Affine invariant texture segmentation and shape from texture by variational methods

We address the problem of texture segmentation by rising a novel affine invariant model. The introduction of affine invariance as a requirement for texture analysis goes beyond what is known of the human performance and also beyond the psychophysical theories. We propose to compute texture features using affine invariant intrinsic neighborhoods and affine invariant intrinsic orientation matrices. We discuss several possibilities for the definition of the channels and give comparative experimental results where an affine invariant Mumford-Shah type energy functional is used to compute the multichannel affine invariant segmentation. We prove that the method is able to retrieve faithfully the texture regions and to recover the shape from texture information in images where several textures are present. The numerical algorithm is multiscale.