You are provided with the abstract of a scientific paper and the abstracts of the papers it references. Your task is to write a Related Work section for the main paper. This section should concisely summarize and integrate the key points from the cited abstracts, reflecting how they relate to the main paper's contributions and context. In your summary, use numerical citation markers like [1], [2], etc., to refer to the corresponding papers.

Main Abstract:
Over four decades, the majority addresses the problem of optical flow estimation using variational methods. With the advance of machine learning, some recent works have attempted to address the problem using convolutional neural network (CNN) and have showed promising results. FlowNet2, the state-of-the-art CNN, requires over 160M parameters to achieve accurate flow estimation. Our LiteFlowNet2 outperforms FlowNet2 on Sintel and KITTI benchmarks, while being 25.3 times smaller in the footprint and 3.1 times faster in the running speed. LiteFlowNet2 which is built on the foundation laid by conventional methods has marked a milestone to achieve the corresponding roles as data fidelity and regularization in variational methods. We present an effective flow inference approach at each pyramid level through a novel lightweight cascaded network. It provides high flow estimation accuracy through early correction with seamless incorporation of descriptor matching. A novel flow regularization layer is used to ameliorate the issue of outliers and vague flow boundaries through a novel feature-driven local convolution. Our network also owns an effective structure for pyramidal feature extraction and embraces feature warping rather than image warping as practiced in FlowNet2. Comparing to our earlier work, LiteFlowNet2 improves the optical flow accuracy on Sintel clean pass by 24 , Sintel final pass by 8.9 , KITTI 2012 by 16.8 , and KITTI 2015 by 17.5 . Our network protocol and trained models will be made publicly available on this https URL .

Cited Abstract(s):
[1]: Optical flow cannot be computed locally, since only one independent measurement is available from the image sequence at a point, while the flow velocity has two components. A second constraint is needed. A method for finding the optical flow pattern is presented which assumes that the apparent velocity of the brightness pattern varies smoothly almost everywhere in the image. An iterative implementation is shown which successfully computes the optical flow for a number of synthetic image sequences. The algorithm is robust in that it can handle image sequences that are quantified rather coarsely in space and time. It is also insensitive to quantization of brightness levels and additive noise. Examples are included where the assumption of smoothness is violated at singular points or along lines in the image.

[2]: We study an energy functional for computing optical flow that combines three assumptions: a brightness constancy assumption, a gradient constancy assumption, and a discontinuity-preserving spatio-temporal smoothness constraint. In order to allow for large displacements, linearisations in the two data terms are strictly avoided. We present a consistent numerical scheme based on two nested fixed point iterations. By proving that this scheme implements a coarse-to-fine warping strategy, we give a theoretical foundation for warping which has been used on a mainly experimental basis so far. Our evaluation demonstrates that the novel method gives significantly smaller angular errors than previous techniques for optical flow estimation. We show that it is fairly insensitive to parameter variations, and we demonstrate its excellent robustness under noise.

[3]: We propose a novel approach for optical flow estimation, targeted at large displacements with significant occlusions. It consists of two steps: i) dense matching by edge-preserving interpolation from a sparse set of matches; ii) variational energy minimization initialized with the dense matches. The sparse-to-dense interpolation relies on an appropriate choice of the distance, namely an edge-aware geodesic distance. This distance is tailored to handle occlusions and motion boundaries - two common and difficult issues for optical flow computation. We also propose an approximation scheme for the geodesic distance to allow fast computation without loss of performance. Subsequent to the dense interpolation step, standard one-level variational energy minimization is carried out on the dense matches to obtain the final flow estimation. The proposed approach, called Edge-Preserving Interpolation of Correspondences (EpicFlow) is fast and robust to large displacements. It significantly outperforms the state of the art on MPI-Sintel and performs on par on Kitti and Middlebury.

