Title :
Rigid-Motion-Invariant Classification of 3-D Textures
Author :
Jain, Saurabh ; Papadakis, Manos ; Upadhyay, Sanat ; Azencott, Robert
Author_Institution :
Center for Imaging Sci., John Hopkins Univ., Baltimore, MD, USA
fDate :
5/1/2012 12:00:00 AM
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 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 R1 and R2 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 R1 and R2 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.
Keywords :
Gaussian processes; Markov processes; image classification; image texture; 3-D Gaussian Markov random fields; 3-d rigid-motion-invariant texture discrimination; Gaussian random fields; Haar measure; Kullback-Leibler divergence; discrete textures; multitiscale 3-D rigid-motion-invariant testing; rigid-motion-invariant classification; Computational modeling; Covariance matrix; Lattices; Multiresolution analysis; Orbits; Stochastic processes; Vectors; 3-D texture classification; Gaussian Markov random fields (GMRF); Kullback–Leibler (KL) divergence; isotropic multiresolution analysis (IMRA); rigid-motion invariance; volumetric textures; Algorithms; Artificial Intelligence; Image Enhancement; Image Interpretation, Computer-Assisted; Imaging, Three-Dimensional; Motion; Pattern Recognition, Automated; Reproducibility of Results; Sensitivity and Specificity;
Journal_Title :
Image Processing, IEEE Transactions on
DOI :
10.1109/TIP.2012.2185939