Fast Covariance Computation and Dimensionality Reduction for Sub-Window Features in Images

This paper presents algorithms for efficiently computing the covariance matrix for features that form sub-windows in a large multidimensional image. For example, several image processing applications, e.g. texture analysis/synthesis, image retrieval, and compression, operate upon patches within an image. These patches are usually projected onto a low-dimensional feature space using dimensionality reduction techniques such as Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA), which in-turn requires computation of the covariance matrix from a set of features. Covariance computation is usually the bottleneck during PCA or LDA (O(nd2 ) where n is the number of pixels in the image and d is the dimensionality of the vector). Our approach reduces the complexity of covariance computation by exploiting the redundancy between feature vectors corresponding to overlapping patches. Specifically, we show that the covariance between two feature components can be reduced to a ...

• Type: Conference
• Year: 2010
• Where: ECCV
• Keywords: Computer Vision, Covariance, Covariance Computation, Covariance Matrix, ECCV 2010