Results 1  10
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14
Computing Local Surface Orientation and Shape from Texture for Curved Surfaces
, 1997
"... Shape from texture is best analyzed in two stages, analogous to stereopsis and structure from motion: (a) Computing the `texture distortion' from the image, and (b) Interpreting the `texture distortion' to infer the orientation and shape of the surface in the scene. We model the texture distortion f ..."
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Cited by 88 (4 self)
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Shape from texture is best analyzed in two stages, analogous to stereopsis and structure from motion: (a) Computing the `texture distortion' from the image, and (b) Interpreting the `texture distortion' to infer the orientation and shape of the surface in the scene. We model the texture distortion for a given point and direction on the image plane as an affine transformation and derive the relationship between the parameters of this transformation and the shape parameters. We have developed a technique for estimating affine transforms between nearby image patches which is based on solving a system of linear constraints derived from a differential analysis. One need not explicitly identify texels or make restrictive assumptions about the nature of the texture such as isotropy. We use nonlinear minimization of a least squares error criterion to recover the surface orientation (slant and tilt) and shape (principal curvatures and directions) based on the estimated affine transforms in a number of different directions. A simple linear algorithm based on singular value decomposition of the linear parts of the affine transforms provides the initial guess for the minimization procedure. Experimental results on both planar and curved surfaces under perspective projection demonstrate good estimates for both orientation and shape. A sensitivity analysis yields predictions for both computer vision algorithms and human perception of shape from texture.
Spherical shell: A higher order bounding volume for fast proximity queries
 In Proc. of Third International Workshop on Algorithmic Foundations of Robotics
"... Hierarchical data structures have been widely used to design e cient algorithms for interference detection for robot motion planning and physicallybased modeling applications. Most of the hierarchies involve use of bounding volumes which enclose the underlying geometry. These bounding volumes are u ..."
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Cited by 46 (9 self)
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Hierarchical data structures have been widely used to design e cient algorithms for interference detection for robot motion planning and physicallybased modeling applications. Most of the hierarchies involve use of bounding volumes which enclose the underlying geometry. These bounding volumes are used to test for interference orcompute distance bounds between the underlying geometry. The e ciency of a hierarchy is directly proportional to the choice ofabounding volume. In this paper, we introduce spherical shells, a higher order bounding volume for fast proximity queries. Each shell corresponds to a portion of the volume between two concentric spheres. We present algorithms to compute tight tting shells and fast overlap between two shells. Moreover, we show that spherical shells provide local cubic convergence to the underlying geometry. As aresult, in many cases they provide faster algorithms for interference detection and distance computation as compared toearlier methods. We also describe an implementation and compare it with other hierarchies. 1
Surface orientation and curvature from differential texture distortion
, 1995
"... A unified differential geometric framework for estimation of local surface shapeand orientation from projective texture distortion is proposed, based on a differential version of the texture stationarity assumption introduced by Malik and Rosenholtz. This framework allows the information content of ..."
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Cited by 24 (0 self)
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A unified differential geometric framework for estimation of local surface shapeand orientation from projective texture distortion is proposed, based on a differential version of the texture stationarity assumption introduced by Malik and Rosenholtz. This framework allows the information content of the gradient of any texture descriptor defined inalocal coordinate frametobe characterized in a very compact form. The analysis encompasses both full a ne texture descriptors and the classical "texture gradients". For estimation of local surface orientation and curvature from uncertain observations of affine texture distortion, the proposed framework allows the dimensionality of the search space tobereduced from five to one.
Isometric Embedding and Continuum ISOMAP
 In Proceedings of the Twentieth International Conference on Machine Learning
, 2003
"... Recently, the Isomap algorithm has been proposed for learning a nonlinear manifold from a set of unorganized highdimensional data points. It is based on extending the classical multidimensional scaling method for dimension reduction. In this paper, we present a continuous version of Isomap wh ..."
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Cited by 18 (1 self)
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Recently, the Isomap algorithm has been proposed for learning a nonlinear manifold from a set of unorganized highdimensional data points. It is based on extending the classical multidimensional scaling method for dimension reduction. In this paper, we present a continuous version of Isomap which we call continuum isomap and show that manifold learning in the continuous framework is reduced to an eigenvalue problem of an integral operator. We also show that the continuum isomap can perfectly recover the underlying natural parametrization if the nonlinear manifold can be isometrically embedded onto an Euclidean space. Several numerical examples are given to illustrate the algorithm.
