保角曲面形變的應用---虛擬播報

Abstract

形變是一個圖像變成另一個圖像的過程。本論文中，我們將著重在人臉曲面的保角形變。根據黎曼映射定理，一個簡單的連通曲面，存在唯一的黎曼保角映射，可將此曲面映射到單位圓盤上。因此我們將三維人臉曲面的對應問題化簡成二維的單位圓盤對應問題。其中我們還透過保角映射與拓樸同倫的概念，進行曲面三角網格的統一，再進行曲面的對應以完成形變。本論文的結果，將根據上述的概念，重建三維人臉虛擬播報的影片。

Morphing is the process of changing one figure to another. In this study, we focus on the conformal morphing on the facial surface. According to the Riemann mapping theorem, we know that there exists a unique Riemann conformal mapping to map a simply connected surface to a unit disk. Hence, we reduce the 3D facial surface matching problem to a unit disk matching problem. Among the process of morphing, we also use the concept of conformal mapping and homotopy to uniform structure of triangular mesh on surface, and then complete the surface matching. The result of this study will be based on those concepts to reconstruct the virtual broadcasting film with facial surface.