טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentAlexander Brook
SubjectAspects of Invariant Shape Processing
DepartmentDepartment of Applied Mathematics
Supervisor Full Professor Kimmel Ron


Abstract

In this thesis we consider two of the basic subjects of image processing and computer vision research: binary shapes and invariance. The two parts of this manuscript deal with scale invariance in image processing and affine-invariant shape matching.

In the first part, after introducing some of the basic principles behind similarity-invariant smoothness measures for curves and surfaces, with references to the relevant literature, we discuss the ramifications of scale-invariance in various problems of image processing and analysis, and point out some novel properties and new considerations. We also consider the different ways in which an image processing algorithm can be scale invariant.

We present a careful study of some basic assumptions about scale invariance.  In particular, we stress the difference between the invariance of smoothness measures and the invariance of the resulting curves and surfaces. We also analyze some papers that introduce scale-invariant edge detection and edge integration, and point out the benefits and the dangers of scale-invariant edge detection.

In the second part of the thesis we present an affine invariant shape matching method, which is also invariant to resampling, robust to pixelization noise and can still perform under occlusion. The algorithm is a unification of ideas from semi-differential invariants, shape contexts, and shape distributions.

As opposed to most algorithms in the literature, our algorithm provides a point-to-point matching between the two curves. We demonstrate matching results, equi-affine invariance and robustness to noise. We analyze our algorithm and provide the theoretical foundations for the invariant properties of our algorithm.

The third part of this thesis is a review of the inpainting problem. We have systematized the existing literature and discussed the main concepts and ideas used to solve this problem.