Mathematical Problems in Engineering

Advances in Variational and Partial Differential Equation-Based Models for Image Processing and Computer Vision


Lead Editor

1Institute of Computer Science of the Romanian Academy, Iaşi, Romania

2Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy (ISMMA), Bucharest, Romania

3“Al. I. Cuza” University, Iaşi, Romania

4Bielefeld University, Bielefeld, Germany

Advances in Variational and Partial Differential Equation-Based Models for Image Processing and Computer Vision


The mathematical models have been increasingly used in some traditional engineering fields, such as image processing and analysis and computer vision, over the past three decades. So, since the 1980s, the partial differential equations (PDEs) have been successfully used for solving numerous image processing and computer vision tasks.

Many existing image processing and analysis techniques make use of PDE-based techniques and variational calculus, because of their modeling flexibility and some advantages of their numerical implementation. Image denoising and restoration represents an important image processing domain that has been successfully approached by using the PDE models. The nonlinear diffusion-based schemes remove successfully the additive image noise, while preserving the essential image features. Also, the PDE variational approaches have been widely used in many computer vision areas in the last years. Thus, a lot of PDE-based image inpainting, segmentation, registration, and compression techniques have been developed. Video object motion estimation constitutes another important computer vision domain that is successfully approached by using variational frameworks that compute the optical flow. Many challenges still exist in this domain, such as overcoming the unintended effects like the image blurring, staircasing, or speckle noise.

The objective of this special issue is to disseminate advanced research in these domains and to bring together the research achievements of scientists in the PDE-based image processing areas, so as to extend the existing knowledge in these fields. Therefore, we encourage the authors to contribute original high-quality manuscripts that describe novel theoretical and practical results on relevant topics, as well as review articles describing the current state of the art.

Potential topics include but are not limited to the following:

  • Novel PDE variational image restoration solutions using second- and fourth-order diffusion models
  • Nonlinear anisotropic diffusion schemes for image boundary detection
  • Advanced second- and higher-order PDE-based image interpolation techniques
  • Partial differential equation-based compression and decompression approaches
  • Variational level-set based frameworks for image segmentation
  • Effective variational PDE models for optical flow computation
  • Computational techniques for nonlinear image registration using variational solutions
  • Rigorous mathematical investigation of these PDE-based models and their numerical approximation schemes: well-posedness, stability, convergence, and consistency
  • Hybrid denoising and restoration methods involving nonlinear PDE filters
Mathematical Problems in Engineering
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