Regression on multivariate images: Principal component regression for modeling, prediction and visual diagnostic tools

Abstract

Abstract Regression between two blocks (usually called ‘dependent’ or Y and ‘independent’ or X ) of data is a very important scientific and data‐analytical tool. Regression on multivariate images is possible and constitutes a meaningful addition to existing univariate and multivariate techniques of image analysis. The regression can be used as a modeling tool or for prediction. The form of the regression equation chosen is dependent upon problem specification and information at hand. This paper describes the use of principal component regression (PCR). Both model building and prediction are presented for continuous Y ‐variables. The final goal is to supply new image material that can be used for visual inspection on a screen. Also, visual tools for diagnosis of model and prediction are provided, often based on derived image material. Examples of modeling and prediction are given for six channels in a seven‐channel satellite image.