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

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.

scholarly journals Fractional-order variational optical flow model for motion estimation

2013 ◽  
Vol 371 (1990) ◽  
pp. 20120148 ◽  
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.

scholarly journals An Adaptive Smoothness Parameter Strategy for Variational Optical Flow Model

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Hussain Zaid H. Alsharif ◽  
Tong Shu ◽  
Bin Zhu ◽  
Zeyad Farisi
Keyword(s):  
Image Quality ◽  
Optical Flow ◽  
Flow Model ◽  
Quality Parameters ◽  
Flow Models ◽  
Flow Estimation ◽  
Proposed Model ◽  
Smoothness Parameter ◽  
Smoothness Term ◽  
Public Datasets

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.

scholarly journals An Improved Fractional-Order Optical Flow Model for Motion Estimation

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Bin Zhu ◽  
Lianfang Tian ◽  
Qiliang Du ◽  
Qiuxia Wu ◽  
Lixin Shi
Keyword(s):  
Flow Field ◽  
Motion Estimation ◽  
Optical Flow ◽  
Fractional Order ◽  
Field Experiments ◽  
Flow Model ◽  
Lagrange Equation ◽  
Taylor Series Expansion ◽  
Constraint Equation ◽  
Optical Flow Field

The Horn and Schunck (HS) optical flow model cannot preserve discontinuity of motion estimation and has low accuracy especially for the image sequence, which includes complex texture. To address this problem, an improved fractional-order optical flow model is proposed. In particular, the fractional-order Taylor series expansion is applied in the brightness constraint equation of the HS model. The fractional-order flow field derivative is also used in the smoothing constraint equation. The Euler-Lagrange equation is utilized for the minimization of the energy function of the fractional-order optical flow model. Two-dimensional fractional differential masks are proposed and applied to the calculation of the model simplification. Considering the spatiotemporal memory property of fractional-order, the algorithm preserves the edge discontinuity of the optical flow field while improving the accuracy of the estimation of the dense optical flow field. Experiments on Middlebury datasets demonstrate the predominance of our proposed algorithm.

scholarly journals Adaptive dual fractional‐order variational optical flow model for motion estimation

2019 ◽  
Vol 13 (3) ◽  
pp. 277-284 ◽  
Author(s):  
Bin Zhu ◽  
Lian‐Fang Tian ◽  
Qi‐Liang Du ◽  
Qiu‐Xia Wu ◽  
Farisi Zeyad Sahl ◽  
...  
Keyword(s):  
Motion Estimation ◽  
Optical Flow ◽  
Fractional Order ◽  
Flow Model

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

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.

Fractional-Order Viscoelasticity in One-Dimensional Blood Flow Models

2014 ◽  
Vol 42 (5) ◽  
pp. 1012-1023 ◽  
Author(s):  
Paris Perdikaris ◽  
George Em. Karniadakis
Keyword(s):  
Blood Flow ◽  
Fractional Order ◽  
One Dimensional ◽  
Flow Models ◽  
Blood Flow Models

Study of the Response of PW Traffic Flow Model to a Bottleneck on a Circular Road and its Suitability for Heterogeneous Traffic Conditions

2021 ◽  
Vol 9 (4) ◽  
pp. 460-463
Keyword(s):  
Fluid Flow ◽  
Traffic Flow ◽  
Flow Model ◽  
Equation Model ◽  
Heterogeneous Traffic ◽  
Flow Conditions ◽  
Flow Models ◽  
Traffic Conditions ◽  
Model Response ◽  
Traffic Flow Models

The traffic flow conditions in developing countries are predominantly heterogeneous. The early developed traffic flow models have been derived from fluid flow to capture the behavior of the traffic. The very first two-equation model derived from fluid flow is known as the Payne-Whitham or PW Model. Along with the traffic flow, this model also captures the traffic acceleration. However, the PW model adopts a constant driver behavior which cannot be ignored, especially in the situation of heterogeneous traffic.This research focuses on testing the PW model and its suitability for heterogeneous traffic conditions by observing the model response to a bottleneck on a circular road. The PW model is mathematically approximated using the Roe Decomposition and then the performance of the model is observed using simulations.

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