隨著3D建模技術的快速發展，我們可以獲得虛擬的物體，像是山形、建築、橋梁、人臉等等。但是如何運用3D的虛擬資訊來探討物體的形變是一個很重要的課題。3D建模的資料型式主要可以分為兩類：立體像素和點雲。本文探討的目標是物體的表面結構，因此以點雲作為實驗的資料。
在傳統二維影像上要進行兩物體間差異的比對，經常是使用影像直接相減的方式，既簡單又快速，然而在三維影像上，除了多了一個維度所造成的較大變異性外，點雲資料座標系統一致性的問題也必須考慮（例如：經由不同的三維建模技術所獲得的資料間比對），因此若要直接比對兩物體間的差異則更加困難。疊代最近點演算法（Iterative Closest Point, ICP）提供了找出對應點的方法，相關的應用也陸續出現，例如：兩物體間的對齊、人臉與手部辨識、相機追蹤等等。但這些應用皆未探討物體型變的問題，更無提供型變程度量化的估算方法。本文在兩物體的比對過程中，先經由物體的位置偵測使兩物體進行初估的疊合，再使用ICP演算法做細部的定位，接著利用所找到的對應點，計算出法向量與歐式距離等特徵，並進而確認兩物體間有形變差異的點雲資料，最後，提出一個幾何估算方法了解物體形變的程度。從實驗結果中可知本論文的方法能有效的比對出物體的形變位置，以及提供幾何形變程度估算的量化數據。

With 3D modeling technologies, we can build virtual objects (point clouds), such as mountains, buildings, and faces. These 3D virtual objects help us obtain more information than traditional 2D images. In 2D cases, we can easily evaluate the similarity measure between two images. However, it is not easy for us to do so between two 3D virtual objects, especially when they are obtained from different devices (different coordinate systems). Iterative Closest Point (ICP) provides a way to find corresponding points between two point cloud data. It has been applied to many fields, such as object alignment, face and hand recognition, camera tracking, etc. However, it does not provide a geometric measure between two models for deformation evaluation. In this thesis, we propose a geometric measure method based on ICP. This measure is used to evaluate the degree of deformation. From experimental results, the proposed method can detect the local deformation area and give a quantitative evaluation between the original object and deformed one.

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