A filter method for tomographic 3D displays is disclosed, in which a volume model is used for display, which reproduces the volume of the examination object in the form of a large number of three-dimensional image voxels, and the image value of each voxel reproduces one object-specific characteristic of the examination object in this volume. According to the method, the original image voxels are processed using a 2D filter which is the same over the entire image area, and two different linear filters with selected directions which are obtained from the extremes of the previously calculated variances thus resulting in three data records with differently filtered image voxels, and in which, furthermore, the original image voxels and the filtered image voxels are mixed using local weights to form a result image. In addition, original image data can be processed using a steepening linear filter with a filter direction in the direction of the maximum local variance, resulting in a data record which is mixed into the final image with locally different weighting.