The subject of this paper is a technical improvement of an algorithmic method for recognition of isolated, single, two-dimensional patterns that is scale-invariant and rotation-invariant.

The Fourier-Mellin transform is essentially a Fourier transform of a log-polar transformation of the ratio of the absolute value of a two-dimensional discrete Fourier transform to its maximum value at zero frequency. It achieves the desired invariance properties for single objects in a continuous background space, but not if the space is regarded as a discrete finite grid, such as a representation in pixels.

The paper presents simplified versions of the basic method. The simplifications are intended to achieve scale and rotation invariances in the discrete space and also to reduce the computing time that is needed. Perhaps surprisingly, these results are obtained by discarding some of the details of the original method, including the final Fourier transform. Approximations that perform well in the authors’ trials and that are even less demanding computationally are also considered. These approximations are the use of second moments of representations of objects and a test for similarity that involves a sum over values of a discrete Fourier-Mellin transform at different points. The trials use simple geometrical shapes and one human figure, which is not shown in the paper.

In practice, the pattern recognition problem deals with multiple and overlapping objects seen against noisy or otherwise intrusive backgrounds. The paper is of technical interest, but it is not clear if particular solutions to the problem can be developed in any direct or obvious way from this starting point.