and pattern recognition: The constraints toward regularization (Pragnanz) characterize not the complete object but the object's components. Representational power derives from an allowance of free combinations of the geons. A Principle of Componential Recovery can account for the major phenomena of object recognition: If an arrangement of two or three geons can be recovered from the input, objects can be quickly recognized even when they are occluded, novel, rotated in depth, or extensively degraded. The results from experiments on the perception of briefly presented pictures by human observers provide empirical support for the theory. Any single object can project an infinity of image configurations to the retina. The orientation of the object to the viewer can vary continuously, each giving rise to a different twodimensional projection. The object can be occluded by other objects or texture fields, as when viewed behind foliage. The object need not be presented as a fullcolored textured image but instead can be a simplified line drawing. Moreover, the object can even be missing some of its parts or be a novel exemplar of its
Actions as spacetime shapes
 In ICCV
, 2005
"... Human action in video sequences can be seen as silhouettes of a moving torso and protruding limbs undergoing articulated motion. We regard human actions as threedimensional shapes induced by the silhouettes in the spacetime volume. We adopt a recent approach [14] for analyzing 2D shapes and genera ..."
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Cited by 370 (4 self)
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Human action in video sequences can be seen as silhouettes of a moving torso and protruding limbs undergoing articulated motion. We regard human actions as threedimensional shapes induced by the silhouettes in the spacetime volume. We adopt a recent approach [14] for analyzing 2D shapes and generalize it to deal with volumetric spacetime action shapes. Our method utilizes properties of the solution to the Poisson equation to extract spacetime features such as local spacetime saliency, action dynamics, shape structure and orientation. We show that these features are useful for action recognition, detection and clustering. The method is fast, does not require video alignment and is applicable in (but not limited to) many scenarios where the background is known. Moreover, we demonstrate the robustness of our method to partial occlusions, nonrigid deformations, significant changes in scale and viewpoint, high irregularities in the performance of an action, and low quality video. Index Terms Action representation, action recognition, spacetime analysis, shape analysis, poisson equation
Estimating The Tensor Of Curvature Of A Surface From A Polyhedral Approximation
, 1995
"... Estimating principal curvatures and principal directions of a surface from a polyhedral approximation with a large number of small faces, such as those produced by isosurface construction algorithms, has become a basic step in many computer vision algorithms. Particularly in those targeted at medic ..."
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Cited by 184 (5 self)
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Estimating principal curvatures and principal directions of a surface from a polyhedral approximation with a large number of small faces, such as those produced by isosurface construction algorithms, has become a basic step in many computer vision algorithms. Particularly in those targeted at medical applications. In this paper we describe a method to estimate the tensor of curvature of a surface at the vertices of a polyhedral approximation. Principal curvatures and principal directions are obtained by computing in closed form the eigenvalues and eigenvectors of certain # # # symmetric matrices defined by integral formulas, and closely related to the matrix representation of the tensor of curvature. The resulting algorithm is linear, both in time and in space, as a function of the number of vertices and faces of the polyhedral surface. 1
ICP Registration using Invariant Features
, 2002
"... This paper investigates the use of Euclidean invariant features in a generalization of iterative closest point registration of range images. Pointwise correspondences are chosen as the closest point with respect to a weighted linear combination of positional and feature distances. It is shown that u ..."
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Cited by 90 (0 self)
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This paper investigates the use of Euclidean invariant features in a generalization of iterative closest point registration of range images. Pointwise correspondences are chosen as the closest point with respect to a weighted linear combination of positional and feature distances. It is shown that under ideal noisefree conditions, correspondences formed using this distance function are correct more often than correspondences formed using the positional distance alone. In addition, monotonic convergence to at least a local minimum is shown to hold for this method. When noise is present, a method that automatically sets the optimal relative contribution of features and positions is described. This method trades off error in feature values due to noise against error in positions due to misalignment. Experimental results suggest that using invariant features decreases the probability of being trapped in a local minimum, and may be an effective solution for difficult range image registration problems where the scene is very small compared to the model.
Using a Deformable Surface Model to Obtain a Shape Representation of the Cortex
 IEEE Trans. Med. Imag
, 1996
"... The problem of obtaining a mathematical representation of the cortex of the human brain is examined. A parametrization of the outer cortex is first obtained using a deformable surface algorithm which, motivated by the structure of the cortex, is constructed to find the central layer of thick surface ..."
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Cited by 87 (11 self)
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The problem of obtaining a mathematical representation of the cortex of the human brain is examined. A parametrization of the outer cortex is first obtained using a deformable surface algorithm which, motivated by the structure of the cortex, is constructed to find the central layer of thick surfaces. Based on this parametrization, a hierarchical representation of the cortical structure is proposed through its depth map and its curvature maps at various scales. Various experiments on magnetic resonance data are presented. I. Introduction The problem of finding and parametrizing boundaries in two and threedimensional images is often an important step toward shape visualization and analysis, and has been extensively studied in the image analysis and computer vision literature. Several methods have been proposed, basedboth on bottomup and topbottom procedures. One very promising model which combines robustness to noise and the flexibility to represent a broad class of shapes is base...
