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 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

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 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.

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.

Analysis of a New Class of Impulsive Implicit Sequential Fractional Differential Equations

2020 ◽  
Vol 21 (6) ◽  
pp. 571-587 ◽  
Author(s):  
Akbar Zada ◽  
Sartaj Ali ◽  
Tongxing Li
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Sufficient Conditions ◽  
Uniqueness Of Solutions ◽  
Integer Order ◽  
New Class ◽  
Proposed Model ◽  
Fractional Differential ◽  
Sequential Fractional Differential Equations

AbstractIn this paper, we study an implicit sequential fractional order differential equation with non-instantaneous impulses and multi-point boundary conditions. The article comprehensively elaborate four different types of Ulam’s stability in the lights of generalized Diaz Margolis’s fixed point theorem. Moreover, some sufficient conditions are constructed to observe the existence and uniqueness of solutions for the proposed model. The proposed model contains both the integer order and fractional order derivatives. Thus, the exponential function appearers in the solution of the proposed model which will lead researchers to study fractional differential equations with well known methods of integer order differential equations. In the last, few examples are provided to show the applicability of our main results.

scholarly journals Ego-Motion Estimation Using Recurrent Convolutional Neural Networks through Optical Flow Learning

Electronics ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 222
Author(s):  
Baigan Zhao ◽  
Yingping Huang ◽  
Hongjian Wei ◽  
Xing Hu
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Motion Estimation ◽  
Optical Flow ◽  
Feature Representation ◽  
Sequential Learning ◽  
Navigation Systems ◽  
Motion State ◽  
Training Schemes ◽  
Sequential Images

Visual odometry (VO) refers to incremental estimation of the motion state of an agent (e.g., vehicle and robot) by using image information, and is a key component of modern localization and navigation systems. Addressing the monocular VO problem, this paper presents a novel end-to-end network for estimation of camera ego-motion. The network learns the latent subspace of optical flow (OF) and models sequential dynamics so that the motion estimation is constrained by the relations between sequential images. We compute the OF field of consecutive images and extract the latent OF representation in a self-encoding manner. A Recurrent Neural Network is then followed to examine the OF changes, i.e., to conduct sequential learning. The extracted sequential OF subspace is used to compute the regression of the 6-dimensional pose vector. We derive three models with different network structures and different training schemes: LS-CNN-VO, LS-AE-VO, and LS-RCNN-VO. Particularly, we separately train the encoder in an unsupervised manner. By this means, we avoid non-convergence during the training of the whole network and allow more generalized and effective feature representation. Substantial experiments have been conducted on KITTI and Malaga datasets, and the results demonstrate that our LS-RCNN-VO outperforms the existing learning-based VO approaches.

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