The rapid growth of image data has led to the development of advanced image processing and computer vision techniques, which are crucial in various applications such as image classification, image segmentation, and pattern recognition. Texture is an important feature that has been widely used in many image processing tasks. Therefore, analyzing and understanding texture plays a pivotal role in image analysis and understanding.Local binary pattern (LBP) is a powerful operator that describes the local texture features of images. This paper provides a novel mathematical representation of the LBP by separating the operator into three matrices, two of which are always fixed and do not depend on the input data. These fixed matrices are analyzed in depth, and a new algorithm is proposed to optimize them for improved classification performance. The optimization process is based on the singular value decomposition (SVD) algorithm. As a result, the authors present optimal LBPs that effectively describe the texture of human face images. Several experiment results presented in this paper convincingly verify the efficiency and superiority of the optimized LBPs for face detection and facial expression recognition tasks.

翻译：图像数据的快速增长推动了先进图像处理与计算机视觉技术的发展，这些技术在图像分类、图像分割和模式识别等众多应用中至关重要。纹理作为一种重要特征，已被广泛应用于多种图像处理任务中，因此分析与理解纹理在图像分析与理解中发挥着关键作用。局部二值模式(LBP)是一种描述图像局部纹理特征的有效算子。本文通过将LBP算子分解为三个矩阵，提出了一种新颖的数学表示方法，其中两个矩阵始终保持固定且不依赖于输入数据。我们对这些固定矩阵进行了深入分析，并提出了一种基于奇异值分解(SVD)算法的新优化方法以提升分类性能。最终，作者提出了能够有效描述人脸图像纹理的最优LBP算子。本文展示的多组实验结果有力验证了优化后LBP在人脸检测与面部表情识别任务中的高效性与优越性。