
Previous Article
Image retinex based on the nonconvex TVtype regularization
 IPI Home
 This Issue

Next Article
On the identification of the nonlinearity parameter in the Westervelt equation from boundary measurements
Inbetweening autoanimation via FokkerPlanck dynamics and thresholding
1.  Department of Mathematics, Duke University, Durham, NC 27708, USA 
2.  College of Marine Ecology and Environment, Shanghai Ocean University, China 
3.  Southern marine science and engineering Guangdong laboratory, Zhuhai, China 
4.  Department of Mathematics and Department of Physics, Duke University, Durham, NC 27708, USA 
We propose an equilibriumdriven deformation algorithm (EDDA) to simulate the inbetweening transformations starting from an initial image to an equilibrium image, which covers images varying from a greyscale type to a colorful type on planes or manifolds. The algorithm is based on the FokkerPlanck dynamics on manifold, which automatically incorporates the manifold structure suggested by dataset and satisfies positivity, unconditional stability, mass conservation law and exponentially convergence. The thresholding scheme is adapted for the sharp interface dynamics and is used to achieve the finite time convergence. Using EDDA, three challenging examples, (I) facial aging process, (II) coronavirus disease 2019 (COVID19) pneumonia invading/fading process, and (III) continental evolution process are computed efficiently.
References:
[1] 
M. Cong, M. Bao, Jane L. E., K. S. Bhat and R. Fedkiw, Fully automatic generation of anatomical face simulation models, In Proceedings of the 14th ACM SIGGRAPH/Eurographics Symposium on Computer Animation, (2015), 175–183. doi: 10.1145/2786784.2786786. Google Scholar 
[2] 
Q. Du, M. D. Gunzburger and L. Ju, Voronoibased finite volume methods, optimal voronoi meshes, and pdes on the sphere, Computer Methods in Applied Mechanics and Engineering, 192 (2003), 39333957. doi: 10.1016/S00457825(03)003943. Google Scholar 
[3] 
R. Eymard, T. Gallouët and R. Herbin, Finite volume methods, Handbook of numerical analysis, Vol. VII, Handb. Numer. Anal., VII, NorthHolland, Amsterdam, 2000, 713–1020. doi: 10.1086/phos.67.4.188705. Google Scholar 
[4] 
Y. Gao, T. Li, X. Li and J.G. Liu, Transition path theory for langevin dynamics on manifold: optimal control and datadriven solver, arXiv: 2010.09988, 2020. Google Scholar 
[5] 
Y. Gao, J.G. Liu and N. Wu, Datadriven efficient solvers and predictions of conformational transitions for langevin dynamics on manifold in high dimensions, arXiv: 2005.12787, 2020. Google Scholar 
[6] 
Z. Leng, R. Zhu, W. Hou, Y. Feng, Y. Yang, Q. Han, G. Shan, F. Meng, D. Du, S. Wang, J. Fan, W. Wang, L. Deng, H. Shi, H.Li, Z. Hu, F. Zhang, J. Gao, H. Liu, X. Li, Y. Zhao, K. Yin, X. He, Z. Gao, Y. Wang, B. Yang, R. Jin, I. Stambler, L. W. Lim, H. Su, A. Moskalev, A. Cano, S. Chakrabarti, K.. Min, G. EllisonHughes, C. Caruso, K. Jin and R. C. Zhao, Transplantation of ACE2mesenchymal stem cells improves the outcome of patients with COVID19 pneumonia, Aging and disease, 11 (2020), 216. Google Scholar 
[7] 
The Sydney Morning Herald, July 4, 2014, 'Can your face reveal how long you'll live?', http://www.dailylife.com.au/healthandfitness/dlfitness/canyourfacerevealhowlongyoulllive201407083bjsk.html. Google Scholar 
[8] 
R. J. Renka, Algorithm 772: Stripack: Delaunay triangulation and voronoi diagram on the surface of a sphere, ACM Transactions on Mathematical Software (TOMS), 23 (1997), 416434. doi: 10.1145/275323.275329. Google Scholar 
[9] 
