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In this correspondence, a completed modeling of the local binary pattern (LBP) operator is proposed and an associated completed LBP (CLBP) scheme is developed for texture classification. A local region is represented by its center pixel and a local difference sign-magnitude transform (LDSMT). The center pixels represent the image gray level and they are converted into a binary code, namely CLBP-Center (CLBP_C), by global thresholding. LDSMT decomposes the image local differences into two complementary components: the signs and the magnitudes, and two operators, namely CLBP-Sign (CLBP_S) and CLBP-Magnitude (CLBP_M), are proposed to code them. The traditional LBP is equivalent to the CLBP_S part of CLBP, and we show that CLBP_S preserves more information of the local structure than CLBP_M, which explains why the simple LBP operator can extract the texture features reasonably well. By combining CLBP_S, CLBP_M, and CLBP_C features into joint or hybrid distributions, significant improvement can be made for rotation invariant texture classification.