Smooth Limits of Piecewise-Linear Approximations

Piecewise-Linear Approximations of Uncertain Functions

We study the problem of approximating a function F : R→ R by a piecewise-linear function F when the values of F at {x1, . . . , xn} are given by a discrete probability distribution. Thus, for each xi we are given a discrete set yi,1, . . . , yi,mi of possible function values with associated probabilities pi,j such that Pr[F(xi) = yi,j ] = pi,j . We define the error of F as error(F,F) = maxi=1 E...

Invertible Piecewise Linear Approximations for Color Reproduction

We consider the use of linear splines with variable knots for the approximation of unknown functions from data , motivated by control and estimation problems arising in color systems management. Unlike most popular nonlinear-in-parameters representations, piecewise linear (PL) functions can be simply inverted in closed form. For the one-dimensional case, we present a study comparing P L and neu...

Piecewise Linear Approximation of Smooth Compact Fibers

Optimal Approximations by Piecewise Smooth Functions and Associated Variational Problems

The purpose of this paper is to introduce and study the most basic properties of three new variational problems which are suggested by applications to computer vision. In computer vision, a fundamental problem is to appropriately decompose the domain R of a function g ( x , y) of two variables. To explain this problem, we have to start by describing the physical situation whch produces images: ...

Piecewise Linear Approximations of Digitized Space Curves with Applications

Generating piecewise linear approximations of digitized or "densely sampled" curves is an important problem in image processing, pattern recognition, geometric modeling, and computer graphics. Even though much attention bas been paid to the planar curve case, little work has addressed space curve approximation. In this paper, we consider how to approximate an arbitrary digitized 3-D space CUnlC...