Persistent homology for object segmentation in multidimensional grayscale images
Persistent homology for object segmentation in multidimensional grayscale images
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DOI：
10.1016/j.patrec.2018.08.007
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发表时间：
2018-09-01
影响因子：
5.1
通讯作者：
Kacim, Mohammad
中科院分区：
文献类型：
--
作者：
Assaf, Rabih;Goupil, Alban;Kacim, Mohammad
在本文中，我们发展了一种源自代数拓扑的方法，并证明了它在不需要先验参数的情况下进行多维对象分割的能力。持久同调是代数拓扑中用于研究数据在不同尺度上持续存在的定性特征的一种方法。在图像上构造拓扑复合体之后是一个过滤方案，该方案由组成一个嵌套的细胞复合体序列组成，在该序列上计算持久的同源性。通过识别具有长寿命的1D和2D链来提取最持久的同源类，从而可以对2D和3D图像中的突出对象进行分割和检测。将该方法与其他合成图像分割技术进行了比较，表明了该方法的优越性。该技术的优点体现在它对输入函数的连续变形和扰动不敏感以及它与先验参数的独立性。在真实和生物医学二维和三维图像上获得的结果也证明了该方法的潜力。(c) 2018 Elsevier B.V.版权所有
In this paper, we develop a methodology originating from algebraic topology, and we demonstrate its capability of performing multidimensional object segmentation without the need of prior parameters. Persistent homology is a method used in algebraic topology to study qualitative features of data that persist across varying scales. The construction of a topological complex on the image is followed by a filtration scheme that consists of composing a nested sequence of cell complexes on which the persistent homology is computed. The most persistent homology classes are extracted by identifying 1D and 2D chains with large lifespans, which allows salient objects in 2D and 3D images to be segmented and detected. A comparison between this method and other segmentation techniques on a synthetic image shows the advantages of the proposed method. The strength of this technique is reflected in its insensitivity to continuous deformations and perturbations of the input function and in its independence of prior parameters. The results obtained on real and biomedical 2D and 3D images also demonstrate the potential of this method. (c) 2018 Elsevier B.V. All rights reserved.