Computer-intensive methods for data analysis in a traditional setting has developed rapidly in the last decade. The application of and adaption of some of these methods to the analysis of multivariate digital images and spatial data are explored, evaluated and compared to well established classical linear methods. Different strategies for selecting projections (linear combinations) of multivariate images are presented. An exploratory, iterative method for finding interesting projections originated in data analysis is compared to principal components. A method for introducing spatial context into the projection pursuit is presented. Examples from remote sensing are given. The ACE algorithm for computing non-linear transformations for maximizing correlation is extended and applied to obtain a non-linear transformation that maximizes autocorrelation or 'signal' in a multivariate image. This is a generalization of the minimum /maximum autocorrelation factors (MAF's) which is a linear method. The non-linear method is compared to the linear method when analyzing a multivariate TM image from Greenland. The ACE method is shown to give a more detailed decomposition of the image than the MAF-transformation and there is a good agreement between the ACEMAF's and geological structures known in the area studied. Geological units are easily recognized even at macro scale, implying potential use in geological mapping. Also the ACE algorithm is modified to finding transformations that minimize correlation which is of interest in change detection studies from two different images of the same area recorded at different time points. An example is given using a TM summer scene and a TM winter scene of an area in Spain. The non-parametric CART classification method is integrated with traditional geostatistical methods in computing structural images for heavy minerals based on irregularly sampled geochemical data. This methodology has proven useful in producing images that reflect real geological structures with potential application in mineral exploration. A method for removing loboratory-produced map-sheet patterns in spatial data by means of local histogram matching is presented and its use is demonstrated in the analysis of geochemical samples on a regional scale.