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Motivated by researching new image texture modeling that improves state-of-the-art LBP variants and non-LBP descriptors, this paper proposes a novel approach for constructing local image descriptors, which are suitable for histogram based image representation. Instead of heuristic code constructions, the proposed approach is based on local concave-and-convex characteristics, which have high ability to extract discriminative and stable texture representation. Different from the majority of descriptors that only encode relationships between the pixels in doublets around central pixel (within 3  ×  3 neighborhood), the proposed approach encodes relationships between the pixels in triplets by including the central pixel in the modeling. We build two distinct descriptors by dividing local features into two distinct groups, i.e., local concave and convex microstructure patterns (LCvMSP and LCxMSP), according to …