An Adaptive Smoothness Parameter Strategy for Variational Optical Flow Model

The smoothness parameter is used to balance the weight of the data term and the smoothness term in variational optical flow model, which plays very significant role for the optical flow estimation, but existing methods fail to obtain the optimal smoothness parameters (OSP). In order to solve this problem, an adaptive smoothness parameter strategy is proposed. First, an amalgamated simple linear iterative cluster (SLIC) and local membership function (LMF) algorithm is used to segment the entire image into several superpixel regions. Then, image quality parameters (IQP) are calculated, respectively, for each superpixel region. Finally, a neural network model is applied to compute the smoothness parameter by these image quality parameters of each superpixel region. Experiments were done in three public datasets (Middlebury, MPI_Sintel, and KITTI) and our self-constructed outdoor dataset with the proposed method and other existing classical methods; the results show that our OSP method achieves higher accuracy than other smoothness parameter selection methods in all these four datasets. Combined with the dual fractional order variational optical flow model (DFOVOFM), the proposed model shows better performance than other models in scenes with illumination inhomogeneity and abnormity. The OSP method fills the blank of the research of adaptive smoothness parameter, pushing the development of the variational optical flow models.

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Fractional-order variational optical flow model for motion estimation

Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rsta.2012.0148 ◽

2013 ◽

Vol 371 (1990) ◽

pp. 20120148 ◽

Cited By ~ 15

Author(s):

Dali Chen ◽

Hu Sheng ◽

YangQuan Chen ◽

Dingyü Xue

Keyword(s):

Motion Estimation ◽

Optical Flow ◽

Fractional Order ◽

Flow Model ◽

Theoretical Implication ◽

Lagrange Equations ◽

Flow Models ◽

New Class ◽

Model Research ◽

Fractional Variational Problem

A new class of fractional-order variational optical flow models, which generalizes the differential of optical flow from integer order to fractional order, is proposed for motion estimation in this paper. The corresponding Euler–Lagrange equations are derived by solving a typical fractional variational problem, and the numerical implementation based on the Grünwald–Letnikov fractional derivative definition is proposed to solve these complicated fractional partial differential equations. Theoretical analysis reveals that the proposed fractional-order variational optical flow model is the generalization of the typical Horn and Schunck (first-order) variational optical flow model and the second-order variational optical flow model, which provides a new idea for us to study the optical flow model and has an important theoretical implication in optical flow model research. The experiments demonstrate the validity of the generalization of differential order.

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Directionally Weakened Diffusion for Optical Flow

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.403-408.2449 ◽

2011 ◽

Vol 403-408 ◽

pp. 2449-2452

Author(s):

Jie Zhao ◽

Huai Bin Wang ◽

Yuan Quan Wang

Keyword(s):

Optical Flow ◽

New Method ◽

Accurate Estimation ◽

Laplacian Operator ◽

Flow Estimation ◽

Optical Flow Computation ◽

Computer Vision Applications ◽

Smoothness Term ◽

Motion Discontinuities ◽

Data Term

Optical flow estimation from image sequences is of paramount importance to computer vision applications. Many optical flow algorithms have been proposed for optical flow computation, which minimize a certain energy function involving a data term and a smoothness term. In this paper, we propose a new method to compute optical flow by decomposing the Laplacian operator along the tangential and gradient direction of the image. Experimental results show that the new method could gain more accurate estimation of optical flow around motion discontinuities compared with the classical methods.

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Optimization methods for l 1 -energy minimization in the estimation of optical flow

Carpathian Journal of Mathematics ◽

10.37193/cjm.2013.01.03 ◽

2013 ◽

Vol 29 (1) ◽

pp. 109-117

Author(s):

MIRCEA DAN RUS ◽

Keyword(s):

Optical Flow ◽

Energy Minimization ◽

Optimization Methods ◽

L1 Norm ◽

Differential Model ◽

Flow Models ◽

Energy Functionals ◽

Flow Estimation ◽

Optical Flow Estimation ◽

Estimation Problems

The aim of this paper is to present a new approach for solving the minimization problem for a large class of energy functionals that appear in the differential models of optical flow estimation problems, and which are expressed using the discrete l1-norm. The choice of l1-energy minimization is motivated by the fact that quadratic l2 optimization is not robust to outliers and that l1-norm is a better choice for modeling real problems involving discrete signals. The method described in this paper is very general, thus the advantage of being applicable to almost every differential model that has been proposed so far for the optical flow estimation problem. In order to test and validate our method, a MATLAB implementation on several optical flow models is currently under development. Also, a multi-core implementation on GP-GPU is to be considered in the near future.