M. Zollhöfer, J. Thies, P. Garrido, D. Bradley, T. Beeler, P. Pérez, M. Stamminger, M. Nießner and C. Theobalt, State of the art on monocular 3d face reconstruction, tracking, and applications, In Computer Graphics Forum, volume 37. Wiley Online Library, 2018, 523–550. Google Scholar 
show all references
References:
[1] 
M. Cong, M. Bao, Jane L. E., K. S. Bhat and R. Fedkiw, Fully automatic generation of anatomical face simulation models, In Proceedings of the 14th ACM SIGGRAPH/Eurographics Symposium on Computer Animation, (2015), 175–183. doi: 10.1145/2786784.2786786. Google Scholar 
[2] 
Q. Du, M. D. Gunzburger and L. Ju, Voronoibased finite volume methods, optimal voronoi meshes, and pdes on the sphere, Computer Methods in Applied Mechanics and Engineering, 192 (2003), 39333957. doi: 10.1016/S00457825(03)003943. Google Scholar 
[3] 
R. Eymard, T. Gallouët and R. Herbin, Finite volume methods, Handbook of numerical analysis, Vol. VII, Handb. Numer. Anal., VII, NorthHolland, Amsterdam, 2000, 713–1020. doi: 10.1086/phos.67.4.188705. Google Scholar 
[4] 
Y. Gao, T. Li, X. Li and J.G. Liu, Transition path theory for langevin dynamics on manifold: optimal control and datadriven solver, arXiv: 2010.09988, 2020. Google Scholar 
[5] 
Y. Gao, J.G. Liu and N. Wu, Datadriven efficient solvers and predictions of conformational transitions for langevin dynamics on manifold in high dimensions, arXiv: 2005.12787, 2020. Google Scholar 
[6] 
Z. Leng, R. Zhu, W. Hou, Y. Feng, Y. Yang, Q. Han, G. Shan, F. Meng, D. Du, S. Wang, J. Fan, W. Wang, L. Deng, H. Shi, H.Li, Z. Hu, F. Zhang, J. Gao, H. Liu, X. Li, Y. Zhao, K. Yin, X. He, Z. Gao, Y. Wang, B. Yang, R. Jin, I. Stambler, L. W. Lim, H. Su, A. Moskalev, A. Cano, S. Chakrabarti, K.. Min, G. EllisonHughes, C. Caruso, K. Jin and R. C. Zhao, Transplantation of ACE2mesenchymal stem cells improves the outcome of patients with COVID19 pneumonia, Aging and disease, 11 (2020), 216. Google Scholar 
[7] 
The Sydney Morning Herald, July 4, 2014, 'Can your face reveal how long you'll live?', http://www.dailylife.com.au/healthandfitness/dlfitness/canyourfacerevealhowlongyoulllive201407083bjsk.html. Google Scholar 
[8] 
R. J. Renka, Algorithm 772: Stripack: Delaunay triangulation and voronoi diagram on the surface of a sphere, ACM Transactions on Mathematical Software (TOMS), 23 (1997), 416434. doi: 10.1145/275323.275329. Google Scholar 
[9] 
M. Zollhöfer, J. Thies, P. Garrido, D. Bradley, T. Beeler, P. Pérez, M. Stamminger, M. Nießner and C. Theobalt, State of the art on monocular 3d face reconstruction, tracking, and applications, In Computer Graphics Forum, volume 37. Wiley Online Library, 2018, 523–550. Google Scholar 
Tolerance  
Steps (Linear)  1737  4026  6304  8581 
Steps (Threshold)  960  960  960  960 
Tolerance  
Steps (Linear)  1737  4026  6304  8581 
Steps (Threshold)  960  960  960  960 
[1] 
Anton Schiela, Julian Ortiz. Second order directional shape derivatives of integrals on submanifolds. Mathematical Control & Related Fields, 2021 doi: 10.3934/mcrf.2021017 
[2] 
Andreu Ferré Moragues. Properties of multicorrelation sequences and large returns under some ergodicity assumptions. Discrete & Continuous Dynamical Systems, 2021, 41 (6) : 28092828. doi: 10.3934/dcds.2020386 
[3] 
Caifang Wang, Tie Zhou. The order of convergence for Landweber Scheme with $\alpha,\beta$rule. Inverse Problems & Imaging, 2012, 6 (1) : 133146. doi: 10.3934/ipi.2012.6.133 
[4] 
Roberto Civino, Riccardo Longo. Formal security proof for a scheme on a topological network. Advances in Mathematics of Communications, 2021 doi: 10.3934/amc.2021009 
[5] 
