The paper provides a mathematical view to the binary numbers presented in the Local Binary Pattern (LBP) feature extraction process. Symmetric finite difference is often applied in numerical analysis to enhance the accuracy of approximations. Then, the paper investigates utilization of the symmetric finite difference in the LBP formulation for face detection and facial expression recognition. It introduces a novel approach that extends the standard LBP, which typically employs eight directional derivatives, to incorporate only four directional derivatives. This approach is named symmetric LBP. The number of LBP features is reduced to 16 from 256 by the use of the symmetric LBP. The study underscores the significance of the number of directions considered in the new approach. Consequently, the results obtained emphasize the importance of the research topic.

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