Fourier-based invariant image descriptors

A new framework for matching images with invariance to rotation is formed. This is done through two novel Global Rotation Invariant Descriptors (GRIDs), based on the Discrete Fourier Transform (DFT). The two descriptors are generated through the transfbormation of rotation into circular shifts by mapping the images from Cartesian to Polar coordinates. The first GRID is based on the Fourier magnitudes, thus allowing images with similar frequency components to be regarded as similar or identical. Experiments are done to show the performance of the descriptor under a variety of practical conditions including scale change and image compression. The need for a more precise ability to match images leads to the derivation of the second GRID, which incorporates the phase information into a Shift Invariant Signal Transform (SIST). The SIST is once again used on the polar representation of the image to generate an inherently rotation-invariant descriptor. This descriptor is shown experimentally to be extremely sensitive to small variations in the image. To increase the performance of the phase-retaining descriptor, a method for phase quantization and sensitivity relaxation is introduced. Once again experiments are done to show how the descriptor performs under varying practical condition. Finally, the concept of entanglement is introduced as a method of increasing the robustness and performance of the rotation-invariant descriptors.;Through experimentation and theoretical analysis it is shown that the proposed descriptors form a very practical method for comparing and matching images under practical conditions. Furthermore, the relative boost in performance resulting from each enhancement is shown through experimentation.