Efficient Sequential Karhunen-Loeve Basis Extraction

The Karhunen-Loeve (KL) transform is an optimal method for approximating a set of vectors or images by a low dimensional subspace. The method provides the optimal partial KL basis, which minimizes the MSE between the given set of vectors and their projections on this basis. In computer vision it is used for a variety of tasks such as object recognition, motion estimation, visual learning and object tracking. Calculating the KL basis for images of size , where , requires roughly operations and units of memory. In many applications, this large computational demands may be prohibitive. Here, we suggest an approach to reduce the computational effort, relying on the relatively small dimension (denoted ) of the partial KL basis, that is usually needed. We propose an algorithm that does not require to store the entire set of input images before proceeding to the calculation of the KL basis. Rather, it takes the images in small blocks and updates the required KL basis sequentially.