PET影像中，高亮度的區塊常被視為疑似腫瘤產生的地方。若能將PET影像中的腫瘤部位精確的分割出來，將會對醫生的診療有很大的幫助。近年來，由於PET/CT的發明，它結合了PET 和CT的優點，能將腫瘤細胞的活動狀況及位置融合在同一張影像中，使醫生對腫瘤診斷有更進一步的發展。而本研究在分割PET影像的同時也加進了CT影像的資訊，目的是希望能將腫瘤細胞更精確的分割出來。
我們使用Gaussian mixture model (GMM) 對PET和CT的融合影像作分割。此外，我們考慮了PET和CT的相關性，使用一個二維的GMM對PET/CT影像作分割。我們還在GMM中加入空間相關性，將影像的中每一個像素都考慮它們的鄰近點，然後使用一個多維的GMM模型去配適。這些方法的結果均較單對PET影像作分割的結果為佳。

The specific brightened regions of PET images are the suspected regions of tumor. Segmenting the region of tumor on PET images will be very helpful to doctors. In recent years, the invention of Positron emission tomography/computed tomography (PET/CT) has allowed combination of the advantages of PET and CT: namely, that the activities and location of tumor cells can be merged in one image. This merged images provides significant progress for doctors diagnosing tumors. In this study, the information of CT is used when segmenting the PET images. The aim is to enhance accuracy of segmenting the regions of tumor.
The fusion images of PET and CT are segmented by Gaussian mixture model (GMM). In addition, a two-dimensional GMM is used to fit the PET and CT image data by considering the correlation of PET and CT. The spatial dependence is also considered in a GMM. Our approach is to consider points surrounding each pixel to fit a multi-dimensional GMM to the data. These methods all have better performance than the result of only implementing segmenting PET images in this study.

Chapter 1 Introduction 1
Chapter 2 Methodologies 1
2.1 Gaussian Mixture Model (GMM) 3
2.2 Using Spatial Dependence in GMM 6
2.3 Determine the Initial Parameters of GMM 8
2.4 Bayesian Information Criterion for Model Selection 10
2.5 The Method of Fused PET and CT Images 10
2.6 F-measure 11
2.7 Procedure 12
Chapter 3 Phantom Study 14
Chapter 4 Conclusions 23
Reference 24

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