In this paper, we introduce a new image descriptor for broad Image Categorization, the Progressive Randomization (PR), that uses perturbations on the values of the Least Significant Bits (LSB) of images. We show that different classes of images have a distinct behavior under our methodology, and that using statistical descriptors of LSB occurrences and enough training examples, the method already performs as well or better than comparable existing techniques in the literature. With few training examples, PR still has good separability, and its accuracy increases with the size of the training set. We validate our method using four image databases with different categories.