November  2007, 1(4): 593-608. doi: 10.3934/ipi.2007.1.593

Conditional image diffusion


Universitat de les Illes Balears, Ctra Valldemossa km 7.5, Palma de Mallorca, 07122, Spain, Spain, Spain


Universitat de les Illes Balears, Crta. de Valldemossa, km 7.5, 07122 Palma de Mallorca

Received  May 2007 Published  October 2007

In this paper, a theoretical framework for the conditional diffusion of digital images is presented. Different approaches have been proposed to solve this problem by extrapolating the idea of the anisotropic diffusion for a grey level images to vector-valued images. Then, the diffusion of each channel is conditioned to a direction which normally takes into account information from all channels. In our approach, the diffusion model assumes the a priori knowledge of the diffusion direction during all the process.
    The consistency of the model is shown by proving the existence and uniqueness of solution for the proposed equation from the viscosity solutions theory. Also a numerical scheme adapted to this equation based on the neighborhood filter is proposed. Finally, we discuss several applications and we compare the corresponding numerical schemes for the proposed model.
Citation: Antoni Buades, Bartomeu Coll, Jose-Luis Lisani, Catalina Sbert. Conditional image diffusion. Inverse Problems & Imaging, 2007, 1 (4) : 593-608. doi: 10.3934/ipi.2007.1.593

Juan C. Moreno, V. B. Surya Prasath, João C. Neves. Color image processing by vectorial total variation with gradient channels coupling. Inverse Problems & Imaging, 2016, 10 (2) : 461-497. doi: 10.3934/ipi.2016008


Xavier Bresson, Tony F. Chan. Fast dual minimization of the vectorial total variation norm and applications to color image processing. Inverse Problems & Imaging, 2008, 2 (4) : 455-484. doi: 10.3934/ipi.2008.2.455


Jianhong (Jackie) Shen, Sung Ha Kang. Quantum TV and applications in image processing. Inverse Problems & Imaging, 2007, 1 (3) : 557-575. doi: 10.3934/ipi.2007.1.557


Jingwei Liang, Jia Li, Zuowei Shen, Xiaoqun Zhang. Wavelet frame based color image demosaicing. Inverse Problems & Imaging, 2013, 7 (3) : 777-794. doi: 10.3934/ipi.2013.7.777


Lekbir Afraites, Abdelghafour Atlas, Fahd Karami, Driss Meskine. Some class of parabolic systems applied to image processing. Discrete & Continuous Dynamical Systems - B, 2016, 21 (6) : 1671-1687. doi: 10.3934/dcdsb.2016017


Yan Jin, Jürgen Jost, Guofang Wang. A new nonlocal variational setting for image processing. Inverse Problems & Imaging, 2015, 9 (2) : 415-430. doi: 10.3934/ipi.2015.9.415


Yong Zheng Ong, Haizhao Yang. Generative imaging and image processing via generative encoder. Inverse Problems & Imaging, , () : -. doi: 10.3934/ipi.2021060


Ruiliang Zhang, Xavier Bresson, Tony F. Chan, Xue-Cheng Tai. Four color theorem and convex relaxation for image segmentation with any number of regions. Inverse Problems & Imaging, 2013, 7 (3) : 1099-1113. doi: 10.3934/ipi.2013.7.1099


Jiangchuan Fan, Xinyu Guo, Jianjun Du, Weiliang Wen, Xianju Lu, Brahmani Louiza. Analysis of the clustering fusion algorithm for multi-band color image. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1233-1249. doi: 10.3934/dcdss.2019085


Zbigniew Gomolka, Boguslaw Twarog, Jacek Bartman. Improvement of image processing by using homogeneous neural networks with fractional derivatives theorem. Conference Publications, 2011, 2011 (Special) : 505-514. doi: 10.3934/proc.2011.2011.505


Kristian Bredies. Weak solutions of linear degenerate parabolic equations and an application in image processing. Communications on Pure & Applied Analysis, 2009, 8 (4) : 1203-1229. doi: 10.3934/cpaa.2009.8.1203


John B. Greer, Andrea L. Bertozzi. $H^1$ Solutions of a class of fourth order nonlinear equations for image processing. Discrete & Continuous Dynamical Systems, 2004, 10 (1&2) : 349-366. doi: 10.3934/dcds.2004.10.349


Tong Li, Jeungeun Park. Stability of traveling waves of models for image processing with non-convex nonlinearity. Communications on Pure & Applied Analysis, 2018, 17 (3) : 959-985. doi: 10.3934/cpaa.2018047


Luca Calatroni, Bertram Düring, Carola-Bibiane Schönlieb. ADI splitting schemes for a fourth-order nonlinear partial differential equation from image processing. Discrete & Continuous Dynamical Systems, 2014, 34 (3) : 931-957. doi: 10.3934/dcds.2014.34.931


Yan Chen, Kewei Zhang. Young measure solutions of the two-dimensional Perona-Malik equation in image processing. Communications on Pure & Applied Analysis, 2006, 5 (3) : 617-637. doi: 10.3934/cpaa.2006.5.617


Dana Paquin, Doron Levy, Eduard Schreibmann, Lei Xing. Multiscale Image Registration. Mathematical Biosciences & Engineering, 2006, 3 (2) : 389-418. doi: 10.3934/mbe.2006.3.389


Xuerui Gao, Yanqin Bai, Shu-Cherng Fang, Jian Luo, Qian Li. A new hybrid $ l_p $-$ l_2 $ model for sparse solutions with applications to image processing. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021211


Jean-Paul Chehab. Damping, stabilization, and numerical filtering for the modeling and the simulation of time dependent PDEs. Discrete & Continuous Dynamical Systems - S, 2021, 14 (8) : 2693-2728. doi: 10.3934/dcdss.2021002


Wenzhong Zhu, Huanlong Jiang, Erli Wang, Yani Hou, Lidong Xian, Joyati Debnath. X-ray image global enhancement algorithm in medical image classification. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1297-1309. doi: 10.3934/dcdss.2019089


Mehdi Bastani, Davod Khojasteh Salkuyeh. On the GSOR iteration method for image restoration. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 27-43. doi: 10.3934/naco.2020013

2020 Impact Factor: 1.639


  • PDF downloads (48)
  • HTML views (0)
  • Cited by (11)

[Back to Top]