טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentKatzir Oren
SubjectOn the Scale-Space of Filters and Their Applications
DepartmentDepartment of Electrical Engineering
Supervisor Dr. Guy Gilboa
Full Thesis textFull thesis text - English Version


Abstract

In this work we examine how to extend spatial and multi-scale image decomposition algorithms, through a scale-space perspective.

First, we examine the problem of matching patches of internal and external data. A new patch quality indicator based on interest-points is proposed which aims at maximizing the ratio of the number of points of interest to the area. We prove that the best convex polygon maximizing the indicator is the triangle. Thus data-driven triangle patches are used in the patch-matching algorithm, considerably improving the matching quality. The triangle representation inherently allows affine correction of the patches, thereby increasing the matching probability and enabling a smaller external data-set. We employ this technique for image quality enhancement of low resolution facial data using a data bank of external faces. The results here are preliminary.

Second, we propose a spectral decomposition framework that is applicable for a very broad family of (possibly nonlinear) operators (e.g. denoisers like BM3D, MRFs, deep nets, etc.). Our key insight is that the fundamental “generalized frequencies” induced by an operator, can be revealed by repeatedly applying this operator on an input image and analyzing the rate of decay of structures in the resulting scale-space. We formalize this observation, and present a practical algorithm for decomposing images w.r.t. arbitrary image priors. Our framework allows to obtain a spectrum plot depicting frequency activity and to rigorously define low-pass, high-pass and band-pass filters. We demonstrate the strength and generality of our framework in various image manipulation tasks, and illustrate its advantages w.r.t. several recent methods which are based on progressive coarsening processes.