Visual reconstruction
3D shape representation by contours
Computer Vision, Graphics, and Image Processing
ACM Transactions on Mathematical Software (TOMS)
A Survey of Numerical Mathematics
A Survey of Numerical Mathematics
Digital Picture Processing
Computer Aided Geometric Design; Proceedings of a Conference Held at the University of Utah, Salt Lake City, Utah, March 18-21, 1974
Multi-Level Reconstruction of Visual Surfaces: Variational Principles and Finite Element Representations
Smoothed Local Symmetries and Their Implementation
Smoothed Local Symmetries and Their Implementation
Computing Visible-Surface Representations
Computing Visible-Surface Representations
Finite-Element Methods for Active Contour Models and Balloons for 2-D and 3-D Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
On Discontinuity-Adaptive Smoothness Priors in Computer Vision
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multiscale Medial Loci and Their Properties
International Journal of Computer Vision - Special Issue on Research at the University of North Carolina Medical Image Display Analysis Group (MIDAG)
CIARP '08 Proceedings of the 13th Iberoamerican congress on Pattern Recognition: Progress in Pattern Recognition, Image Analysis and Applications
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A central class of image understanding problems is concerned with reconstructing a shape from an incomplete data set, such as fitting a surface to (partially) given contours. A new theory for solving such problems is presented. Unlike the current heuristic methods, the method used starts from fundamental principles that should be followed by any reconstruction method, regardless of its mathematical or physical implementation. A mathematical procedure which conforms to these principles is presented. One major advantage of the method is the ability to handle shapes containing both smooth and sharp parts without using thresholds. A sharp variation, such as a corner, requires a high-resolution mesh for adequate representation, while slowly varying sections can be represented with sparser mesh points. Unlike current methods, this procedure fits the surface on a varying mesh. The mesh is constructed automatically to be more dense at parts of the image that have more rapid variation. Analytical examples are given in simple cases, followed by numerical experiments.