  This paper introduces Multiscale Anisotropic Harmonic Filters (MAHFs) aimed
at extracting signal variations over non-Euclidean domains, namely 2D-Manifolds
and their discrete representations, such as meshes and 3D Point Clouds as well
as graphs. The topic of pattern analysis is central in image processing and,
considered the growing interest in new domains for information representation,
the extension of analogous practices on volumetric data is highly demanded. To
accomplish this purpose, we define MAHFs as the product of two components,
respectively related to a suitable smoothing function, namely the heat kernel
derived from the heat diffusion equations, and to local directional
information. We analyse the effectiveness of our approach in multi-scale
filtering and variation extraction. Finally, we present an application to the
surface normal field and to a luminance signal textured to a mesh, aiming to
spot, in a separate fashion, relevant curvature changes (support variations)
and signal variations.
