Abstract
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.
Highlights
T HERE are many imaging applications where more than one piece of information is given at one single point in space
Another example is given in medical imaging where different scanners measure different properties for the same spatial point - for instance a computed tomography (CT) scanner measures the absorption of X-rays by the body or a magnetic resonance tomography (MR) scanner can measure the response of water molecules to a magnetic field
We propose a new framework based on parallel level sets which can be used for image enhancement of vector-valued images
Summary
T HERE are many imaging applications where more than one piece of information is given at one single point in space. One prominent example of using information between channels is color total variation [4] This extension of the scalar-valued version [5] leads to a non-linear diffusion scheme where the diffusivity depends on all channels. We will see that this approach of enhancing common structures can be used in image processing applications like denoising or demosaicking of color images [3], [8] We distinguish this usage of the term ‘‘level sets’’ from its usage in applications that evolve a (N + 1) dimensional function such that its zero-level-set describes the evolution and topological change in the boundary between two or more objects in an image, for example for segmentation [9], [10].
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