Robust FFT-based scale-invariant image registration with image gradients

We present a robust FFT-based approach to scale-invariant image registration. Our method relies on FFT-based correlation twice: once in the log-polar Fourier domain to estimate the scaling and rotation and once in the spatial domain to recover the residual translation. Previous methods based on the same principles are not robust. To equip our scheme with robustness and accuracy, we introduce modifications which tailor the method to the nature of images. First, we derive efficient log-polar Fourier representations by replacing image functions with complex gray-level edge maps. We show that this representation both captures the structure of salient image features and circumvents problems related to the low-pass nature of images, interpolation errors, border effects, and aliasing. Second, to recover the unknown parameters, we introduce the normalized gradient correlation. We show that, using image gradients to perform correlation, the errors induced by outliers are mapped to a uniform distribution for which our normalized gradient correlation features robust performance. Exhaustive experimentation with real images showed that, unlike any other Fourier-based correlation techniques, the proposed method was able to estimate translations, arbitrary rotations, and scale factors up to 6.