應用位能場模型於三維物體之骨架抽取

Abstract

本篇論文是在探討一有效率擷取三維物體骨架的方法。為求有效率的計算 ﹐我們運用廣義位能場模型取代了距離函數。對距離而言﹐廣義位能場的 強度比牛頓位能場衰退得快﹐且這些位能場方程式和它們的階度對多面體 區域而言﹐具有解析形式﹐因而被我們所採用。三維物體內部之位能谷點 相當於其骨架位置﹐且能應用類似二維的演算法[1]而取得。不似二維物 體的中心軸不能直接推廣成為三維物體之一維骨架﹐這些經廣義位能場所 得之位能谷點能構成較有意義的一維骨架。 This thesis is concerned with efficient derivation of the skeleton of a three-dimensional(3D) object. A generalized potential field model is used in place of the distance function for computational efficieny. A set of generalized potential fields which decay faster than the Newtonian potential with distance canbe used. It is shown that these functions and their gradients can be obtained in closed forms for polyhedral regions. The potential valleys of a region can thus be obtained with algorithms similar to those used in [1] for 2D regions. While the medial axis can not be generalized directly to the 3D space as 1D skeleton, the potential valleys, being one dimensional, form a valid skeleton.