1. Microscope image processing method for execution on a computer the computer including a working memory having a pre-specified available memory capacity and a mass storage device that has a longer access time than said working memory, for processing a digital microscope image that comprises pixels (P i,j ), is n-dimensional, where n>1, comprises at least two partial images (TB 1 ) each partial image being a simple contiguous pixel area that is a subpart of the digital microscope image, and wherein the digital microscope image has a size that exceeds the available memory capacity of said working memory, by applying a computing operation to at least one part of said microscope image, comprising: (a) storing said microscope image in said mass storage device, (b) breaking down said microscope image into at least two image segments (BA k ) that are small enough to be loaded into said working memory and that have a dimension m, where m≦n, each image segment defining a selected quantity of pixels that have preselected coordinates, (c) for one image segment (BA k ), determining all pixels that are located in said image segment (BA k ) and in at least one of said partial images (TB 1 ), so that a filled image segment results, the filled image segment being made up of all of the pixels that are located both in the image segment and also in the at least one of the partial images, (d) storing said filled image segment in said working memory, (e) applying said computing operation to said pixels (P i,j ) located in said filled image segment so that an image segment result is created, (f) repeating steps (c), (d), and (e) for all the image segments (BA k ), (g) combining all images the segment results to create an overall result; capturing said microscope image by moving a positioning unit for a microscope in a pre-specified grid for recording said microscope images, recording a partial image (TB 1 ) of a specimen affixed to said positioning unit at each grid position with a camera of said microscope, and storing said partial images (TB 1 ) in said mass storage device of said computer.