Using the spatial dependence of observations from multivariate images, it is possible to construct methods for data reduction that perform better than the widely used principal components procedure. Switzer and Green introduced the min/max autocorrelation factors (MAF) process for transforming the data to a new set of vectors where the components are arranged according to the amount of autocorrelation. MAF performs well when the underlying image consists of large homogeneous regions. For images with many transitions between smaller homogeneous regions, however, MAF may not perform well. A modification of the MAF process, the restricted min/max autocorrelation factors (RMAF) process, which takes into account the transitions between homogeneous regions, is introduced. Simulation experiments show that large improvements can be achieved using RMAF rather than MAF.