A compact information-theoretic framework for texture classification: Hilbert curves, amplitude-aware permutation entropy, and explainability

Texture classification requires characterizing spatial arrangements of pixel intensities, such as periodicity, directionality, and surface roughness. This task is critical across diverse domains, including remote sensing, materials science, and biomedical imaging. In this paper, we propose a two-step information-theoretic framework for texture discrimination. First, each image is transformed into a one-dimensional time series using a space-filling Hilbert curve. This approach preserves spatial locality while avoiding the introduction of a privileged scanning direction. Second, we extract a comprehensive set of eight complementary quantifiers from the resulting series: permutation entropy, statistical complexity, Fisher information (under both lexicographic and colexicographic orderings), Wasserstein distances between the ordinal-pattern distribution and the uniform distribution, weighted permutation entropy, and amplitude-aware permutation entropy. These scalar features are then used to train a support vector machine with a radial basis function kernel, utilizing nested cross-validation for hyperparameter optimization. We validate this framework on the Kylberg texture database, a benchmark consisting of 280 images across 28 classes. Our results demonstrate that while the classical complexity-entropy causality plane offers some discriminative power, amplitude-sensitive quantifiers (specifically weighted permutation entropy) are the primary drivers of performance. These findings underscore the necessity of encoding amplitude information alongside ordinal patterns for effective texture characterization.