On the Occurrence Probability of Local Binary Patterns: A Theoretical Study

It is well-known that local binary pattern (LBP) histograms of real textures exhibit a markedly uneven distribution, which is dominated by the so-called uniform patterns. The widely accepted interpretation of this phenomenon is that uniform patterns correspond to texture microfeatures, such as edges, corners, and spots. In this paper we present a theoretical study about the relative occurrence of LBPs based on the consideration that the LBP operator partitions the set of grayscale patterns into an ensemble of disjoint multidimensional polytopes. We derive exact prior probabilities of LBPs by calculating the volume of such polytopes. Our study puts in evidence that both the uneven distribution of the LBP histogram and the high occurrence of uniform patterns are direct consequences of the mathematical structure of the method rather than an intrinsic property of real textures.