Abstract

This paper is inspired by a relatively recent work of Seitz and Baker which introduced the so-called Filter Flow model. Filter flflow fifinds the transformation relating a pair of (or multiple) images by identifying a large set of local linear fifilters; imposing additional constraints on certain structural properties of these fifilters enables Filter Flow to serve as a general “one stop” construction for a spectrum of problems in vision: from optical flflow to defocus to stereo to affifine alignment. The idea is beautiful yet the benefifits are not borne out in practice because of signififi- cant computational challenges. This issue makes most (if not all) deployments for practical vision problems out of reach. The key thrust of our work is to identify mathematically (near) equivalent reformulations of this model that can eliminate this serious limitation. We demonstrate via a detailed optimization-focused development that Filter Flow can indeed be solved fairly effificiently for a wide range of instantiations. We derive effificient algorithms, perform extensive theoretical analysis focused on convergence and parallelization and show how results competitive with the state of the art for many applications can be achieved with negligible application specifific adjustments or post-processing. The actual numerical scheme is easy to understand and, implement (30 lines in Matlab) — this development will enable Filter Flow to be a viable general solver and testbed for numerous applications in the community, going forward