Robot vision
Reconstruction of polygons from projections
Information Processing Letters
Reconstructing Convex Sets from Support Line Measurements
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fundamentals of statistical signal processing: estimation theory
Fundamentals of statistical signal processing: estimation theory
On the Estimation of a Convex Set With Corners
IEEE Transactions on Pattern Analysis and Machine Intelligence
A new mesh simplification algorithm based on triangle collapses
Journal of Computer Science and Technology
Scattered Data Techniques for Surfaces
Dagstuhl '97, Scientific Visualization
Asymptotic global confidence regions in parametric shape estimation problems
IEEE Transactions on Information Theory
Cramer-Rao bounds for parametric shape estimation in inverse problems
IEEE Transactions on Image Processing
Shape description from generalized support functions
Pattern Recognition Letters
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We address the problem of reconstructing a planar shape from a finite number of noisy measurements of its support function or its diameter function. New linear and non-linear algorithms are proposed, based on the parametrization of the shape by its Extended Gaussian Image. This parametrization facilitates a systematic statistical analysis of the problem via the Cramér-Rao lower bound (CRLB), which provides a fundamental lower bound on the performance of estimation algorithms. Using CRLB, we also generate confidence regions which conveniently display the effect of parameters like eccentricity, scale, noise, and measurement direction set, on the quality of the estimated shapes, as well as allow a performance analysis of the algorithms.