Image Alignment by Online Robust PCA via Stochastic Gradient Descent

Aligning a given set of images is usually conducted in batch mode manner, which not only requires large amount of memory but also adjusts all the previous transformations to register an input image. To address this issue, we propose a novel approach to image alignment by incorporating the geometric transformation into online robust principal component analysis (PCA). Instead of calculating the warp update using noisy input samples like the conventional methods, we suggest directly linearizing the object function by performing warp update on the recovered samples, which corresponds to an efficient inverse composition algorithm. Since the basis matrix is kept constant for a given sample, both the latent vector and warp update can be very efficiently computed. Moreover, we present two basis updating methods for robust PCA, including the closed-form solution and stochastic gradient descent scheme. We have conducted the extensive experiments on the real-world tasks of background subtraction with camera motion and visual tracking on the challenging video sequences, whose promising results demonstrate the efficacy of our presented approach.