The completion of interrupted lines or the enhancement of flow-like structures is a challenging task in computer vision, human vision, and image processing. We address this problem by presenting a multiscale method in which a nonlinear diffusion filter is steered by the so-called interest operator (second-moment matrix, structure tensor). An m-dimensional formulation of this method is analysed with respect to its well-posedness and scale-space properties. An efficient scheme is presented which uses a stabilization by a semi-implicit additive operator splitting (AOS), and the scale-space behaviour of this method is illustrated by applying it to both 2-D and 3-D images.

In this paper we describe a new strategy for using local structure adaptive filtering in normalized convolution. The shape of the filter, used as the applicability function in the context of normalized convolution, adapts to the local image structure and avoids filtering across borders. The size of the filter is also adaptable to the local sample density to avoid unnecessary smoothing over high certainty regions. We compared our adaptive interpolation technique with conventional normalized averaging methods. We found that our strategy yields a result that is much closer to the original signal both visually and in terms of MSE, meanwhile retaining sharpness and improving the SNR.

Lecture Notes in Computer Science, Springer Verlag, Berlin, pp. 230--237. Weickert, J. (1997). Recursive separable schemes for nonlinear diffusion filters, in B. ter Haar Romeny et. al. (ed.), Scale-Space Theory in Computer Vision, Vol. 1252, Springer Verlag. Witkin, A. P. (1983). Scale-space filtering, 8th International Conference on Artificial Intelligence, Karlsruhe, Germany, pp. 1019--1022. Xiao, Q. & Raafat, H. (1991). Fingerprint image postprocessong: A combined statistical and structural approach, Pattern Recognition 24(10): 985--992. 118 REFERENCES O'Gorman, L. & Nickerson, J. V. (1989). An approach to fingerprint filter design, Pattern Recognition 22(1): 29--38. Pal, S. K. & Mitra, S. (1996). Noisy fingerprint classification using mutilayer perceptron with fuzzy geometrical and textural features, Fuzzy Sets and Systems 80(2): 121-