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The majority of supervised models estimate optical flow through minimizing the numerical difference between the predicted flow and the ground truth, resulting in the loss of positional and geometric characteristics of the calculated flow fields. In addition, these models require a large number of parameters and high computational cost when computing optical flow. To address these issues, this paper presents a novel loss function and a lightweight framework for optical flow estimation. The proposed loss function, called the random epipolar constraint loss function (RECLoss), incorporates epipolar geometry into supervised optimization to transform the numerical difference into geometry constraint. The RECLoss can make the optical flow estimation models more effective and enhance their generalization abilities. Moreover, the design of RECLoss is more interpretable and the estimated optical flow fields from RECLoss have clearly defined mathematical meanings. A lightweight recurrent neural network for optical flow estimation (LRFlow) that balances computational cost and estimation accuracy is also proposed. The LRFlow, containing only 3.0M parameters, consists of a feature extractor, a correlation matching module, and an iterative update unit. The proposed lightweight network achieves state-of-the-art results compared to all other lightweight networks on the challenging MPI-Sintel and KITTI2015 datasets. The effectiveness of RECLoss in improving the accuracy of LRFlow and other state-of-the-art methods such as RAFT and GMA has been validated through extensive experiments. The source code of the project are available at https://github.com/Eryo-iPython/RECLoss. • A loss function incorporates epipolar geometry into supervised optical flow models. • More interpretable and clear mathematical meaning for optical flow estimation. • A lightweight recurrent neural network for optical flow calculation. [ABSTRACT FROM AUTHOR]

This paper proposes a variational formulation with a smoothness constraint for extraction of pressure from two-dimensional velocity field. The method of characteristics is first described as a reduced case to obtain pressure data by a line integral along a given line. Then, a global optimization method is developed, and the Euler–Lagrange equation is obtained to determine a pressure field from velocity data in a domain with suitable boundary conditions. Numerical algorithms are developed to solve the Euler–Lagrange equation with suitable boundary conditions. The accuracy of the developed methods and the effects of the relevant parameters on extraction of pressure are evaluated on a simulated two-dimensional oblique Hiemenz flow. Subsequently, in an experimental case, pressure fields near a freely flying hawkmoth are estimated from high-resolution velocity fields that are obtained by applying the optical flow method to high-speed Schlieren photography images. Pressure field near the hawkmoth wingtip obtained by using (a) Direct-QR method. And (b) iterative method. [ABSTRACT FROM AUTHOR]

The physics-based optical flow (PBOF) model was derived from typical flow visualizations and it provided a more solid physical foundation for optical flow calculation. However, like many recent variational optical flow methods, it is not formulated to deal with the effect of illumination variation. In this paper, we propose a new efficient illumination-invariant optical flow estimation method, which improves the physics-based optical flow model. The proposed method introduces a multiplicative product of the velocity gradient and intensity from PBOF and an additive diffusion component to relax the brightness constancy assumption. The proposed method employs a linear transformation to reduce the influence of varying illumination on the data term. Then, a smoothness-sparsity regularization is used to constrain the minimization problem to have good edge-preserving for optical flow. Furthermore, the numerical implementation is given to solve the optimization problem. The accuracy of the developed method and the robustness against varying illumination are evaluated. The proposed method can provide motion estimation with acceptable accuracy for three optical flow datasets and cloud images of Jupiter's great red spot, which have challenging illumination variations. • More solid physical foundation for optical flow estimation. • A linear transformation to reduce the influence of varying illumination. • A smoothness-sparsity regularization to achieve good edge-preserving. • Flow patterns extracted from Jupiter's great red spot. [ABSTRACT FROM AUTHOR]

Fast and accurate optical flow estimation is a challenging problem in computer vision. In this paper, we present a novel model to solve the optical flow problem by combining the strengths of the Split Bregman method with the advantages of an efficient variational framework. It allows us to employ different regularization tensors for the Split Bregman regularizer to preserve motion discontinuities. Simultaneously, a novel nonlocal Split Bregman method with adaptive support weights is also developed for the smoothness regularization to preserve motion details, repel outliers, enhance contrast, and reduce motion blurring and staircase effect. The proposed algorithm shows significant improvements in preserving sharp flow edges and important motion details. Most of all, it requires only a few iterations to achieve fast convergence and runs faster than the classic TV-L1 flow method. Our method significantly outperforms the current state-of-the-art methods on the challenging MPI-Sintel dataset and shows good performance on the Kitti flow 2015 and Middlebury datasets. [ABSTRACT FROM PUBLISHER]

A variational solution of the physics-based optical flow equation is studied for extraction of high-resolution velocity fields from flow visualization images. The solution to preserve discontinuities in a fluid velocity field is mathematically justified. The uniqueness of the solution and the convergence of a successive approximation sequence are proven. A numerical algorithm is developed and examined through numerical experiments. [ABSTRACT FROM AUTHOR]