  This article introduces the Stochastic Texture Difference method for
analyzing data at prescribed spatial and value scales. This method relies on
constrained random walks around each pixel, describing how nearby image values
typically evolve on each side of this pixel. Textures are represented as
probability distributions of such random walks, so a texture difference
operator is statistically defined as a distance between these distributions in
a suitable reproducing kernel Hilbert space. The method is thus not limited to
scalar pixel values: any data type for which a kernel is available may be
considered, from color triplets and multispectral vector data to strings,
graphs, and more. By adjusting the size of the neighborhoods that are compared,
the method is implicitly scale-dependent. It is also able to focus on either
small changes or large gradients. We demonstrate how it can be used to infer
spatial and data value characteristic scales in measured signals and natural
images.
