  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.
