Estimation bias from using nonlinear Fourier plane correlators for sub-pixel image shift measurement and implications for the binary joint transform correlator

Thomas J. Grycewicz; Christopher J. Florio; Geoffrey A. Franz; Ross E. Robinson

doi:10.1117/12.729661

20 September 2007 Estimation bias from using nonlinear Fourier plane correlators for sub-pixel image shift measurement and implications for the binary joint transform correlator

Thomas J. Grycewicz, Christopher J. Florio, Geoffrey A. Franz, Ross E. Robinson

Author Affiliations +

Proceedings Volume 6695, Optics and Photonics for Information Processing; 66950J (2007) https://doi.org/10.1117/12.729661
Event: Optical Engineering + Applications, 2007, San Diego, California, United States

Abstract

When using Fourier plane digital algorithms or an optical correlator to measure the correlation between digital images, interpolation by center-of-mass or quadratic estimation techniques can be used to estimate image displacement to the sub-pixel level. However, this can lead to a bias in the correlation measurement. This bias shifts the sub-pixel output measurement to be closer to the nearest pixel center than the actual location. The paper investigates the bias in the outputs of both digital and optical correlators, and proposes methods to minimize this effect. We use digital studies and optical implementations of the joint transform correlator to demonstrate optical registration with accuracies better than 0.1 pixels. We use both simulations of image shift and movies of a moving target as inputs. We demonstrate bias error for both center-of-mass and quadratic interpolation, and discuss the reasons that this bias is present. Finally, we suggest measures to reduce or eliminate the bias effects. We show that when sub-pixel bias is present, it can be eliminated by modifying the interpolation method. By removing the bias error, we improve registration accuracy by thirty percent.

Citation Download Citation

Thomas J. Grycewicz, Christopher J. Florio, Geoffrey A. Franz, and Ross E. Robinson "Estimation bias from using nonlinear Fourier plane correlators for sub-pixel image shift measurement and implications for the binary joint transform correlator", Proc. SPIE 6695, Optics and Photonics for Information Processing, 66950J (20 September 2007); https://doi.org/10.1117/12.729661

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