Registration of Finite Resolution Images: A Second-order Analysis

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.