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To capture such correlations, we propose a geometric modeling framework in which the image ensemble is treated as a sampling of points from a low-dimensional manifold in the ambient signal space.
We also assume that the image ensemble is spatially uncorrelated.
In reality, the assumption that the image ensemble is spatially uncorrelated is clearly wrong.
It's helpful if these frequency components are absent from the image ensemble.
This confirmed that each step in the binarizing nonlinearity further decorrelated the image ensemble.
In conclusion, if the image ensemble is spatially uncorrelated (at second and fourth-order), then the image ensemble only affects the correlation coefficient between the velocity and a 2-point correlator through its kurtosis.
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Thus, the second-order and fourth-order statistics of the image ensembles are the critical determinants of a 2-point correlator's motion estimation accuracy.
The preceding analysis shows that only the second-order and fourth-order statistics of the natural image ensemble contribute to the correlation coefficient between an arbitrary 2-point correlator and the true velocity.
Binarization attenuated spatial correlations more strongly than contrast equalization over the natural image ensemble, and spatial correlations can enhance the performance of the HRC (Appendices 4, 5).
Binarization attenuated spatial correlations more strongly than contrast equalization over the natural image ensemble, which leads us to hypothesize that correlations present in the natural image ensemble might benefit the HRC's performance.
(C ) Second-order correlation function between pairs of spatially separated contrast signals (across the natural image ensemble [ van Hateren and van der Schaaf, 1998 ]).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com