Bounds for Haralick features in synthetic images with sinusoidal gradients

Abstract

Introduction: The gray-level co-occurrence matrix (GLCM) reduces the dimension of an image to a square matrix determined by the number of gray-level intensities present in that image. Since GLCM only measures the co-occurrence frequency of pairs of gray levels at a given distance from each other, it also stores information regarding the gradients of gray-level intensities in the original image.Methods: The GLCM is a second-order statical method of encoding image information and dimensionality reduction. Image features are scalars that reduce GLCM dimensionality and allow fast texture classification. We used Haralick features to extract information regarding image gradients based on the GLCM.Results: We demonstrate that a gradient of k gray levels per pixel in an image generates GLCM entries on the kth parallel line to the main diagonal. We find that, for synthetic sinusoidal periodic gradients with different wavelengths, the number of gray levels due to intensity quantization follows a power law that also transpires in some Haralick features. We estimate bounds for four of the most often used Haralick features: energy, contrast, correlation, and entropy. We find good agreement between our analytically predicted values of Haralick features and the numerical results from synthetic images of sinusoidal periodic gradients.Discussion: This study opens the possibility of deriving bounds for Haralick features for targeted textures and provides a better selection mechanism for optimal features in texture analysis applications.