自組織映射網路及核算理論於隱函曲面重建

Implicit Surface Reconstruction Based on SOM Network and Kernel Method

10.29948/JAE.201104.0003

王中行(Chung-Shing Wang)；賴泰華(Tai-Hua Lai)；張庭瑞(Teng-Ruey Chang)

逆向工程 ； 曲面重建 ； 隱函曲面 ； 類神經網路 ； 核算法 ； reverse engineering ； surface reconstruction ； implicit surface ； neural network ； kernel methods

先進工程學刊

6卷2期（2011 / 04 / 01）

87 - 95

繁體中文

諸多有關隱函曲面(Implicit Surface)的文獻指出，透過徑向基函數(Radial Basis Function, RBF)核算(Kernel Method)來建立隱函曲面雖有許多好處，卻也存在某些限制：龐大的樣本數除了需要大量的系統資源來存取矩陣資料外，大量的RBF中心將造成系統計算上嚴重之負擔，使得以該方法為基礎的隱函曲面建構論毫無用處。故本研究運用自組織映射(Self-Organizing Map, SOM)網路結合核算理論，由快速重建為方向，從事深入的理論探討及模擬，研擬的課題包括「SOM特徵擷取」及「RBF建面」等子題。由研究結果可知，透過SOM網路，我們可得到足以描述原模型幾何的特徵資料，而核化的算則，則使得隱函曲面的計算更加簡單且有效率，也確實達到文中所預期的破面修補效果。

The benefits of modeling implicit surface with RBF Kernel have been recognized by numerous bibliographies. Nonetheless, this work was restricted to small problems by the storage and arithmetic operations of direct method. When processing the RBF kernel estimate, to considerate whole Euclidean distance between RBF centers and instances is required. A large number of instances require enormous system resources to access the matrix data, and considerable RBF centers may cause heavy computational burden. Therefore, fitting RBF Kernel to 3D scattered data has not been regarded as computationally feasible for large data sets. For this purpose, we crystallize our research goal that aimed at an in-depth investigation of several related domestic and international research in the scope of implicit surface, with SOM network and kernel method, both in theory and experiment. Depend on research results; we can obtain geometric features which describe the original model sufficiently by using the SOM network. Otherwise, kernel methods make calculating of the implicit surface more simply and efficiently, and perform the hole-filling processing indeed what we expected.