RECONSTRUCTION OF DAMAGED IMAGES USING RADIAL BASIS FUNCTIONS

RECONSTRUCTION OF DAMAGED IMAGES USING RADIAL BASIS FUNCTIONS Karel Uhlíř, Václav Skala email: kuhlir|skala@kiv. zcu. cz

Content • • • Introduction Problem definition RBF method Image reconstruction Error estimation Results

Introduction • How to reconstruct an image as well as possible from damaged or incomplete original? • What value was in a corrupted position and how can I restore it? Inpainting Noise Scratches

Problem definition Problem: We have an image Wi with resolution M x N with 256 gray levels. Some pixels have incorrect values (missing or overwritten). We would like to restore the original image W. However, find that value of incorrect pixels in Wi which is “equal” with the pixel value in W.

RBF method – Radial basis functions are circularly symmetric functions centered at a particular point. – Radial basis functions may be used to interpolate a function with n points by using n radial basis functions centered at these points. – The resulting interpolated function thus becomes ci – locations of constraints, ci = [cix, ciy]T x – arbitrary point f – radial basis function li – unknown coefficients P(x) - polynomial

RBF method – The input points (known pixels) => constraints – For li solving the linear system must be defined

Image reconstruction – Standard method: • • • global radial function over hole image => computational expensive fine results over big gaps speedup with CSRBF => sparse matrix CSRBF appropriate for small damage problem with reconstruction of noise – Our method • global radial function over sliding window => computational inexpensive • better results then CSRBF • suitable for highly damage images • more iterations

Image reconstruction – sliding window – process the k-neighborhood of current corrupted pixel