本文研究一種以熵加權局部強度聚類為基礎的不均勻影像分割模型，用於分割因為採集過程偏置場所產生的強度不均勻影像。該模型最小化一個由分割區域邊界總長度的正則化項和局部熵加權的數據擬合項所組成的能量泛函，其中分割邊界的長度由熱核與分割區域的特徵函數進行卷積來近似，而數據擬合項由偏置場模型與局部強度聚類性質相結合後，再進一步由局部熵加權所產生。最終所得出的熵加權模型可以同時分割影像並估計用於校正強度不均勻影像的偏置場。此外，所考慮的熵加權模型可以應用迭代卷積閾值法有效地實現。最後，我們進行一系列數值實驗以展示所提出方法的有效性與穩健性。

In this thesis, we study an entropy-weighted local intensity clustering-based model for inhomogeneous image segmentation. The intensity inhomogeneity mainly arises from the bias field in improper image acquisition. The considered model minimizes an energy functional consisting of a regularization term for the total length of the segmentation boundary and a data fitting term weighted by local entropy. The total length is approximated by the convolution of the heat kernel and the characteristic functions of the segmentation regions. The data fitting term is generated by combining the bias field model and the local intensity clustering property, further weighted by the local entropy. The model can simultaneously segment the inhomogeneous image and estimate the bias field for image correction. Furthermore, we can efficiently realize the model using an iterative convolution-thresholding scheme. Finally, we conduct many numerical experiments to demonstrate the effectiveness and robustness of the method.

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