The project managed to find a combined invariants (i.e. w.r.t both convolution and geometric distortion) with different variants of a combination of convolution and geometric transformations based on moments of image function. On the side of the convolution transformation, it is primarily blurring by centrally symmetric energy-preserving linear filter. The results can be generalized for energy-nonpreserving filters or filters with a higher degree of symmetry. On the side of the geometric transformations, different combinations of translation, scaling and rotation can be used.