Vector-valued image processing by parallel level sets

Matthias Joachim Ehrhardt, Simon R. Arridge

Research output: Contribution to journalArticlepeer-review

54 Citations (SciVal)


Vector-valued images such as RGB color images or multimodal medical images show a strong interchannel correlation, which is not exploited by most image processing tools. We propose a new notion of treating vector-valued images which is based on the angle between the spatial gradients of their channels. Through minimizing a cost functional that penalizes large angles, images with parallel level sets can be obtained. After formally introducing this idea and the corresponding cost functionals, we discuss their Gâteaux derivatives that lead to a diffusion-like gradient descent scheme. We illustrate the properties of this cost functional by several examples in denoising and demosaicking of RGB color images. They show that parallel level sets are a suitable concept for color image enhancement. Demosaicking with parallel level sets gives visually perfect results for low noise levels. Furthermore, the proposed functional yields sharper images than the other approaches in comparison.

Original languageEnglish
Article number6576903
Pages (from-to)9-18
Number of pages10
JournalIEEE Transactions on Image Processing
Issue number1
Publication statusPublished - 1 Jan 2014


  • Demosaicking
  • Denoising
  • Non-linear diffusion
  • Parallel level sets
  • Variational methods
  • Vector-valued images

ASJC Scopus subject areas

  • Software
  • Computer Graphics and Computer-Aided Design


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