Rigid motion invariant classification of 3D-textures

Abstract—This paper studies the problem of 3-D rigid-motion-invariant texture discrimination for discrete 3-D textures that are spatially homogeneous by modeling them as stationary Gaussian random fields. The latter property and our formulation of a 3-D rigid motion of a texture reduce the problem to the study of 3-D rotations of discrete textures. We formally develop the concept of 3-D texture rotations in the 3-D digital domain. We use this novel concept to define a “distance ” between 3-D textures that remains invariant under all 3-D rigid motions of the texture. This concept of “distance ” can be used for a monoscale or a multiscale 3-D rigid-motion-invariant testing of the statistical similarity of the 3-D tex-tures. To compute the “distance ” between any two rotation