Spatial and Spatially Weighted Principal Component Analysis for Images Processing

Principal component analysis (PCA) has become a standard method for processing multiple remote sensing image bands in order for replacing the large number of correlated bands with a small number of independent components which carry the similar information but with clearer physical meaning for interpretation. The base of the ordinary PCA is the symmetrical correlation or covariance matrixes calculated from pixel values on multiple image bands. However, the construction of the correlation matrix does not usually take into account the spatial association and structural properties of the images which are not only common properties but also essential for image filtering and classification. Incorporating spatial information of the images into the PCA is a natural consideration which forms the main objective of this paper. Several generalizations were proposed in the current research to be applied to the ordinary PCA in the context of image processing and spatial analysis. These include (1) optimizing correlations coefficient matrix by applying image stretching transformation prior to the calculation of correlation coefficient; (2) spatially weighted correlation coefficient matrix by incorporating a fuzzy mask defined on the basis of sample (pixel) location in relation to other features showing relative importance of pixels; and (3) spatial correlation coefficient matrix on the basis of spatial auto-correlation and cross-correlation matrix. These methods have been implemented in a newly developed GeoDAS GIS.