Curve Analysis with Applications to Archaeology

Abstract

In this thesis we discuss methods for the definition, detection, analysis, and application ofcurves on surfaces. While doubtlessly as important as curves in images, curves on surfacesgained 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 objectproperties, ridges and valleys fail to capture the shape of some objects, for example ofobjects with reliefs. We propose a new type of curves, termed relief edges, which addressesthe 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 thanother curves. Moreover, we present a novel framework for automatic estimation of theoptimal scale for curve detection on surfaces. This framework enables correct estimationof curves on surfaces of objects consisting of features of multiple scales. It is generic andcan be applied to any type of curve. We define a novel vector field on surfaces, termed theprominent 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, weaddress the problem of reconstruction of a relief object from a line drawing. Our methodis able to automatically reconstruct reliefs from complex drawings composed of hundredsof lines. Finally, we successfully apply our algorithms to archaeological objects. Theseobjects provide a significant challenge from an algorithmic point of view, since after severalthousand years underground they are seldom as smooth and nice as manually modeledobjects.