This paper introduces a new orthogonal transformation, the multivariate alteration detection (MAD) transformation, based on an established multivariate statistical technique canonical correlation analysis. The theory for canonical correlation analysis is sketched and a result necessary for the definition of the MAD transformation is proven. As opposed to traditional univariate change detection schemes our scheme transforms two sets of multivariate observations (e.g. two multispectral satellite images covering the same geographical area acquired at different points in time) into a difference between two linear combinations of the original variables explaining maximal change (i.e. the difference explaining maximal variance) in all variables simultaneously. The MAD transformation is invariant to linear scaling. The MAD transformation can be used iteratively. First, it can be used to detect outliers (such as drop-outs) or noise and in a second iteration, it can be used to perform the actual change detection after appropriate action on outliers or noise. Also, if an analyst has additional information such as geographical position of certain changes of interest that show up in certain bands only, our method can be applied to any spatial and/or spectral subset of the full data set to direct the analysis in any desired manner. In order to obtain a spatially more coherent representation of the detected change as obtained from the MAD analysis, post-processing by means of a minimum/maximum autocorrelation factor (MAF) transformation of the MAD variates can be performed. Whereas the traditionally used principal component (PC) transformation optimizes the data variance in each new component the MAF transformation optimizes the autocorrelation represented by each component. This post-processing introduces a new spatial element into our change detection scheme which is highly relevant for image data. Two case studies using multispectral SPOT HRV data from 5 February 1987 and 12 February 1989 covering coffee and pineapple plantations in central Kenya, and Landsat TM data from 6 June 1986 and 27 June 1988 covering a forested region in northern Sweden show the usefulness of these new concepts. Because of their ability to detect change in many channels simultaneously, the MAD transformation and the MAF post-processing are expected to be even more useful when applied to image data with more bands.
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Informatics and Mathematical Modelling (IMM), Technical University of Denmark, 1997