Computational geometry: an introduction
Computational geometry: an introduction
Journal of Algorithms
Probing convex polygons with X-rays
SIAM Journal on Computing
Introduction to matrix analysis (2nd ed.)
Introduction to matrix analysis (2nd ed.)
Detection, Estimation, and Modulation Theory: Radar-Sonar Signal Processing and Gaussian Signals in Noise
Robot Vision
FORTRAN Codes for Mathematical Programming: Linear, Quadratic and Discrete
FORTRAN Codes for Mathematical Programming: Linear, Quadratic and Discrete
Geometric probing
PAC learning with generalized samples and an application to stochastic geometry
COLT '92 Proceedings of the fifth annual workshop on Computational learning theory
Shapes Recognition Using the Straight Line Hough Transform: Theory and Generalization
IEEE Transactions on Pattern Analysis and Machine Intelligence
On the Estimation of a Convex Set With Corners
IEEE Transactions on Pattern Analysis and Machine Intelligence
PAC Learning with Generalized Samples and an Applicaiton to Stochastic Geometry
IEEE Transactions on Pattern Analysis and Machine Intelligence
Shape Estimation from Support and Diameter Functions
Journal of Mathematical Imaging and Vision
Shape from silhouettes in discrete space
CAIP'05 Proceedings of the 11th international conference on Computer Analysis of Images and Patterns
Shape reconstruction by line voting in discrete space
ISVC'06 Proceedings of the Second international conference on Advances in Visual Computing - Volume Part I
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Algorithms are proposed for reconstructing convex sets given noisy support line measurements. It is observed that a set of measured support lines may not be consistent with any set in the plane. A theory of consistent support lines which serves as a basis for reconstruction algorithms that take the form of constrained optimization algorithms is developed. The formal statement of the problem and constraints reveals a rich geometry that makes it possible to include prior information about object position and boundary smoothness. The algorithms, which use explicit noise models and prior knowledge, are based on maximum-likelihood and maximum a posteriori estimation principles and are implemented using efficient linear and quadratic programming codes. Experimental results are presented. This research sets the stage for a more general approach to the incorporation of prior information concerning the estimation of object shape.