Visual reconstruction
Segmentation through Variable-Order Surface Fitting
IEEE Transactions on Pattern Analysis and Machine Intelligence
International Journal of Computer Vision
A multiscale algorithm for image segmentation by variational method
SIAM Journal on Numerical Analysis
Variational methods in image segmentation
Variational methods in image segmentation
SIAM Journal on Applied Mathematics
Foundations of real and abstract analysis
Foundations of real and abstract analysis
Computer and Robot Vision
Digital Picture Processing
Nonparametric Optimal Binarization
ICPR '98 Proceedings of the 14th International Conference on Pattern Recognition-Volume 1 - Volume 1
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In this article we present an approach to the segmentation problem by a piecewise approximation of the given image with continuous functions. Unlike the common approach of Mumford and Shah in our formulation of the problem the number of segments is a parameter, which can be estimated. The problem can be stated as: Compute the optimal segmentation with a fixed number of segments, then reduce the number of segments until the segmentation result fulfills a given suitability. This merging algorithm results in a multi-objective optimization, which is not only resolved by a linear combination of the contradicting error functions. To constrain the problem we use a finite dimensional vector space of functions in our approximation and we restrict the shape of the segments. Our approach results in a multi-objective optimization: On the one hand the number of segments is to be minimized, on the other hand the approximation error should also be kept minimal. The approach is sound theoretically and practically: We show that for L 2-images a Pareto-optimal solution exists and can be computed for the discretization of the image efficiently.