Multivariate image regression (MIR): implementation of image PLSR-first forays

In the effort of analysing multivariate images, image PLS has been consider ed interesting. In this paper, image PLS (MIR) is compared with image PCA ( MW) by studying a comparison data set. While MIA has been commercially avai lable for some time, image PLS has not. The kernel PLS algorithm of Lindgre n has been implemented in a development environment which is a combination of G (LabVIEW) and MATLAB. In this presentation the power of this environme nt, as well as an early example in image regression, will be demonstrated. With kernel PLS, all PLS vectors (eigenvectors and eigenvalues) can be calc ulated from the joint variance-covariance (X'Y and Y'X) and association (Y' Y and X'X) matrices. The dimensions of the kernel matrices X'YY'X and Y'XX' Y are K x K (K is the number of X-variables) and M x M (M is the number of Y-variables) respectively. Hence their size is dependent only on the number of X and Y-variables and not on the number of observations (pixels), which is crucial in image analysis. The choice of LabVIEW as development platfor m has been based on our experience of a very short implementation time comb ined with user-friendly interface possibilities. Integrating LabVIEW with M ATLAB has speeded up the decomposition calculations, which otherwise are sl ow, Also, algorithms for matrix calculations are easier to formulate in MAT LAB than in LabVIEW. Applying this algorithm on a representative test image which shows many of the typical features found in technical imagery, we ha ve shown that image PLS (MIR) decomposes the data differently than image PC A (MIA), in accordance with chemometric experience from ordinary two-way ma trices. In the present example the Y-reference texture-related image used t urned out to be able to force a rather significant 'tilting' compared with an 'ordinary MIA' of the primary structures in the original, spectral R/G i mage. Copyright (C) 2000 John Wiley & Sons, Ltd.