Image compression and manipulation by weighted finite automata exploit similarities in the images in order to obtain notable compression ratios and manipulation tools. The investigations are often based on two-dimensional images. A natural extension is to consider three- or even n-dimensional images which are decomposed in two- dimensional slices, e. g. data produced by tomography. By applying the two-dimensional methods to the slices the volume similarities may be disregarded. Building three-dimensional patterns by merging sequenced images of movie scenes may result in increased similarities. Here we consider transformations of the input strings for weighted finite automata in order to obtain dimension transformations which preserve multidimensional similarities. We focus our investigations on the state complexity and show that a noticeable reduction of the number of states can be achieved.