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.
Relation:
先進工程學刊，6(2)，87-95 Journal of Advanced Engineering, 6(2), 87-95
