Characterization of Complex Image Spatial Structures Based on Symmetrical Weibull Distribution Model for Texture Pattern Classification

Texture pattern classification has long been an essential issue in computer vision (CV). However, texture is a kind of perceptual concept of human beings in scene observation or content understanding, which cannot be defined or described clearly in CV. Visually, the visual appearance of the complex spatial structure (CSS) of texture pattern (TP) generally depends on the random organization (or layout) of local homogeneous fragments (LHFs) in the imaged surface. Hence, it is essential to investigate the latent statistical distribution (LSD) behavior of LHFs for distinctive CSS feature characterization to achieve good classification performance. This work presents an image statistical modeling-based TP identification (ISM-TPI) method. It firstly makes a theoretical explanation of the Weibull distribution (WD) behavior of the LHFs of the imaged surface in the imaging process based on the sequential fragmentation theory (SFT), which consequently derives a symmetrical WD model (SWDM) to characterize the LSD of the TP’s SS. Multidirectional and multiscale TP features are then characterized by the SWDM parameters based on the oriented differential operators; in other words, texture images are convolved with multiscale and multidirectional Gaussian derivative filters (GDFs), including the steerable isotropic GDFs (SIGDFs) and the oriented anisotropic GDFs (OAGDFs), for the omnidirectional and multiscale SS detail exhibition with low computational complexity. Finally, SWDM-based TP feature parameters, demonstrated to be directly related to the human vision perception system with significant physical perception meaning, are extracted and used to TP classification with a partial least squares-discriminant analysis- (PLS-DA-) based classifier. The effectiveness of the proposed ISM-TPI method is verified by extensive experiments on three texture image databases. The classification results demonstrate the superiority of the proposed methods over several state-of-the-art TP classification methods.