论文信息 - Piecewise smooth approximations of functions

Piecewise smooth approximations of functions

A variational formulation for piecewise smooth approximation of functions which smooths out small discontinuities while retaining larger ones is analyzed. An elliptic approximation of the formulation is developed for practical applications to the segmentation problem in computer vision.

J. Shah

[1] P. Grisvard. Elliptic Problems in Nonsmooth Domains , 1985 .

[2] D. Mumford,et al. Optimal approximations by piecewise smooth functions and associated variational problems , 1989 .

[3] E. D. Giorgi,et al. Existence theorem for a minimum problem with free discontinuity set , 1989 .

[4] Thomas J. Richardson,et al. Scale independent piecewise smooth segmentation of images via variational methods , 1990 .

[5] L. Ambrosio. Existence theory for a new class of variational problems , 1990 .

[6] L. Ambrosio,et al. Approximation of functional depending on jumps by elliptic functional via t-convergence , 1990 .

[7] G. Congedo,et al. On the existence of solutions to a problem in multidimensional segmentation , 1991 .

[8] Jayant Shah. Segmentation by nonlinear diffusion. II , 1992, Proceedings 1992 IEEE Computer Society Conference on Computer Vision and Pattern Recognition.

[9] J. Shah. Properties of energy-minimizing segmentations , 1992 .

[10] Jean-Michel Morel,et al. A variational method in image segmentation: Existence and approximation results , 1992 .

[11] G. D. Maso,et al. An Introduction to-convergence , 1993 .