In this article we consider via critical point theory the existence of homoclinic orbits of the first-order differential difference equation z（t）＋B（t）z（t）＋f（t,z（t＋τ）,z（t）,z（t-τ））=0.
The problem of robust alignment of batches of images can be formulated as a low-rank matrix optimization problem, relying on the similarity of well-aligned images. Going further, observing that the images to be aligned are sampled from a union of low-rank subspaces, we propose a new method based on subspace recovery techniques to provide more robust and accurate alignment. The proposed method seeks a set of domain transformations which are applied to the unaligned images so that the resulting images are made as similar as possible. The resulting optimization problem can be linearized as a series of convex optimization problems which can be solved by alternative sparsity pursuit techniques. Compared to existing methods like robust alignment by sparse and low-rank models, the proposed method can more effectively solve the batch image alignment problem,and extract more similar structures from the misaligned images.
Xianhui LinZhu Liang YuZhenghui GuJun ZhangZhaoquan Cai
