Smoothing of Data Using Mumford-Shah Type Functionals

Abstract

As results of 3d sensors using the ”time of flight” technology we get noise information of the shape of objects together with intensities. From the mathematical point of view these information are scalar fields d and I.For filtering and smoothing of images we minimize a Mumford‐Shah functional by solving the boundary value problem of the relevant Euler‐Lagrange equations.For the numerical solution of the boundary value problem we use a finite volume discretization and we solve the resulting nonlinear equation system on the finite volume grid by Newtons method and the steepest descent method.