טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentKolomenkin Michael
SubjectCurve Analysis with Applications to Archaeology
DepartmentDepartment of Electrical Engineering
Supervisors Professor Ayellet Tal
Professor Ilan Shimshoni
Full Thesis textFull thesis text - English Version


Abstract

In this thesis we discuss methods for the definition, detection, analysis, and application of curves on surfaces. While doubtlessly as important as curves in images, curves on surfaces gained less attention. A number of definitions of curves on surfaces has been proposed. The most famous among them are ridges and valleys. While portraying important object properties, ridges and valleys fail to capture the shape of some objects, for example of objects with reliefs. We propose a new type of curves, termed relief edges, which addresses the limitations of the ridges and the valleys, and demonstrate how to compute it effectively. We demonstrate that relief edges portray the shape of some objects more accurately than other curves. Moreover, we present a novel framework for automatic estimation of the optimal scale for curve detection on surfaces. This framework enables correct estimation of curves on surfaces of objects consisting of features of multiple scales. It is generic and can be applied to any type of curve. We define a novel vector field on surfaces, termed the prominent field, which is a smooth direction field perpendicular to the object's features. The prominent field is useful for surface enhancement and visualization. In addition, we address the problem of reconstruction of a relief object from a line drawing. Our method is able to automatically reconstruct reliefs from complex drawings composed of hundreds of lines. Finally, we successfully apply our algorithms to archaeological objects. These objects provide a significant challenge from an algorithmic point of view, since after several thousand years underground they are seldom as smooth and nice as manually modeled objects.