Spatial Regularization in Subspace Learning for Face Recognition: Implicit Vs. Explicit

In applying traditional statistical method to face recognition, each original face image is often vectorized as a vector. But such a vectorization not only leads to high-dimensionality, thus small sample size (SSS) problem, but also loses the original spatial relationship between image pixels. It has been proved that spatial regularization (SR) is an effective means to compensate the loss of such relationship and at the same time, and mitigate SSS problem by explicitly imposing spatial constraints. However, SR still suffers from two main problems: one is high computational cost due to high dimensionality and the other is the selection of the key regularization factors controlling the spatial regularization and thus learning performance. Accordingly, in this paper, we provide a new idea, coined as implicit spatial regularization (ISR), to avoid losing the spatial relationship between image pixels and deal with SSS problem simultaneously for face recognition. Different from explicit spatial regularization (ESR), which introduces directly spatial regularization term and is based on vector representation, the proposed ISR constrains spatial smoothness within each small image region by reshaping image and then executing 2D-based feature extraction methods. Specifically, we follow the same assumption as made in SSSL (a typical ESR method) that a small image region around an image pixel is smooth, and reshape each original image into a new matrix whose each column corresponds to a vectorized small image region, and then we extract features from the newly-formed matrix using any off-the-shelf 2D-based method which can take the relationship between pixels in the same row or column into account, such that the original spatial relationship within the neighboring region can be greatly retained. Since ISR does not impose constraint items, compared with ESR, ISR not only avoids the selection of the troublesome regularization parameter, but also greatly reduces computational cost. Experimental results on four face databases show that the proposed ISR can achieve competitive performance as SSSL but with lower computational cost.