The equivalence of two-dimensional PCA to line-based PCA

The state-of-the-art in human face recognition is the subspace methods originated by the Principal Component Analysis (PCA), the Eigenfaces of the facial images. Recently, a technique called Two-Dimensional PCA (2DPCA) was proposed for human face representation and recognition. It was developed for image feature extraction based on 2D matrices as opposed to the standard PCA, which is based on 1D vectors. In this note, we show that 2DPCA is equivalent to a special case of an existing feature extraction method, block-based PCA, which has been used for face recognition in a number of systems.