Accurate Shift Estimation under One-Parameter Geometric Distortion using the Brosc Filter

Abstract

Shift estimation is the task of estimating an unknown translation factor which best relates two relatively distorted representations of the same image data. Where distortion is large and also includes rotation and scaling, estimates of the global distortion can be obtained with good accuracy using RST-matching methods, but such algorithms are slow and complicated. Where geometric distortion is small, correlation-based methods can achieve millipixel accuracy. These methods begin to fail, however, when even quite small geometric distortions are present, such as rotation by 1° or 2°, or a scaling by as little as 5%. A new spatially-variant filter, the brosc filter ("better rotation or scaling"), can be used to preserve the accuracy of correlation-based shift estimation where the expected distortion can be modelled as a single parameter, for example, as a pure rotation, a pure scaling, or a pure scaling along a known axis. By applying the brosc filter before shift estimation, shift accuracy under geometric distortion is improved, and a variant of the brosc filter using complex arithmetic provides in addition an estimate of the single parameter representing the unknown distortion.