Nonlinear covariance for multi-band image data
Multi-band data is often (unavoidably) pre-processed by nonlinear mappings, or is comprised of measurements taken across non-commensurate bands. We treat such cases using rank order statistics, avoiding problems of dimensionality and nonlinearity. Our aim is to reduce multi-band data to two images; one showing inhomogeneous image regions common to all of the image bands and another image which reflects the differences. The measure used is a nonlinear analog of linear covariance, the ‘co-diversity’, which responds to the relative homogeneity of local image regions in terms of rank. Algorithms to determine the ‘co-diversity’ are presented and applied to the interpretation of edges in multispectral data and to the combination of information from different sources, for example, binary and greyscale data. The method is robust to contrast variations across the data, but relies on some prior morphologic smoothing to ensure the local rank order is not dominated by noise.
Keywordsnonlinear statistics multivariate techniques mathematical morphology
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