Rigid-Motion-Invariant Classification of 3-D Textures

• Published in: IEEE transactions on image processing 2012-05, Vol.21 (5), p.2449-2463
• Main Authors: Jain, S., Papadakis, M., Upadhyay, S., Azencott, R.
• Format: Article
• Language: English
• Subjects: 3-D texture classification; Algorithms; Applied sciences; Artificial Intelligence; Classification; Computational modeling; Covariance matrix; Discrimination; Exact sciences and technology; Gaussian; Gaussian Markov random fields (GMRF); Image Enhancement - methods; Image Interpretation, Computer-Assisted - methods; Image processing; Imaging, Three-Dimensional - methods; Information, signal and communications theory; isotropic multiresolution analysis (IMRA); Kullback-Leibler (KL) divergence; Lattices; Mathematical models; Motion; Multiresolution analysis; Orbits; Pattern Recognition, Automated - methods; Reproducibility of Results; rigid-motion invariance; Sensitivity and Specificity; Signal processing; Stochastic processes; Studies; Surface layer; Telecommunications and information theory; Texture; Three dimensional; Three dimensional models; Vectors; volumetric textures
• ISSN: 1057-7149; 1941-0042
• DOI: 10.1109/TIP.2012.2185939

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 mill tiscale 3-D rigid- motion-invariant testing of the statistical similarity of the 3-D textures. To compute the "distance" between any two rotations R 1 and R 2 of two given 3-D textures, we use the Kullback-Leibler divergence between 3-D Gaussian Markov random fields fitted to the rotated texture data. Then, the 3-D rigid-motion-invariant texture distance is the integral average, with respect to the Haar measure of the group SO(3), of all of these divergences when rotations R 1 and R 2 vary throughout SO(3). We also present an algorithm enabling the computation of the proposed 3-D rigid-motion-invariant texture distance as well as rules for 3-D rigid-motion-invariant texture discrimination/classification and experimental results demonstrating the capabilities of the proposed 3-D rigid-motion texture discrimination rules when applied in a multiscale setting, even on very general 3-D texture models.