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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 215 (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
Anisotropic Polygonal Remeshing
"... In this paper, we propose a novel polygonal remeshing technique that exploits a key aspect of surfaces: the intrinsic anisotropy of natural or manmade geometry. In particular, we use curvature directions to drive the remeshing process, mimicking the lines that artists themselves would use when cre ..."
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Cited by 204 (17 self)
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In this paper, we propose a novel polygonal remeshing technique that exploits a key aspect of surfaces: the intrinsic anisotropy of natural or manmade geometry. In particular, we use curvature directions to drive the remeshing process, mimicking the lines that artists themselves would use when creating 3D models from scratch. After extracting and smoothing the curvature tensor field of an input genus0 surface patch, lines of minimum and maximum curvatures are used to determine appropriate edges for the remeshed version in anisotropic regions, while spherical regions are simply pointsampled since there is no natural direction of symmetry locally. As a result our technique generates polygon meshes mainly composed of quads in anisotropic regions, and of triangles in spherical regions. Our approach provides the flexibility to produce meshes ranging from isotropic to anisotropic, from coarse to dense, and from uniform to curvature adapted.
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 103 (12 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...
RealTime 100 Object Recognition System
, 1996
"... A realtime vision system is described that can recognize 100 complex threedimensional objects. In contrast to traditional strategies that rely on object geometry and local image features, the present system is founded on the concept of appearance matching. Appearance manifolds of the 100 objects w ..."
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Cited by 82 (9 self)
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A realtime vision system is described that can recognize 100 complex threedimensional objects. In contrast to traditional strategies that rely on object geometry and local image features, the present system is founded on the concept of appearance matching. Appearance manifolds of the 100 objects were automatically learned using a computercontrolled turntable. The entire learning process was completed in 1 day. A recognition loop has been implemented that performs scene change detection, image segmentation, region normalizations, and appearance matching, in less than 1 second. The hardware used by the recognition system includes no more than a CCD color camera and a workstation. The realtime capability and interactive nature of the system have allowed numerous observers to test its performance. To quantify performance, we have conducted controlled experiments on recognition and pose estimation. The recognition rate was found to be 100 % and object pose was estimated with a mean abso...
Computing differential properties of 3D shapes from stereoscopic images without 3D models
, 1994
"... We are considering the problem of recovering the threedimensional geometry of a scene from binoculor stereo disparity. Once a dense disparity map has been computed from a stereo pair of images, one often needs to calculate some local diferential properties of the cowesponding 30 surface such as ..."
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Cited by 72 (9 self)
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We are considering the problem of recovering the threedimensional geometry of a scene from binoculor stereo disparity. Once a dense disparity map has been computed from a stereo pair of images, one often needs to calculate some local diferential properties of the cowesponding 30 surface such as orientation or curvatures. The wual approach is to build a 30 reconstruction of the surface(s) from which all shape properties will then be derived without ever going back to the original images. In this paper, we depart from this paradigm and propose to w e the images directly to compute the shape properties. We thus propose a new method extending the classical cowelation method to estimate accurately both the disparity and its derivatives directly from the image data. We then relate those derivatives to diferential properties of the surface such as orientation and curvatures.
Superquadrics for Segmenting and Modeling Range Data
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1997
"... We present a novel approach to reliable and efficient recovery of partdescriptions in terms of superquadric models from range data. We show that superquadrics can directly be recovered from unsegmented data, thus avoiding any presegmentation steps (e.g., in terms of surfaces). The approach is b ..."
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Cited by 67 (4 self)
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We present a novel approach to reliable and efficient recovery of partdescriptions in terms of superquadric models from range data. We show that superquadrics can directly be recovered from unsegmented data, thus avoiding any presegmentation steps (e.g., in terms of surfaces). The approach is based on the recoverandselect paradigm [10]. We present several experiments on real and synthetic range images, where we demonstrate the stability of the results with respect to viewpoint and noise.
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 58 (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
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 53 (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.
The Alignment of Objects with Smooth Surfaces
 Computer Vision, Graphics, and Image Processing: Image Understanding
, 1988
"... This report describes research partially done at the Massachusetts Institute of Technology within the Artificial Intelligence Laboratory. Support for the laboratory's artificial intelligence research is provided in part by the Advanced Research Projects Agency of the Department of Defense under ..."
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Cited by 47 (9 self)
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This report describes research partially done at the Massachusetts Institute of Technology within the Artificial Intelligence Laboratory. Support for the laboratory's artificial intelligence research is provided in part by the Advanced Research Projects Agency of the Department of Defense under Office of Naval Research contract N0001485K0124. *Artificial Intelligence Laboratory, Massachusetts Institute of Technology, Cambridge, MA 02139 tDept. of Applied Mathematics, Weizmann Institute of Science, Rehovot 76100, Israel
Gradient and curvature from the photometricstereo method, including local confidence estimation
 J. Opt. Soc. Am. A
, 1994
"... The photometricstereo method is one technique for threedimensional shape determination that has been implemented in a variety of experimental settings and that has produced consistently good results. The idea is to use intensity values recorded from multiple images obtained from the same viewpoint ..."
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Cited by 41 (1 self)
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The photometricstereo method is one technique for threedimensional shape determination that has been implemented in a variety of experimental settings and that has produced consistently good results. The idea is to use intensity values recorded from multiple images obtained from the same viewpoint but under different conditions of illumination. The resulting radiometric constraint makes it possible to obtain local estimates of both surface orientation and surface curvature without requiring either global smoothness assumptions or prior image segmentation. Photometric stereo is moved one step closer to practical possibility by a description of an experimental setting in which surface gradient estimation is achieved on fullframe video data at nearvideoframe rates (i.e., 15 Hz). The implementation uses commercially available hardware. Reflectance is modeled empirically with measurements obtained from a calibration sphere. Estimation of the gradient (p, q) requires only simple table lookup. Curvature estimation additionally uses the reflectance map R(p, q). The required lookup table and reflectance maps are derived during calibration. Because reflectance is modeled empirically, no prior physical model of the reflectance characteristics of the objects to be analyzed is assumed. At the same time, if a good physical model is available, it can be retrofitted to the method for implementation purposes. Photometric stereo is subject to error in the presence of cast shadows and interreflection. No purely local technique can succeed because these phenomena are inherently nonlocal. Nevertheless, it is demonstrated that one can exploit the redundancy in threelightsource photometric stereo to detect locally, in most cases, the presence of cast shadows and interreflection. Detection is facilitated by the explicit inclusion of a local confidence estimate in the lookup table used for gradient estimation. 1.