Misha Perepelitsa. A model of cultural evolution in the context of strategic conflict. Kinetic & Related Models, , () : . doi: 10.3934/krm.2021014 
[6] 
Pengyu Chen. Nonautonomous stochastic evolution equations with nonlinear noise and nonlocal conditions governed by noncompact evolution families. Discrete & Continuous Dynamical Systems, 2021, 41 (6) : 27253737. doi: 10.3934/dcds.2020383 
[7] 
WolfJüergen Beyn, Janosch Rieger. The implicit Euler scheme for onesided Lipschitz differential inclusions. Discrete & Continuous Dynamical Systems  B, 2010, 14 (2) : 409428. doi: 10.3934/dcdsb.2010.14.409 
[8] 
Alina Chertock, Alexander Kurganov, Mária LukáčováMedvi${\rm{\check{d}}}$ová, Șeyma Nur Özcan. An asymptotic preserving scheme for kinetic chemotaxis models in two space dimensions. Kinetic & Related Models, 2019, 12 (1) : 195216. doi: 10.3934/krm.2019009 
[9] 
Pengyu Chen. Periodic solutions to nonautonomous evolution equations with multidelays. Discrete & Continuous Dynamical Systems  B, 2021, 26 (6) : 29212939. doi: 10.3934/dcdsb.2020211 
[10] 
Caichun Chai, Tiaojun Xiao, Zhangwei Feng. Evolution of revenue preference for competing firms with nonlinear inverse demand. Journal of Industrial & Management Optimization, 2021 doi: 10.3934/jimo.2021071 
[11] 
Matheus C. Bortolan, José Manuel Uzal. Upper and weaklower semicontinuity of pullback attractors to impulsive evolution processes. Discrete & Continuous Dynamical Systems  B, 2021, 26 (7) : 36673692. doi: 10.3934/dcdsb.2020252 
[12] 
K. Ravikumar, Manil T. Mohan, A. Anguraj. Approximate controllability of a nonautonomous evolution equation in Banach spaces. Numerical Algebra, Control & Optimization, 2021, 11 (3) : 461485. doi: 10.3934/naco.2020038 
[13] 
Zhaoqiang Ge. Controllability and observability of stochastic implicit systems and stochastic GEevolution operator. Numerical Algebra, Control & Optimization, 2021 doi: 10.3934/naco.2021009 
[14] 
Tomáš Roubíček. An energyconserving timediscretisation scheme for poroelastic media with phasefield fracture emitting waves and heat. Discrete & Continuous Dynamical Systems  S, 2017, 10 (4) : 867893. doi: 10.3934/dcdss.2017044 
[15] 
ChihChiang Fang. Bayesian decision making in determining optimal leased term and preventive maintenance scheme for leased facilities. Journal of Industrial & Management Optimization, 2020 doi: 10.3934/jimo.2020127 
[16] 
Rabiaa Ouahabi, NasrEddine Hamri. Design of new scheme adaptive generalized hybrid projective synchronization for two different chaotic systems with uncertain parameters. Discrete & Continuous Dynamical Systems  B, 2021, 26 (5) : 23612370. doi: 10.3934/dcdsb.2020182 
[17] 
Mario Bukal. Wellposedness and convergence of a numerical scheme for the corrected DerridaLebowitzSpeerSpohn equation using the Hellinger distance. Discrete & Continuous Dynamical Systems, 2021, 41 (7) : 33893414. doi: 10.3934/dcds.2021001 
[18] 
Tôn Việt Tạ. Strict solutions to stochastic semilinear evolution equations in Mtype 2 Banach spaces. Communications on Pure & Applied Analysis, , () : . doi: 10.3934/cpaa.2021050 
[19] 
Siqi Chen, YongKui Chang, Yanyan Wei. Pseudo $ S $asymptotically Bloch type periodic solutions to a damped evolution equation. Evolution Equations & Control Theory, 2021 doi: 10.3934/eect.2021017 
[20] 
Qi Deng, Zhipeng Qiu, Ting Guo, Libin Rong. Modeling withinhost viral dynamics: The role of CTL immune responses in the evolution of drug resistance. Discrete & Continuous Dynamical Systems  B, 2021, 26 (7) : 35433562. doi: 10.3934/dcdsb.2020245 
2019 Impact Factor: 1.373
Tools
Article outline
Figures and Tables
[Back to Top]