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Estimation of Planar Curves, Surfaces, and Nonplanar Space Curves Defined by Implicit Equations with Applications to Edge and Range Image Segmentation
, 1991
"... This paper addresses the problem of parametric representation and estimation of complex planar curves in 2D, surfaces in 3D and nonplanar space curves in 3D. Curves and surfaces can be defined either parametrically or implicitly, and we use the latter representation. A planar curve is the set o ..."
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Cited by 307 (2 self)
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This paper addresses the problem of parametric representation and estimation of complex planar curves in 2D, surfaces in 3D and nonplanar space curves in 3D. Curves and surfaces can be defined either parametrically or implicitly, and we use the latter representation. A planar curve is the set of zeros of a smooth function of two variables XY, a surface is the set of zeros of a smooth function of three variables X~Z, and a space curve is the intersection of two surfaces, which are the set of zeros of two linearly independent smooth functions of three variables X!/Z. For example, the surface of a complex object in 3D can be represented as a subset of a single implicit surface, with similar results for planar and space curves. We show how this unified representation can be used for object recognition, object position estimation, and segmentation of objects into meaningful subobjects, that is, the detection of “interest regions ” that are
ModelBased Recognition in Robot Vision
 ACM Computing Surveys
, 1986
"... This paper presents a comparative study and survey of modelbased objectrecognition algorithms for robot vision. The goal of these algorithms is to recognize the identity, position, and orientation of randomly oriented industrial parts. In one form this is commonly referred to as the “binpicking ” ..."
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Cited by 199 (0 self)
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This paper presents a comparative study and survey of modelbased objectrecognition algorithms for robot vision. The goal of these algorithms is to recognize the identity, position, and orientation of randomly oriented industrial parts. In one form this is commonly referred to as the “binpicking ” problem, in which the parts to be recognized are presented in a jumbled bin. The paper is organized according to 2D, 2&D, and 3D object representations, which are used as the basis for the recognition algorithms. Three
Partitioning 3D Surface Meshes Using Watershed Segmentation
 IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS
, 1999
"... This paper describes a method for partitioning 3D surface meshes into useful segments. The proposed method generalizes morphological watersheds, an image segmentation technique, to 3D surfaces. This surface segmentation uses the total curvature of the surface as an indication of region boundaries. ..."
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Cited by 178 (1 self)
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This paper describes a method for partitioning 3D surface meshes into useful segments. The proposed method generalizes morphological watersheds, an image segmentation technique, to 3D surfaces. This surface segmentation uses the total curvature of the surface as an indication of region boundaries. The surface is segmented into patches, where each patch has a relatively consistent curvature throughout, and is bounded by areas of higher, or drastically different, curvature. This algorithm has applications for a variety of important problems in visualization and geometrical modeling including 3D feature extraction, mesh reduction, texture mapping 3D surfaces, and computer aided design.
Meshless deformations based on shape matching
 ACM TRANS. GRAPH
, 2005
"... We present a new approach for simulating deformable objects. The underlying model is geometrically motivated. It handles pointbased objects and does not need connectivity information. The approach does not require any preprocessing, is simple to compute, and provides unconditionally stable dynamic ..."
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Cited by 169 (12 self)
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We present a new approach for simulating deformable objects. The underlying model is geometrically motivated. It handles pointbased objects and does not need connectivity information. The approach does not require any preprocessing, is simple to compute, and provides unconditionally stable dynamic simulations. The main idea of our deformable model is to replace energies by geometric constraints and forces by distances of current positions to goal positions. These goal positions are determined via a generalized shape matching of an undeformed rest state with the current deformed state of the point cloud. Since points are always drawn towards welldefined locations, the overshooting problem of explicit integration schemes is eliminated. The versatility of the approach in terms of object representations that can be handled, the efficiency in terms of memory and computational complexity, and the unconditional stability of the dynamic simulation make the approach particularly interesting for games.
Expressioninvariant 3D face recognition
, 2003
"... We present a novel 3D face recognition approach based on geometric invariants introduced by Elad and Kimmel. The key idea of the proposed algorithm is a representation of the facial surface, invariant to isometric deformations, such as those resulting from different expressions and postures of the ..."
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Cited by 108 (17 self)
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We present a novel 3D face recognition approach based on geometric invariants introduced by Elad and Kimmel. The key idea of the proposed algorithm is a representation of the facial surface, invariant to isometric deformations, such as those resulting from different expressions and postures of the face. The obtained geometric invariants allow mapping 2D facial texture images into special images that incorporate the 3D geometry of the face. These signature images are then decomposed into their principal components. The result is an efficient and accurate face recognition algorithm that is robust to facial expressions. We demonstrate the results of our method and compare it to existing 2D and 3D face recognition algorithms.
