Log-polar sampling incorporating a novel spatially variant filter to improve object recognition

The Fourier-Mellin transform (FMT) is a method for making images rotation, scale and translation (RST) invariant, with applications in object recognition. It can be implemented in either optical or digital form. However, if the transform is to be performed digitally then there are improvements which can be made to the processing to enhance the result. We suggest that the use of a spatially variant filter to modify the output of the Fourier transform (FT) improves the output of the FMT. This paper explains the need to filter an image by varying amounts, which depends on the spatial position of the filter on the image, before log-polar transformation. The implementation of the filter ensures that pixels are filtered along each circumference which is to be sampled, and that the amount of filtering depends upon the radius of the circumference from the centre of sampling. The implementation of the filter requires little extra complexity in comparison with the log-polar transform, while being able to achieve circumferential filtering of the Fourier transform by mapping pixel coordinates and convolving a 1D mask with a square image. The results which have been obtained show that filtering in this way improves the desired phase correlation peak