A Measure Theoretic Approach to Image Segmentation Framed in Terms of Intensities

For the case of gray-scale images, we will formulate the problem of image segmentation based on the distribution of intensities in the image interpreted in a probabilistic sense. This leads to a finite-dimensional optimization problem, for which the optimality system will be derived and discussed. Application of a fixed-point iteration to this system leads to the well-known k-means clustering algorithm, for which this therefore is a measure theoretic justification and derivation. The reformulation also enables very ecient