Image segmentation aims at identifying regions of interest within an image, by grouping pixels according to their properties. This task resembles the statistical one of clustering, yet many standard clustering methods fail to meet the basic requirements of image segmentation: segment shapes are often biased toward predetermined shapes and their number is rarely determined automatically. Nonparametric clustering is, in principle, free from these limitations and turns out to be particularly suitable for the task of image segmentation. This is also witnessed by several operational analogies, as, for instance, the resort to topological data analysis and spatial tessellation in both the frameworks. We discuss the application of nonparametric clustering to image segmentation and provide an algorithm specific for this task. Pixel similarity is evaluated in terms of density of the color representation and the adjacency structure of the pixels is exploited to introduce a simple, yet effective method to identify image segments as disconnected high-density regions. The proposed method works both to segment an image and to detect its boundaries and can be seen as a generalization to color images of the class of thresholding methods.

中文翻译：

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非参数聚类的图像分割

图像分割旨在通过根据像素的属性对像素进行分组来识别图像中的关注区域。此任务类似于统计上的聚类之一，但是许多标准聚类方法无法满足图像分割的基本要求：片段形状经常偏向预定形状，并且很少自动确定其数量。原则上，非参数聚类不受这些限制，并且特别适合于图像分割任务。几个操作类比也证明了这一点，例如，在两个框架中都采用拓扑数据分析和空间细分。我们讨论了非参数聚类在图像分割中的应用，并提供了专门针对此任务的算法。根据颜色表示的密度评估像素相似度，并利用像素的邻接结构引入一种简单而有效的方法，将图像段识别为断开的高密度区域。所提出的方法既可以分割图像也可以检测其边界，并且可以看作是对阈值方法类别的彩色图像的概括。