Pseudopolar-based estimation of large translations, rotations, and scalings in images

Abstract

One of the major challenges related to image registration is the estimation of large motions without prior knowledge. This paper presents a Fourier-based approach that estimates large translations, scalings, and rotations. The algorithm uses the pseudopolar (PP) Fourier transform to achieve substantial improved approximations of the polar and log-polar Fourier transforms of an image. Thus, rotations and scalings are reduced to translations which are estimated using phase correlation. By utilizing the PP grid, we increase the performance (accuracy, speed, and robustness) of the registration algorithms. Scales up to 4 and arbitrary rotation angles can be robustly recovered, compared to a maximum scaling of 2 recovered by state-of-the-art algorithms. The algorithm only utilizes one-dimensional fast Fourier transform computations whose overall complexity is significantly lower than prior works. Experimental results demonstrate the applicability of the proposed algorithms.

Linear Estimation of Time-Warped Signals

“…Many such global methods exist both for 1-D and 2-D signals (see, e.g., [17] and the references therein) however their scope is restricted to a relatively small family of transformations. Thus, in the case of images for example, there are explicit methods for handling translation only, rotation only, or global scale (moderate factor) only, but they turn into combined explicit/implicit methods for the combined transformation of rotation, scaling and translation, [18]. Translation estimation is conveniently carried out in the Fourier domain based on the phase shift of the Fourier transforms of the two images to be registered, by employing the normalized phase-correlation algorithm, e.g., [19].…”

FFT-based estimation of large motions in images: A robust gradient-based approach

“…2, where the reference image is scaled, rotated and translated according to the estimated motion parameters, and then superimposed on the target image. To show the gain in performance compared to other FFT-based approaches, we have also implemented an improved version of the state-of-the-art method given in [3]. In particular, the pseudopolar FFT is replaced with an accurate polar FFT [9].…”

“…The methods in [3], [4] are considered state-of-the art in FFT-based motion estimation. Performance is improved by introducing new sampling schemes which reduce the inaccuracies induced by resampling the magnitude of the FT on the log-polar grid.…”

“…Performance is improved by introducing new sampling schemes which reduce the inaccuracies induced by resampling the magnitude of the FT on the log-polar grid. To recover scalings and rotations, the method in [3] relies on the pseudopolar FT which rapidly computes a discrete FT on a nearly polar grid. The pseudopolar grid serves as an intermediate step for a log-polar Fourier representation which is obtained using nearest-neighbor interpolation.…”

Performance of correlation approaches for the evaluation of spatial distortion reductions

“…If an image , , where image pixels are indexed using , , is shifted by an arbitrary distance along the x-direction, noted∆ , and an arbitrary distance along the y-direction, noted ∆ , then these shifts noted as ∆ ∆ , ∆ can be related in the frequency domain (Averbuch and Keller 2002;Foroosh et al 2002;Hoge 2003;Keller et al 2005;Leprince et al 2007;Ojansivu and Heikkila 2007;Reddy and Chatterji 1996;Tzimiropoulos et al 2010;Xie et al 2003) as follows:…”