Eigenvector spatial filtering for image analysis: An efficient algorithm

Eigenvector Spatial Filtering (ESF) is an established method in social science literature for incorporating spatial information in model specifications. ESF computes spatial eigenvectors, which are defined by the spatial structure associated with a variable. One important limitation of this technique is that it becomes computationally intensive in image analysis because of the massive number of image pixels. This research develops an algorithm, which makes ESF more efficient, by using the analytical solution for the eigenvalues and spatial eigenvectors, which are essentially a series of orthogonal, uncorrelated map patterns that describe positively spatial autocorrelated patterns through negatively spatially autocorrelated patterns, and global, regional, and local patterns of spatial dependencies in a surface. A reformulation of the analytical solution reduces the required computations and allows the eigenvectors to be computed sequentially. Finally, a series of sampling methods are explored. This algorithm is applied to three example multispectral images of different sizes: small (i.e., ∼200,000 pixels), medium (i.e., ∼1,000,000 pixels) and large (i.e., ∼110,000,000 pixels) and is evaluated in terms of output for each sampling technique and the complete spectral information. The output spatial filters of these sampling techniques compare to the filter generated with the complete spectral information. In terms of efficiency evaluation, the time is required to construct filters through sampling versus through analysis of the complete image surface is evaluated and the complexity of set-up and execution of the sampled and distributed algorithms are assessed.