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Finite-Sample Analysis of Image Registration
We study the problem of image registration in the finite-resolution regime
and characterize the error probability of algorithms as a function of
properties of the transformation and the image capture noise. Specifically, we
define a channel-aware Feinstein decoder to obtain upper bounds on the minimum
achievable error probability under finite resolution. We specifically focus on
the higher-order terms and use Berry-Esseen type CLTs to obtain a stronger
characterization of the achievability condition for the problem. Then, we
derive a strong type-counting result to characterize the performance of the MMI
decoder in terms of the maximum likelihood decoder, in a simplified setting of
the problem. We then describe how this analysis, when related to the results
from the channel-aware context provide stronger characterization of the
finite-sample performance of universal image registration.Comment: 16 pages, 3 figure