A method is for filtering tomographic 3D images of an examination object. The examination object is imaged by using a volume model that divides the volume of the examination object into a multiplicity of three-dimensional image voxels with individual image values, wherein the image value of each voxel reproduces an object-specific property of the examination object in this volume. After the reconstruction of the total volume for each voxel, variances are calculated in a prescribed region or radius R in order to determine contrast jumps and their spatial orientation with their tangential planes T. The image values in the tangential plane T are filtered with a two-dimensional convolution, and subsequently the original voxel data are mixed in weighted fashion with the filtered voxel data.