A method and an apparatus reduce the temporary random access memory required when determining disparity values for at least two stereoscopically recorded images with known epipolar geometry, in which a disparity is determined for each pixel of an image. Path-dependent dissimilarity costs are calculated on the basis of a disparity-dependent cost function, and compared, in two runs for a number of paths which open in the pixel. The disparity-dependent cost function evaluates a pixel-based dissimilarity measure between the pixel and the corresponding pixel, according to the respective disparity, in a second image. The path-dependent dissimilarity costs for a first predetermined set of disparities are calculated in a first run for a number of first paths and in a second run for a number of remaining paths, and the corresponding path-dependent dissimilarity costs of the first paths and of the remaining paths are accumulated for a second predetermined set of disparities.