本篇論文中，我們提出一個多解析度圖形分割架構，以針對磁振造影頭部影像進行純腦和非腦區域的分割，並達到高敏感度和高精確度的純腦區域擷取目標。首先，我們所提出的方法從一個具有高敏感度和低精確度的腦部影像著手，接著將該影像從較低的解析度到較高的解析度一層一層地修剪非腦部的區域，以修正起始切割的結果。在解析度較低的純腦區域擷取結果會被傳遞到解析度較高的層級，用來做為圖形分割所需的前景和背景種子的限制。我們提出一個在處理非最高層解析度的影像時預先被定義的前景區域，以用來減少圖形分割中的捷徑問題。為了考慮亮度分布不均的影響，我們把每個解析度的影像分成不同數目的小立方體，以進行區域性的亮度分布估算，而圖形分割方法則個別被套用在每一立方體中。我們的實驗使用了四組資料來比較我們所提出的方法和四個文獻上的純腦區域擷取方法，這四組資料分別是： Internet Brain Segmentation Repository (IBSR) 的第一和第二組資料、Montreal Neurological Institute 的 BrainWeb 腦部模擬影像、與台北榮民總醫院的健康受試者。四個一起比較的純腦區域擷取方法則分別是：Brain Surface Extractor、Brain Extraction Tool、Hybrid Watershed algorithm 和 ISTRIP。在對純腦區域擷取的表現評估方面，使用 IBSR 的第一和第二組資料以及 BrainWeb 的腦部模擬影像時，我們的方法比其他的方法表現傑出；而在使用台北榮民總醫院的資料方面，我們所提方法的準確度和 BET 與 ISTRIP 是相當的。

We proposed a multiresolutional brain extraction framework which utilize graph cuts technique to classify head magnetic resonance (MR) images into brain and non-brain regions.Our goal is to achieve both high sensitivity and specificity results of brain extraction. Started with an extracted brain with high sensitivity and low specificity, we refine the segmentation results by trimming non-brain regions in a coarse-to-fine manner.
The extracted brain at the coarser level will be propagated to the finer level to estimate foreground/background seeds as constraints.
The short-cut problem of graph cuts is reduced by the proposed pre-determined foreground from the coarser level.
In order to consider the impact of the intensity inhomogeneities, we estimated the intensity distribution locally by partitioning volume images of each resolution into different numbers of smaller cubes.
The graph cuts method is individually applied for each cube.
The proposed method was compared to four existing methods, Brain Surface Extractor, Brain Extraction Tool, Hybrid Watershed algorithm, and ISTRIP, by using four data sets, the first and the second IBSR data set of the Internet Brain Segmentation Repository, BrainWeb phantom images from the Montreal Neurological Institute, and healthy subjects collected by Taipei Veterans General Hospital.
The performance evaluation for brain extraction, our method outperforms others for the first/second IBSR data set and BrainWeb phantom data set, and performs comparably with the BET and ISTRIP methods when using the VGHTPE data set.

1 Introduction 1
1.1 Brain extraction . . . . . . . . . . . . . 2
1.1.1 Related works of brain extraction . . . . . . . . . . . . . . . . . . 4
1.2 Max-flow and min-cut . . . ....... . . . . 9
1.2.1 Ford and Fulkerson max-flow algorithm .. . 9
1.2.2 Graph cuts . ... . . . . . . . . . . . . . 11
1.3 Motivation of this work . . . . . . . . . . . . 17
2 Multiresolutional graph cuts for brain extraction 19
2.1 Flowchart of multiresolutional brain extraction . 20
2.2 Removal of bright voxels in non-WM regions . . 22
2.3 Graph cuts for brain extraction . . . . . . . . 25
2.3.1 Edge weights in the graph cuts method .. . . . 25
2.3.2 Multiresolutional graph cuts for brain extraction . . . 30
2.4 Postprocessing to fill holes that dark brain region be classified as background by graph cuts . 33
3 Results for brain extraction 41
3.1 Image data sets for performance evaluation . . . . 42
3.2 Evaluation metrics for brain extraction . . 43
3.3 Experimental results . . . . . . . . . . 45
4 Discussion 59
5 Conclusions 63

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