Texture Feature Extraction: GMRF, HMT, Laws Texture Measures, and Fractal Box Dimension

This article provides a detailed explanation of image processing and analysis techniques using Gaussian Markov Random Field (GMRF), Hidden Markov Tree (HMT), Laws texture measures, and fractal box dimension features. The GMRF method analyzes pixel relationships through spatial dependencies modeled by Markov random fields, typically implemented using neighborhood-based parameter estimation and maximum likelihood approaches. HMT methodology determines pixel classification by analyzing surrounding structures through wavelet-domain hidden Markov models, where tree-structured EM algorithms are commonly employed for training. Laws texture measurement decomposes images into multiple frequency bands using predefined convolution masks (L5, E5, S5, W5, R5) and extracts energy features from each band through filtering and variance calculations. Finally, we introduce fractal box dimension features, which describe image complexity by measuring spatial dimensions at different scales using box-counting algorithms that involve grid partitioning and logarithmic regression analysis. By implementing these methods with appropriate parameter tuning and validation protocols, researchers can gain deeper insights into image characteristics and structures, establishing foundations for advanced research and practical applications in computer vision and pattern recognition.