近年來，3D風潮如同旱地驚雷般地在所有領域颳起一陣旋風，諸如遊戲、動畫、網路、機械、娛樂，大量的三維模型應運而生。如此大量的三維模型資料庫在搜尋上將造成相當大的問題。
一般關鍵字的搜尋方式不僅不直覺，而且隨著每個人主觀的分類不同，往往不能滿足我們在三維模型萃取上的需求。而傳統二維影像的搜尋、比對，其資訊僅止於顏色，較為容易處理。而三維模型則擁有相當多而且複雜的特性，至目前為止，仍未有可以稱作標準的處理方式。我們在此延伸skeletal matching的方式，建立一新的比對方式-拼圖式axis to axis的比對來解決三維模型相似度的比較問題。
本論文主要是利用表面距離來建立一個類似骨架的Reeb graph，Reeb graph能夠抵抗各種三維模型的旋轉、平移、縮放等等問題，並且概略地表示整個模型的骨架。而評比兩個模型相似度則可以透過簡單的評比兩個Reeb graph來達成，我們模擬人類拼圖的方式將較為特殊、容易辨識的部分先對應起來，藉此降低對應錯誤的機率，有別於一般深度優先（depth-first）或廣度優先(width-first)的循序對應方式，我們比對的順序將是依照發生對應錯誤的機率的順序來處理。
我們採用不同的表面距離估算方式來達到即使不需切割模型三角形也能估計出相當正確的表面距離值，並由此建立Reeb graph。最後採用拼圖式axis to axis的比對降低錯誤對應的發生，使三維模型萃取的結果更加合理。

Due to the fast development of three dimensional model in many fileds, like game, animation, network, mechanical engineering and entertainments, we believe that searching three dimensional models in database will become more important.
A traditional searching method, keyword searching, is not a stable method. Because the classify standard of each people is different, it can’t satisfy our requirement in three dimensional retrieval. In two dimensional image retrieval, the problem is easier because only one information, color, in a image. But in three dimensional model retrieval problem, there isn’t a standard function which can evaluate similarity between two models. We use a matching method to evaluate similarity between two skeletal graphs of models, namely 2-pass axis-to-axis matching method. The method is like a jigsaw puzzle.
We first use geodesic distance to establish a skeletal graph - Reeb graph. It can roughly represent the skeleton of model and invariant to translation, rotation, scaling. Then we match two Reeb graphs and evaluate similarity. When matching two Reeb graphs, a concept of matching significant node first is used. It is different to depth-first and width-first, and we will matching most significant node first.
We don’t need to subdivide triangles of model by using modified fast marching method, and we can approximate the geodesic distance. Building Reeb graph by geodesic distance and evaluating similarity between two Reeb graph by using our 2-pass axis-to-axis matching method.

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