Four-Color Theorem and Level Set Methods for Watershed Segmentation
Four-Color Theorem and Level Set Methods for Watershed Segmentation
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DOI：
10.1007/s11263-008-0199-4
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发表时间：
2009-05-01
影响因子：
19.5
通讯作者：
Gerdes, Hans-Hermann
中科院分区：
文献类型：
--
作者：
Hodneland, Erlend;Tai, Xue-Cheng;Gerdes, Hans-Hermann
提出了一种基于标记控制的正则化分水岭分割方法。只有少数以前的研究解决的任务，正规化从传统的标记控制的分水岭分割得到的分水岭线。在本公式中，地形距离函数应用于水平集公式中以执行分割，并且通过正则化水平集函数来容易地完成正则化。基于著名的四色定理，数学模型的建议的想法。利用该模型，可以用一个或两个水平集函数分割具有任意相位数的任何二维图像。该算法已在显示大鼠癌细胞的真实的2D荧光显微图像上进行了测试，并且该算法在MATLAB中实现时也与标准分水岭分割进行了比较。对于一组固定的标记和一组具有挑战性的图像，这两种方法的比较表明，目前的水平集制定执行比标准的分水岭分割。
A marker-controlled and regularized watershed segmentation is proposed for cell segmentation. Only a few previous studies address the task of regularizing the obtained watershed lines from the traditional marker-controlled watershed segmentation. In the present formulation, the topographical distance function is applied in a level set formulation to perform the segmentation, and the regularization is easily accomplished by regularizing the level set functions. Based on the well-known Four-Color theorem, a mathematical model is developed for the proposed ideas. With this model, it is possible to segment any 2D image with arbitrary number of phases with as few as one or two level set functions. The algorithm has been tested on real 2D fluorescence microscopy images displaying rat cancer cells, and the algorithm has also been compared to a standard watershed segmentation as it is implemented in MATLAB. For a fixed set of markers and a set of challenging images, the comparison of these two methods shows that the present level set formulation performs better than a standard watershed segmentation.