Recent progress in coded structured light as a technique to solve the correspondence problem: a survey
 NCE PROBLEM: A SURVEY, PATTERN RECOGNITION
, 1998
"... We present a survey of the most significant techniques, used in the last few years, concerning the coded structured light methods employed to get 3D information. In fact, depth perception is one of the most important subjects in computer vision. Stereovision is an attractive and widely used method, ..."
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Cited by 81 (17 self)
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We present a survey of the most significant techniques, used in the last few years, concerning the coded structured light methods employed to get 3D information. In fact, depth perception is one of the most important subjects in computer vision. Stereovision is an attractive and widely used method, but, it is rather limited to make 3D surface maps, due to the correspondence problem. The correspondence problem can be improved using a method based on structured light concept, projecting a given pattern on the measuring surfaces. However, some relations between the projected pattern and the reflected one must be solved. This relationship can be directly found codifying the projected light, so that, each imaged region of the projected pattern carries the needed information to solve the correspondence problem.
An Algorithmic Overview of Surface Registration . . .
 MEDICAL IMAGE ANALYSIS
, 2000
"... This paper presents a literature survey of automatic 3D surface registration techniques emphasizing the mathematical and algorithmic underpinnings of the subject. The relevance of surface registration to medical imaging is that there is much useful anatomical information in the form of collected ..."
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Cited by 58 (1 self)
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This paper presents a literature survey of automatic 3D surface registration techniques emphasizing the mathematical and algorithmic underpinnings of the subject. The relevance of surface registration to medical imaging is that there is much useful anatomical information in the form of collected surface points which originate from complimentary modalities and which must be reconciled. Surface registration
Face recognition based on depth maps and surface curvature
 SPIE Geometric methods in Computer Vision
, 1991
"... This paper explores the representation of the human face by features based on shape and curvature of the face surface. Curvature captures many features necessary to accurately describe the face, such as the shape of the forehead, jawline, and cheeks, which are not easily detected from standard inten ..."
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Cited by 50 (0 self)
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This paper explores the representation of the human face by features based on shape and curvature of the face surface. Curvature captures many features necessary to accurately describe the face, such as the shape of the forehead, jawline, and cheeks, which are not easily detected from standard intensity images. Moreover, the value of curvature at a point on the surface is also viewpointinvariant. Until recently range data of high enough resolution and accuracy to perform useful curvature calculations on the scale of the human face had been unavailable. Although several researchers have worked on the problem of interpreting range data from curved (although usually highly geometrically structured) surfaces, the main approaches have centered on segmentation by signs of mean and Gaussian curvature which have not proved su cient for classi cation of human faces. This paper details the calculation of principal curvature for our particular data set, the calculation of general surface descriptors based on curvature, and the calculation of face speci c descriptors based both on curvature features and aprioriknowledge about the structure of the face. These face speci c descriptors can be incorporated into many di erent recognition strategies. We describe a system which implements one such strategy, depth template comparison, giving excellent recognition rates in our test cases. 1
Optimal Triangulation and QuadricBased Surface Simplification
 Journal of Computational Geometry: Theory and Applications
, 1999
"... Many algorithms for reducing the number of triangles in a surface model have been proposed, but to date there has been little theoretical analysis of the approximations they produce. Previously we described an algorithm that simplifies polygonal models using a quadric error metric. This method is fa ..."
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Cited by 48 (1 self)
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Many algorithms for reducing the number of triangles in a surface model have been proposed, but to date there has been little theoretical analysis of the approximations they produce. Previously we described an algorithm that simplifies polygonal models using a quadric error metric. This method is fast and produces high quality approximations in practice. Here we provide some theory to explain why the algorithm works as well as it does. Using methods from differential geometry and approximation theory, we show that in the limit as triangle area goes to zero on a differentiable surface, the quadric error is directly related to surface curvature. Also, in this limit, a triangulation that minimizes the quadric error metric achieves the optimal triangle aspect ratio in that it minimizes the L 2 geometric error. This work represents a new theoretical approach for the analysis of simplification algorithms. Keywords: triangle aspect ratio, curvature, approximation theory, anisotropic mesh gen...
A robot vision system for recognizing 3D objects in loworder polynomial time
 IEEE Trans. Syst., Man, Cybern
, 1989
"... AhsrrucrThe two factors that determine the time complexity associated with modeldriven interpretation of range maps are: 1) the particular strategy used for the generation of object hypotheses; and 2) the manner in which both the model and the sensed data are organized, data organization being a p ..."
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Cited by 45 (6 self)
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AhsrrucrThe two factors that determine the time complexity associated with modeldriven interpretation of range maps are: 1) the particular strategy used for the generation of object hypotheses; and 2) the manner in which both the model and the sensed data are organized, data organization being a primary determinant of the efficiency of verification of a given hypothesis. 3DPOLY, a working system for recognizing objects in the presence of occlusion and against cluttered backgrounds is presented. The time complexity of this system is only O ( n *) for single object recognition, where 17 is the number of features on the object. The most novel aspect of this system is the manner in which the feature data are organized for the models; we use a data structure called the feature sphere for the purpose. Efficient constant time algorithms for assigning a feature to its proper place on a feature sphere and for extracting the neighbors of a given feature from the feature sphere representation are present. For hypothesis generation, we use local feature sets, a notion similar to those used before us by Rolles, Shirai and others. The combination of the feature sphere idea for streamlining verification and the local feature sets for hypothesis generation results in a system whose time complexity has a loworder polynomial bound. I.