Similarity measure has long played a critical role and attracted great interest in various areas such as pattern recognition and machine perception. Nevertheless, there remains the issue of developing an efficient two-dimensional (2D) robust similarity measure method for images. Inspired by the properties of subspace, we develop an effective 2D image similarity measure technique, named transformation similarity measure (TSM), for robust face recognition. Specifically, the TSM method robustly determines the similarity between two well-aligned frontal facial images while weakening interference in the face recognition by linear transformation and singular value decomposition. We present the mathematical features and some odds to reveal the feasible and robust measure mechanism of TSM. The performance of the TSM method, combined with the nearest neighbor rule, is evaluated in face recognition under different challenges. Experimental results clearly show the advantages of the TSM method in terms of accuracy and robustness.

相似性度量长期以来一直发挥着至关重要的作用，并在模式识别和机器感知等各个领域引起了极大的兴趣。然而，仍然存在为图像开发有效的二维（2D）鲁棒相似度测量方法的问题。受子空间属性的启发，我们开发了一种有效的2D图像相似性度量技术，称为变换相似性度量（TSM），用于鲁棒的人脸识别。具体而言，TSM方法可稳固地确定两个对齐良好的正面人脸图像之间的相似性，同时通过线性变换和奇异值分解来减弱人脸识别中的干扰。我们介绍了数学特征和一些可能性，以揭示TSM可行且健壮的度量机制。TSM方法的性能，结合最近邻规则，在不同挑战下对人脸识别进行评估。实验结果清楚地表明了TSM方法在准确性和鲁棒性方面的优势。