目前，已有理論證實模糊辨識系統(fuzzy inference system)與徑向基底函數(Radial Basis Function ,RBF)神經網路可視為功能上的相等。本篇論文目的在於根據fuzzy inference中的模糊規則，來辨識腹腔CT影像中的器官，並使用RBF神經網路完成模糊辨識系統之架構。我們將運用一些模糊描述符號(fuzzy descriptors)來描述CT影像分割後的各個區域，並在我們的模糊辨識系統中，建構出模糊規則。

傳統的RBF使用Gaussian函數做為其基底函數，並以最小均方(Least Mean Square)法則為網路的目標函數。然而，這裡存在主要的二個問題。第一，網路輸出值無法逼近常數。第二，當訓練樣本含有重大誤差時，網路將無法正確地逼近這些訓練樣本。為了克服這二個問題，我們將在本篇論文應用robust RBF做為器官辨識的網路。

It has been demonstrated that the RBF neural network and the fuzzy inference are functional equivalent. This paper proposes to identify abdominal organs from CT images by using the fuzzy rules, and fuzzy inference system based on the Radial Basis Function (RBF) neural network. A number of fuzzy descriptors are applied to ascertain the segmented regions and to form fuzzy rules in our inference system.

The traditional RBF network takes Gaussian functions as its basis functions and adopts the least squares criterion as the objective function. However, it suffers from two major problems. First, it is difficult to approximate constant values. Second, when the training patterns incur a large error, the network will interpolate these training patterns incorrectly. In order to cope with these problems, a robust RBF network is employed in this paper to recognize the organ of interest.

目 錄

書名頁 ……………………………………………………………………… i
中文提要 …………………………………………………………………… ii
英文提要 …………………………………………………………………… iii
目錄 ………………………………………………………………………… iv
圖目錄 ……………………………………………………………………… vi
表目錄 ……………………………………………………………………… viii
符號說明 …………………………………………………………………… ix
一、　　　　 研究動機 …………………………………………………… 1
二、　　　　 模糊推論系統與徑向基底函數神經網路…………………… 5
2.1 模糊推論系統 ……………………………………………… 5
2.2 Takagi-Sugeno 模糊推論之模型…………………………… 7
2.3 徑向基底函數神經網路 …………………………………… 8
2.4 傳統RBF網路的學習過程 ………………………………… 10
2.5 Robust RBF之網路架構 …………………………………… 14
2.6 使用RBF網路完成模糊推論 ……………………………… 16
三、 研究方法……………………………………………………… 17
3.1 研究架構……………………………………………………… 17
3.2 使用之方法…………………………………………………… 18
3.2.1 簡介 …………………………………………………… 18
3.2.2 前置處理 ……………………………………………… 19
3.2.3 使用之模糊變數 ……………………………………… 21
3.2.4 Robust RBF網路使用之目標函數 …………………… 27
3.2.5 建構本實驗之目標函數 ……………………………… 29
3.2.6 Robust RBF網路的學習法則 ………………………… 30
3.2.7 動態調整網路節點數之規則 ………………………… 32
四、 實驗結果……………………………………………………… 33
4.1 函數逼近(function approximation)實驗……………………… 33
4.2 使用robust RBF網路完成CT器官影像辨識 ……………… 36
五、 結果與討論…………………………………………………… 41
參考文獻 ………………………………………………………………… 42

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