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Scene Flow Estimation Based on Adaptive Anisotropic Total Variation Flow-Driven Method

Mathematical Problems in Engineering ◽

10.1155/2018/4908273 ◽

2018 ◽

Vol 2018 ◽

pp. 1-10

Author(s):

Xuezhi Xiang ◽

Rongfang Zhang ◽

Mingliang Zhai ◽

Deguang Xiao ◽

Erwei Bai

Keyword(s):

Optical Flow ◽

Total Variation ◽

Stereo Image ◽

Anisotropic Flow ◽

Flow Estimation ◽

Real Scene ◽

Total Variation Flow ◽

Scene Flow ◽

Smoothness Term ◽

Anisotropic Total Variation

Scene flow estimation based on disparity and optical flow is a challenging task. We present a novel method based on adaptive anisotropic total variation flow-driven method for scene flow estimation from a calibrated stereo image sequence. The basic idea is that diffusion of flow field in different directions has different rates, which can be used to calculate total variation and anisotropic diffusion automatically. Brightness consistency and gradient consistency constraint are employed to establish the data term, and adaptive anisotropic flow-driven penalty constraint is employed to establish the smoothness term. Similar to the optical flow estimation, there are also large displacement problems in the estimation of the scene flow, which is solved by introducing a hierarchical computing optimization. The proposed method is verified by using the synthetic dataset and the real scene image sequences. The experimental results show the effectiveness of the proposed algorithm.

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An Improved Fractional-Order Variational Optical Flow Model Combining Structure Tensor

Mathematical Problems in Engineering ◽

10.1155/2021/9960784 ◽

2021 ◽

Vol 2021 ◽

pp. 1-10

Author(s):

Bin Zhu ◽

Zhaodong Wang ◽

Lianfang Tian ◽

Jinmei Guo ◽

Lingjian Wang ◽

...

Keyword(s):

Optical Flow ◽

Fractional Order ◽

Flow Model ◽

Structure Tensor ◽

Image Feature ◽

Detailed Calculation ◽

Flow Models ◽

Flow Vector ◽

Illumination Changes ◽

Motion Speed

Dealing with problems of illumination changes in optical flow estimation, an improved variational optical flow model is proposed in this paper. The local structure constancy constraint (LSCC) is applied in the data term of the traditional HS (Horn & Schunck) optical flow model to substitute the brightness constancy constraint. The fractional-order smoothness constraint (FSC) is applied in the smoothness term of the HS model. Then, the detailed calculation processes from the optical flow model to the optical flow value are explained. The structure tensor in LSCC is an image feature that is constant in the illumination changes scene. The fractional differential coefficient in FSC can fuse the local neighborhood optical flow vector into the optical flow vector of the target pixel, which can improve the integrity of the motion region with the same motion speed. Combining LSCC with FSC, our improved optical flow model can obtain an accurate optical flow field with clear outline in the illumination abnormity scene. The experimental results show that, compared with other optical flow models, our model is more suitable for the illumination changes scene and can be employed in outdoor motion detection projects.

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Simple explicit model of liquid mean flow in region above axial impeller

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc19852396 ◽

1985 ◽

Vol 50 (11) ◽

pp. 2396-2410

Author(s):

Miloslav Hošťálek ◽

Ivan Fořt

Keyword(s):

Vortex Flow ◽

Flow Model ◽

Quantitative Agreement ◽

Mean Flow ◽

Flat Bottom ◽

Proposed Model ◽

Minimum Number ◽

The Mean ◽

Model Equations ◽

Radial Circulation

The study describes a method of modelling axial-radial circulation in a tank with an axial impeller and radial baffles. The proposed model is based on the analytical solution of the equation for vortex transport in the mean flow of turbulent liquid. The obtained vortex flow model is tested by the results of experiments carried out in a tank of diameter 1 m and with the bottom in the shape of truncated cone as well as by the data published for the vessel of diameter 0.29 m with flat bottom. Though the model equations are expressed in a simple form, good qualitative and even quantitative agreement of the model with reality is stated. Apart from its simplicity, the model has other advantages: minimum number of experimental data necessary for the completion of boundary conditions and integral nature of these data.

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Mathematical modelling of salt purification by recrystallization. A cross-current flow model and its comparison with the countercurrent arrangement

Collection of Czechoslovak Chemical Communications ◽

10.1135/cccc19862489 ◽

1986 ◽

Vol 51 (11) ◽

pp. 2489-2501

Author(s):

Benitto Mayrhofer ◽

Jana Mayrhoferová ◽

Lubomír Neužil ◽

Jaroslav Nývlt

Keyword(s):

Flow Model ◽

Current Flow ◽

Countercurrent Flow ◽

Flow Models ◽

Multi Stage ◽

Stage Crystallization ◽

The Cross ◽

Current Flows ◽

Set Up ◽

Cross Current

A model is derived for a multi-stage crystallization with cross-current flows of the solution and the crystals being purified. The purity of the product is compared with that achieved in the countercurrent arrangement. A suitable function has been set up which allows the cross-current and countercurrent flow models to be compared and reduces substantially the labour of computation for the countercurrent arrangement. Using the recrystallization of KAl(SO4)2.12 H2O as an example, it is shown that, when the cross-current and countercurrent processes are operated at the same output, the countercurrent arrangement is more advantageous because its solvent consumption is lower.

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