  The Lucas-Kanade (LK) method is a classic iterative homography estimation
algorithm for image alignment, but often suffers from poor local optimality
especially when image pairs have large distortions. To address this challenge,
in this paper we propose a novel Deep Star-Convexified Lucas-Kanade (PRISE)
method for multimodel image alignment by introducing strongly star-convex
constraints into the optimization problem. Our basic idea is to enforce the
neural network to approximately learn a star-convex loss landscape around the
ground truth give any data to facilitate the convergence of the LK method to
the ground truth through the high dimensional space defined by the network.
This leads to a minimax learning problem, with contrastive (hinge) losses due
to the definition of strong star-convexity that are appended to the original
loss for training. We also provide an efficient sampling based algorithm to
leverage the training cost, as well as some analysis on the quality of the
solutions from PRISE. We further evaluate our approach on benchmark datasets
such as MSCOCO, GoogleEarth, and GoogleMap, and demonstrate state-of-the-art
results, especially for small pixel errors. Code can be downloaded from
https://github.com/Zhang-VISLab.
