The Biharmonic Eigenface

Abstract

Principal component analysis (PCA) is an elegant mechanism that reduces the dimensionality of a dataset to bring out patterns of interest in it. The preprocessing of facial images for efficient face recognition is considered to be one of the epitomes among PCA applications. In this paper, we introduce a novel modification to the method of PCA whereby we propose to utilise the inherent averaging ability of the discrete Biharmonic operator as a preprocessing step. We refer to this mechanism as the BiPCA. Interestingly, by applying the Biharmonic operator to images, we can generate new images of reduced size while keeping the inherent features in them intact. The resulting images of lower dimensionality can significantly reduce the computational complexities while preserving the features of interest. Here, we have chosen the standard face recognition as an example to demonstrate the capacity of our proposed BiPCA method. Experiments were carried out on three publicly available datasets, namely the ORL, Face95 and Face96. The results we have obtained demonstrate that the BiPCA outperforms the traditional PCA. In fact, our experiments do suggest that, when it comes to face recognition, the BiPCA method has at least 25% improvement in the average percentage error rate.