Piecewise Linear Approximation of Smooth Compact Fibers

Piecewise Linear Approximation of Smooth Compact Fibers

Piecewise Linear Orthogonal Approximation

We derive Sobolev-type inner products with respect to which hat functions on arbitrary triangulations of domains in R are orthogonal. Compared with linear interpolation, the resulting approximation schemes yield superior accuracy at little extra cost.

Approximation and Compression of Piecewise Smooth Functions

Wavelet or subband coding has been quite successful in compression applications, and this success can be attributed in part to the good approximation properties of wavelets. In this paper, we revisit rate-distortion bounds for wavelet approximation of piecewise smooth functions, in particular the piecewise polynomial case. We contrast these results with rate-distortion bounds achievable using a...

Image segmentation algorithm by piecewise smooth approximation

We propose a novel image segmentation algorithm using piecewise smooth (PS) approximation to image. The proposed algorithm is inspired by four well-known active contour models, i.e., Chan and Vese’ piecewise constant (PC)/smooth models, the region-scalable fitting model, and the local image fitting model. The four models share the same algorithm structure to find a PC/smooth approximation to th...

Nearest piecewise linear approximation of fuzzy numbers

The problem of the nearest approximation of fuzzy numbers by piecewise linear 1-knot fuzzy numbers is discussed. By using 1-knot fuzzy numbers one may obtain approximations which are simple enough and flexible to reconstruct the input fuzzy concepts under study. They might be also perceived as a generalization of the trapezoidal approximations. Moreover, these approximations possess some desira...