1. A method for filtering tomographic 3D images of an examination object, the examination object being 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, and the image value of each voxel reproducing an object-specific property of the examination object in this volume, the method comprising: calculating, after the reconstruction of the total volume, variances for each image voxel in a prescribed region or radius to determine contrast jumps and their spatial orientation with their tangential planes; filtering the image values in the tangential plane with a two-dimensional convolution; and mixing the original voxel data in weighted fashion with the filtered voxel data, wherein the spatial orientation of a contrast jump is determined by the tangential plane thereof, this plane being defined by the vectors v min and v ⊥ , the vector v ⊥ in turn being perpendicular to the plane defined by the vectors v min and v max and the vector v min pointing in the direction of the largest magnitude of the variance, and the vector v min pointing in the direction of the smallest magnitude of the variance, the filtering is carried out in the tangential plane by two-dimensional convolution in such a way that the filter is formed as a function of the minimum variance v min and the maximum variance v ⊥ in the tangential plane, a typical variance v typ is determined in the surroundings and the original voxel data are mixed in weighted fashion with the filtered voxel data in such a way that in the case of v max >>v typ a greater weight is ascribed to the original voxel data than to the filtered voxel data, and in the case of v max <<v typ a lesser weight is ascribed to the original voxel data than to the filtered voxel data, and the calculating, the filtering and the mixing is for at least one of Computed Tomography (CT), Nuclear Magnetic Resonance (NMR), and Positron Emission Tomography (PET) pictures of a medical patient using a system including at least one of a CT device, an NMR device, and a PET device.