Detecting Codimension--Two Objects in an Image with Ginzburg-Landau Models
International Journal of Computer Vision
Image Deblurring in the Presence of Impulsive Noise
International Journal of Computer Vision
Segmentation, Classification and Denoising of a Time Series Field by a Variational Method
Journal of Mathematical Imaging and Vision
Nonconvex sparse regularizer based speckle noise removal
Pattern Recognition
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The purpose of this paper is to show the theoretical soundness of a variational method proposed in image processing for supervised classification. Based on works developed for phase transitions in fluid mechanics, the classification is obtained by minimizing a sequence of functionals. The method provides an image composed of homogeneous regions with regular boundaries, a region being defined as a set of pixels belonging to the same class. In this paper, we show the $\Gamma$-convergence of the sequence of functionals which differ from the ones proposed in fluid mechanics in the sense that the perturbation term is not quadratic but has a finite asymptote at infinity, corresponding to an edge-preserving regularization term in image processing.