Optical Flow

Abstract

Motions of physical objects relative to a camera as observer naturally occur in everyday lives and in many scientific applications. Optical flow represents the corresponding motion induced on the image plane. This paper describes the basic problems and concepts related to optical flow estimation together with mathematical models and computational approaches to solve them. Emphasis is placed on common and different modeling aspects and to relevant research directions from a broader perspective. The state of the art and corresponding deficiencies are reported along with directions of future research. The presentation aims at providing an accessible guide for practitioners as well as stimulating research work in relevant fields of mathematics and computer vision.

Disparity and optical flow partitioning using extended Potts priors

“…All examples were executed on a computer with an Intel Core i7-870 Processor (8M Cache, 2.93 GHz) and 8 GB physical memory, 64 Bit Linux. We compare our direct partitioning methods (6) and (7) via Algorithm 1 with a two-stage approach consisting of i) disparity, resp. optical flow estimation, and ii) partitioning of the estimated values.…”

“…Then the models rely on an invariance requirement between these images. Various invariance assumptions were considered in the literature and we refer to [7] for a comprehensive overview. Here we focus on the brightness invariance assumption.…”

“…In other words, we are searching for vector fields now and have to deal with vector-valued data. Variational approaches to optical flow estimation were pioneered by Horn and Schunck [34] followed by a vast number of refinements and extensions, including sophisticated data fidelity terms going beyond the brightness [7,13,31] and nonsmooth regularizers, e.g., TV-like ones [2,33] including also higher order derivatives [62,63,64] and nonlocal regularizers [59], to mention only few of them. In general multiscale approaches have to be taken into account to correctly determine larger and smaller flow vectors [1,12,23].…”

“…In general multiscale approaches have to be taken into account to correctly determine larger and smaller flow vectors [1,12,23]. A good overview is given in [7]. Recent comprehensive empirical evaluations [6,29] show that variational algorithms yield a very good performance.…”

Shape-based image reconstruction using linearized deformations

“…There is by now a rich literature for variational methods for image matching, see, e.g. , [5, 32, 31, 8]. Some parts of this theory is also used for reconstruction, most notably for spatiotemporal imaging as outlined in subsection 11.6.…”