Bounds for Haralick features in synthetic images with sinusoidal gradients - Oprisan, Ana; Oprisan, Sorinel Adrian (Frontiers in Signal Processing, 2023)
The Gray Level Cooccurrence 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 the GLCM only measures the frequency of occurrence of pairs of gray level pixels at a given distance from each other, it stores information regarding the gradients of gray level intensities in the original image. We proved that a gradient of k gray levels per pixel in an image generates GLCM entries on the k-th parallel line to the main diagonal. Haralick features are numerical values associated with GLCM. We found 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 estimated bounds for four of the most often used Haralick features, i.e., Energy, Contrast, Correlation, and Entropy. We found good agreement between our analytically predicted values of Haralick features and the numerical results from synthetic images of sinusoidal periodic gradients. 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.