Minimum-volume transforms for remotely sensed data

Abstract

Scatter diagrams for multispectral remote sensing data tend to be triangular, in the two-band case, pyramidal for three bands, and so on. They radiate away from the so-called darkpoint, which represents the scanner's response to an un-illuminated target. A minimum-volume transform may be described (provisionally) as a nonorthogonal linear transformation of the multivariate data to new axes passing through the dark point, with directions chosen such that they (for two bands), or the new coordinate planes (for three bands, etc.) embrace the data cloud as tightly as possible. The reason for the observed shapes of scatter diagrams is to be found in the theory of linear mixing at the subfootprint scale. Thus, suitably defined, minimum-volume transforms can often be used to unmix images into new spatial variables showing the proportions of the different cover types present, a type of enhancement that is not only intense, but physically meaningful. The present paper furnishes details for constructing computer programs to effect this operation. It will serve as a convenient technical source that may be referenced in subsequent, more profusely illustrated publications that address the intended application, the mapping of surface mineralogy.>