[4]: Optical flow computation is a key component in many computer vision systems designed for tasks such as action detection or activity recognition. However, despite several major advances over the last decade, handling large displacement in optical flow remains an open problem. Inspired by the large displacement optical flow of Brox and Malik, our approach, termed Deep Flow, blends a matching algorithm with a variational approach for optical flow. We propose a descriptor matching algorithm, tailored to the optical flow problem, that allows to boost performance on fast motions. The matching algorithm builds upon a multi-stage architecture with 6 layers, interleaving convolutions and max-pooling, a construction akin to deep convolutional nets. Using dense sampling, it allows to efficiently retrieve quasi-dense correspondences, and enjoys a built-in smoothing effect on descriptors matches, a valuable asset for integration into an energy minimization framework for optical flow estimation. Deep Flow efficiently handles large displacements occurring in realistic videos, and shows competitive performance on optical flow benchmarks. Furthermore, it sets a new state-of-the-art on the MPI-Sintel dataset.

[5]: Optical flow estimation is classically marked by the requirement of dense sampling in time. While coarse-to-fine warping schemes have somehow relaxed this constraint, there is an inherent dependency between the scale of structures and the velocity that can be estimated. This particularly renders the estimation of detailed human motion problematic, as small body parts can move very fast. In this paper, we present a way to approach this problem by integrating rich descriptors into the variational optical flow setting. This way we can estimate a dense optical flow field with almost the same high accuracy as known from variational optical flow, while reaching out to new domains of motion analysis where the requirement of dense sampling in time is no longer satisfied.

[6]: This paper presents interactive image editing tools using a new randomized algorithm for quickly finding approximate nearest-neighbor matches between image patches. Previous research in graphics and vision has leveraged such nearest-neighbor searches to provide a variety of high-level digital image editing tools. However, the cost of computing a field of such matches for an entire image has eluded previous efforts to provide interactive performance. Our algorithm offers substantial performance improvements over the previous state of the art (20-100x), enabling its use in interactive editing tools. The key insights driving the algorithm are that some good patch matches can be found via random sampling, and that natural coherence in the imagery allows us to propagate such matches quickly to surrounding areas. We offer theoretical analysis of the convergence properties of the algorithm, as well as empirical and practical evidence for its high quality and performance. This one simple algorithm forms the basis for a variety of tools -- image retargeting, completion and reshuffling -- that can be used together in the context of a high-level image editing application. Finally, we propose additional intuitive constraints on the synthesis process that offer the user a level of control unavailable in previous methods.

[7]: 

[8]: Most variational optic flow approaches just consist of three constituents: a data term, a smoothness term and a smoothness weight. In this paper, we present an approach that harmonises these three components. We start by developing an advanced data term that is robust under outliers and varying illumination conditions. This is achieved by using constraint normalisation, and an HSV colour representation with higher order constancy assumptions and a separate robust penalisation. Our novel anisotropic smoothness is designed to work complementary to the data term. To this end, it incorporates directional information from the data constraints to enable a filling-in of information solely in the direction where the data term gives no information, yielding an optimal complementary smoothing behaviour. This strategy is applied in the spatial as well as in the spatio-temporal domain. Finally, we propose a simple method for automatically determining the optimal smoothness weight. This method bases on a novel concept that we call "optimal prediction principle" (OPP). It states that the flow field obtained with the optimal smoothness weight allows for the best prediction of the next frames in the image sequence. The benefits of our "optic flow in harmony" (OFH) approach are demonstrated by an extensive experimental validation and by a competitive performance at the widely used Middlebury optic flow benchmark.
Since the pioneering work by Horn and Schunck [1] , variational methods have dominated optical flow estimation. Brox al address illumination changes by combining the brightness and gradient constancy assumptions [1]6 . Brox al integrate rich descriptors into a variational formulation [5] . In DeepFlow [4] , Weinzaepfel al propose to correlate multi-scale patches and incorporate this as the matching term in a functional. In PatchMatch Filter [7] , Lu al establish dense correspondence using the superpixel-based PatchMatch [6] . Revaud al propose a method EpicFlow that uses externally matched flows as the initialization and then performs interpolation [1]8 . Zimmer al design the complementary regularization that exploits directional information from the constraints imposed in data term [8] . Our network that infers optical flow and performs flow regularization is inspired by the use of data fidelity and regularization in variational methods.