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<p><b>Abstract</b>—Often an image <tmath>g(x,y)</tmath> is regularized and even restored by minimizing the Mumford-Shah functional. Properties of the regularized image <tmath>u(x,y)</tmath> depends critically on the numerical value of the two parameters <tmath>\alpha</tmath> and <tmath>\gamma</tmath> controlling smoothness and fidelity. When <tmath>\alpha</tmath> and <tmath>\gamma</tmath> are constant over the image, small details are lost when an extensive filtering is used in order to remove noise. In this paper, it is shown how the two parameters <tmath>\alpha</tmath> and <tmath>\gamma</tmath> can be made self-adaptive. In fact, <tmath>\alpha</tmath> and <tmath>\gamma</tmath> are not constant but automatically adapt to the local scale and contrast of features in the image. In this way, edges at all scales are detected and boundaries are well-localized and preserved. In order to preserve trihedral junctions <tmath>\alpha</tmath> and <tmath>\gamma</tmath> become locally small and the regularized image <tmath>u(x,y)</tmath> maintains sharp and well-defined trihedral junctions. Images regularized by the proposed procedure are well-suited for further processing, such as image segmentation and object recognition.</p>
Image regularization, Mumford-Shah, variational methods.
Walter Vanzella, Vincent Torre, Felice Andrea Pellegrino, "Self-Adaptive Regularization", IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 26, no. , pp. 804-809, June 2004, doi:10.1109/TPAMI.2004.15
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