Towards Understanding the Formation of Uniform Local Binary Patterns

The research reported in this paper focuses on the modeling of Local Binary Patterns (LBPs) and presents an a priori model where LBPs are considered as combinations of permutations. The aim is to increase the understanding of the mechanisms related to the formation of uniform LBPs. Uniform patterns are known to exhibit high discriminative capability; however, so far the reasons for this have not been fully explored. We report an observation that although the overall a priori probability of uniform LBPs is high, it is mostly due to the high probability of only certain classes of patterns, while the a priori probability of other patterns is very low. In order to examine this behavior, the relationship between the runs up and down test for randomness of permutations and the uniform LBPs was studied. Quantitative experiments were then carried out to show that the relative effect of uniform patterns to the LBP histogram is strengthened with deterministic data, in comparison with the i.i.d. model. This was verified by using an a priori model as well as through experiments with natural image data. It was further illustrated that specific uniform LBP codes can also provide responses to salient shapes, that is, to monotonically changing intensity functions and edges within the image microstructure. 1. Introduction The Local Binary Pattern (LBP) methodology [1] was first proposed as a texture descriptor, but it has later been applied to various other fields of computer vision: for example, face recognition, facial expression recognition, modeling motion and actions, as well as medical image analysis. Numerous modifications and improvements have been suggested to the original LBP methodology for various applications, while the LBPs have also been proposed for signal processing tasks beyond image processing (e.g., [2]). A detailed list of various applications and papers related to the LBP methodology is available in CMV Oulu pages [3]. Before the introduction of Local Binary Patterns, co-occurrence statistics descriptors based on binary features and -tuples [4], as well as the texture unit and texture spectrum (TUTS) method [5], have been studied. -tuples have been studied in, for example, [4, 6] for texture retrieval. It was discovered that the distribution of individual -tuples could not reach the classification accuracy of quantized binary features such as BTCS [4]. The possibility of using only uniform and rotation invariant binary patterns distinguishes the Local Binary Pattern methodology from its predecessors, because it enables a more compact image