  In the context of texture segmentation in images, and provide some
theoretical guarantees for the prototypical approach which consists in
extracting local features in the neighborhood of a pixel and then applying a
clustering algorithm for grouping the pixel according to these features. On the
one hand, for stationary textures, which we model with Gaussian Markov random
fields, we construct the feature for each pixel by calculating the sample
covariance matrix of its neighborhood patch and cluster the pixels by an
application of k-means to group the covariance matrices. We show that this
generic method is consistent. On the other hand, for non-stationary fields, we
include the location of the pixel as an additional feature and apply
single-linkage clustering. We again show that this generic and emblematic
method is consistent. We complement our theory with some numerical experiments
performed on both generated and natural textures.
