Self-adaptive regularization

Often an image g(x, y) is regularized and even restored by minimizing the Mumford-Shah functional. Properties of the regularized image u(x, y) depends critically on the numerical value of the two parameters /spl alpha/ and /spl beta/ controlling smoothness and fidelity. When /spl alpha/ and /spl bet...

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Bibliographic Details
Published in:IEEE transactions on pattern analysis and machine intelligence 2004-06, Vol.26 (6), p.804-809
Main Authors: Vanzella, W., Pellegrino, F.A., Torre, V.
Format: Article
Language:English
Subjects:
Algorithms
Artificial Intelligence
Bars
Computer vision
Filtering
Image edge detection
Image Enhancement - methods
Image Interpretation, Computer-Assisted - methods
Image regularization
Image restoration
Image segmentation
Inverse problems
Minimization methods
Mumford-Shah
Object recognition
Pattern Recognition, Automated - methods
Reproducibility of Results
Sensitivity and Specificity
variational methods
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Summary:Often an image g(x, y) is regularized and even restored by minimizing the Mumford-Shah functional. Properties of the regularized image u(x, y) depends critically on the numerical value of the two parameters /spl alpha/ and /spl beta/ controlling smoothness and fidelity. When /spl alpha/ and /spl beta/ 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 /spl alpha/ and /spl beta/ can be made self-adaptive. In fact, /spl alpha/ and /spl beta/ 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 /spl alpha/ and /spl beta/ become locally small and the regularized image u(x, y) 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.
ISSN:0162-8828
1939-3539
DOI:10.1109/TPAMI.2004.15