Local feature patterns are conspicuous and are widely used in computer vision, especially in face recognition and retrieval. However, a statistical descriptor that can be used in various scenarios and effectively present the detailed local discrimination information of face images is a challenging and exploring task even if deep learning technology is widelyspread. In this study, we propose a novel local pattern descriptor called the Local Clustering Pattern (LCP) in high-order derivative space for facial recognition and retrieval. Unlike prior methods, LCP exploits the concept of clustering to analyze the relationship of intra- and inter-classes of the referenced pixel and its adjacent pixels to encode the local descriptor for facial recognition. There are three tasks (1) Local Clustering Pattern (LCP), (2) Clustering Coding Scheme, (3) High-order Local Clustering Pattern. To generate local clustering pattern, the local derivative variations with multi-direction are considered and that are integrated on rectangular coordinate system with the pairwise combinatorial direction. Moreover, to generate the discriminative local pattern, the features of local derivative variations are transformed from the rectangular coordinate system into the polar coordinate system to generate the characteristics of magnitude (m) and orientation (\(\theta \)). Then, we shift and project the features (m and \(\theta \)), which are scattered in the four quadrants of polar coordinate system, into the first quadrant of polar coordinates to strengthen the relationship of intra- and inter-classes of the referenced pixel and its adjacent pixels. To encode the local pattern, we consider the spatial relationship between reference and its adjacent pixels and fuse the clustering algorithm into the coding scheme by utilizing the relationship of intra- and inter-classes in a local patch. In addition, we extend the LCP from low- into high-order derivative space to extract the detailed and abundant information for facial description. LCP efficiently encodes the feature of a local region that is discriminative the inter-classes and robust the intra-class of the related pixels to describe a face image. This study has three main contributions: (1) we generate the novel features with magnitude (m) and orientation (\(\theta \)) based on the pairs of the derivative variations to describe the characteristics of each pixel, (2) we shift and project the features from four quadrants of polar coordinate system into the first quadrant of polar coordinates to strengthen the relationship of intra- and inter-classes between pixels in a local patch, (3) we exploit the concept of clustering, which considers the relationship of intra- and inter-classes of the referenced pixel and its adjacent pixels, to encode the local descriptor in a polar coordinate system for facial recognition and retrieval. Experimental results show that LCP outperforms the existing descriptors (LBP, ELBP LDP, LTrP, LVP, LDZP, LGHP) on six public datasets (ORL, Extend Yale B, CAS PEAL, and LFW, CMU-PIE and FERET) for both face recognition and retrieval tasks. Moreover, we further compare the proposed facial descriptor with the popular deep convolutional neural networks to demonstrate the discrimination of the extracted features and applicability of our approach.

局部特征模式很明显，并且广泛用于计算机视觉，尤其是在面部识别和检索中。然而，即使深度学习技术得到了广泛应用，但是可以在各种情况下使用并有效呈现人脸图像的详细局部歧视信息的统计描述符却是一项具有挑战性的探索任务。在这项研究中，我们提出了一种新颖的局部模式描述符，称为高阶导数空间中的局部聚类模式（LCP），用于面部识别和检索。与现有方法不同，LCP利用聚类的概念来分析参考像素及其相邻像素的类内和类间的关系，以编码用于面部识别的局部描述符。有三个任务：（1）本地聚类模式（LCP），（2）聚类编码方案，（3）高阶局部聚类模式。为了生成局部聚类模式，要考虑具有多方向的局部导数变化，并将其集成在具有成对组合方向的直角坐标系上。此外，为了生成可辨别的局部图案，将局部导数变化的特征从直角坐标系转换为极坐标系以生成幅度特征（m）和方向（\（\ theta \））。然后，我们移动并投影特征（m和\（\ theta \））散布在极坐标系的四个象限中，进入极坐标的第一象限，以增强参考像素及其相邻像素的类内和类间关系。为了对局部模式进行编码，我们考虑了参考像素与其相邻像素之间的空间关系，并通过利用局部补丁中类内和类间的关系将聚类算法融合到编码方案中。此外，我们将LCP从低阶导数空间扩展到高阶导数空间，以提取详细且丰富的信息以进行人脸描述。LCP有效地编码局部区域的特征，该特征可区分类间并增强相关像素的类内来描述人脸图像。这项研究有三个主要贡献：m）和方向（\（\ theta \））基于成对的微分变化来描述每个像素的特征，（2）我们将特征从极坐标系的四个象限移位并投影到极坐标的第一象限中，以增强内部和内部像素之间的关系（3）我们利用聚类的概念，即考虑参考像素与其相邻像素的类内和类间的关系，以便在人脸的极坐标系统中对局部描述符进行编码识别和检索。实验结果表明，对于两个人脸识别，LCP均优于六个公共数据集（ORL，Extended Yale B，CAS PEAL和LFW，CMU-PIE和FERET）的现有描述符（LBP，ELBP LDP，LTrP，LVP，LDZP，LGHP）和检索任务。而且，