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.

翻译：本文从数学视角分析了局部二值模式特征提取过程中呈现的二进制数值。对称有限差分在数值分析中常用于提高近似计算的精度。随后，本文探讨了在面向人脸检测与表情识别的LBP框架中应用对称有限差分的可行性，并提出了一种创新方法。该方法将标准LBP（通常采用八个方向导数）扩展为仅包含四个方向导数的形式，并将其命名为对称LBP。通过采用对称LBP，特征数量从256个减少至16个。本研究强调了新方法中方向数量选择的重要性，最终所得结果凸显了该研究课题的价值。