CramérRao Bounds for Parametric Estimation of Target Boundaries in Nonlinear Inverse Scattering Problems
 IEEE Trans. on Antennas and Propagat
, 1999
"... We present new methods for computing fundamental performance limits for parametric shape estimation in inverse scattering problems, such as passive radar imaging. We evaluate CramerRao lower bounds (CRB) on shape estimation accuracy using the domain derivative technique from nonlinear inverse scatte ..."
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Cited by 3 (3 self)
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We present new methods for computing fundamental performance limits for parametric shape estimation in inverse scattering problems, such as passive radar imaging. We evaluate CramerRao lower bounds (CRB) on shape estimation accuracy using the domain derivative technique from nonlinear inverse scattering theory. The CRB provides an unbeatable performance limit for any unbiased estimator, and under fairly mild regularity conditions, is asymptotically achieved by the maximum likelihood estimator (MLE), hence serving as a predictor of the high signalto noise ratio performance of the MLE. Furthermore, the resultant CRB's are used to define a global confidence region, centered around the true boundary, in which the boundary estimate lies with a prescribed probability. These global confidence regions conveniently display the uncertainty in various geometric parameters such as shape, size, orientation, and position of the estimated target, and facilitate geometric inferences. Numerical simula...
Direct computation of shape cues by multiscale retinotopic processing
 J. OF COMPUTER VISION
, 1994
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Introducing Surfaces
"... This document briey summarizes denitions and hints at proofs of principal results for a rst course on surfaces, beginning with an informal introduction to Euclidean space. It is intended as an aide memoirea companion to lectures, tutorials and computer lab classes, with exercises and proofs to be c ..."
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Cited by 1 (0 self)
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This document briey summarizes denitions and hints at proofs of principal results for a rst course on surfaces, beginning with an informal introduction to Euclidean space. It is intended as an aide memoirea companion to lectures, tutorials and computer lab classes, with exercises and proofs to be completed by the student. Exercises include the statements to be veried mathematics needs to be done, not just read! The prereqisites are: elementary knowledge of Euclidean geometry and the denition of R
unknown title
, 2000
"... Estimation of curl in paper using a combination of shape measurement and leastsquares modelling ..."
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Estimation of curl in paper using a combination of shape measurement and leastsquares modelling
On the invariant spectrum of S¹invariant metrics on S²
 PROC. LONDON MATH. SOC
, 2002
"... A theorem of J. Hersch (1970) states that for any smooth metric on S 2, with total area equal to 4#, the first nonzero eigenvalue of the Laplace operator acting on functions is less than or equal to 2 (this being the value for the standard round metric). For metrics invariant under the standard S ..."
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A theorem of J. Hersch (1970) states that for any smooth metric on S 2, with total area equal to 4#, the first nonzero eigenvalue of the Laplace operator acting on functions is less than or equal to 2 (this being the value for the standard round metric). For metrics invariant under the standard S
Simple Yet Effective Algorithms for Constraint Satisfaction and Related Problems
, 1996
"... Constraintbased reasoning, whose origin came from computer vision research of the 1970's, is now a central topic of growing importance in many disciplines including articial intelligence (AI), computer science, robotics, operations research (OR), management technology, logic programming and others. ..."
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Constraintbased reasoning, whose origin came from computer vision research of the 1970's, is now a central topic of growing importance in many disciplines including articial intelligence (AI), computer science, robotics, operations research (OR), management technology, logic programming and others. This is witnessed by recent international workshops and symposia where constraint processing is contributing exciting new directions in computational linguistics, concurrent and distributed computing, database systems, graphical interfaces, combinatorial optimization, and geographical information systems. A central problem in constraintbased reasoning is the constraint satisfaction problem (CSP): We are given a set of variables, a discrete and nite domain for each variable and a set of constraints. Each constraint is dened over some subset of variables and limits the combination of values that these variables can take simultaneously. The goal is to obtain an assignment that satises eit...