3D motion estimation, understanding and prediction from noisy image sequences
 IEEE Trans. Pattern Analysis and Machine Intelligence
, 1987
"... AbstractThis paper presents an approach to understanding general 3D motion of a rigid body from image sequences. Based on dynamics, a locally constant angular momentum (LCAM) model is introduced. The model is local in the sense that it is applied to a limited number of image frames at a time. Spec ..."
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Cited by 50 (2 self)
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AbstractThis paper presents an approach to understanding general 3D motion of a rigid body from image sequences. Based on dynamics, a locally constant angular momentum (LCAM) model is introduced. The model is local in the sense that it is applied to a limited number of image frames at a time. Specifically, the model constrains the motion, over a local frame subsequence, to be a superposition of precession and translation. Thus, the instantaneous rotation axis of the object is allowed to change through the subsequence. The trajectory of the rotation center is approximated by a vector polynomial. The parameters of the model evolve in time so that they can adapt to long term changes in motion characteristics. The nature and parameters of short term motion can be estimated continuously with the goal of understanding motion through the image sequence. The estimation algorithm presented in this paper is linear, i.e., the algorithm consists of solving simultaneous linear equations. Based on the assumption that the motion is smooth, object positions and motion in the near future can be predicted, and short missing subsequences can be recovered. Noise smoothing is achieved by overdetermination and a leastsquares criterion. The framework is flexible in the sense that it allows both overdetermination in number of feature points and the number of image frames. The number of frames from which the model is derived can be varied according to the complexity of motion and the noise level so as to obtain stable and good estimates of parameters over the entire image sequence. Simulation results are given for noisy synthetic data and images taken of a model airplane. Index TermsComputer vision, dynamic model, image sequence analysis, motion, motion estimation, motion prediction, motion understanding. I.
Finding Surface Correspondence for Object Recognition and Registration using Pairwise Geometric Histograms
 in Computer VisionECCV'98
"... . Pairwise geometric histograms have been demonstrated as an effective descriptor of arbitrary 2dimensional shape which enable robust and efficient object recognition in complex scenes. In this paper we describe how the approach can be extended to allow the representation and classification of arbi ..."
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Cited by 47 (3 self)
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. Pairwise geometric histograms have been demonstrated as an effective descriptor of arbitrary 2dimensional shape which enable robust and efficient object recognition in complex scenes. In this paper we describe how the approach can be extended to allow the representation and classification of arbitrary 2 1 2  and 3dimensional surface shape. This novel representation can be used in important vision tasks such as the recognition of objects with complex freeform surfaces and the registration of surfaces for building 3dimensional models from multiple views. We apply this new representation to both of these tasks and present some promising results. 1 Introduction Finding a correspondence between two or more surfaces is a frequently encountered problem in many computer vision tasks. When surface based descriptions are used for object recognition, the hypothesis that a particular object is in a scene is confirmed by finding a good correspondence between scene and model surfaces [6]. W...
From Surfaces to Objects: Computer Vision and ThreeDimensional Scene Analysis
, 1989
"... This book was originally published by John Wiley and Sons, ..."
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Cited by 38 (11 self)
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This book was originally published by John Wiley and Sons,
Highlevel CAD model acquisition from range image
 ComputerAided Design
, 1997
"... Automatic extraction of CAD descriptions which are ultimately intended for human manipulation requires the accurate inference of geometric and topological information. We present a system which applies segmentation techniques from computer vision to automatically extract CADmodels from range images ..."
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Cited by 37 (6 self)
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Automatic extraction of CAD descriptions which are ultimately intended for human manipulation requires the accurate inference of geometric and topological information. We present a system which applies segmentation techniques from computer vision to automatically extract CADmodels from range images of parts with curved surfaces. The output of the system is a Brep of the object which is suitable for further manipulation in a modelling system. The segmentation process is an improvement upon Besl and Jain's variableorder surface tting 1 extracting general quadric surfaces and planes from the data, with a postprocessing stage to identify surface intersections and to extract a Brep from the segmented image. We present results on a variety of machined objects, which illustrate the highlevel nature of the acquired models, and discuss the numerical accuracy (feature sizes and separations) and the correctness of structural inferences of the system.
Partial Surface and Volume Matching in Three Dimensions
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 1997
"... In this paper we present a new technique for partial surface and volume matching of images in three dimensions. In this ..."
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Cited by 35 (1 self)
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In this paper we present a new technique for partial surface and volume matching of images in three dimensions. In this