Multi-spectral probabilistic diffusion using bayesian classification

(An overview of) Synergistic reconstruction for multimodality/multichannel imaging methods

Imaging is omnipresent in modern society with imaging devices based on a zoo of physical principles, probing a specimen across different wavelengths, energies and time. Recent years have seen a change in the imaging landscape with more and more imaging devices combining that which previously was used separately. Motivated by these hardware developments, an ever increasing set of mathematical ideas is appearing regarding how data from different imaging modalities or channels can be synergistically combined in the image reconstruction process, exploiting structural and/or functional correlations between the multiple images. Here we review these developments, give pointers to important challenges and provide an outlook as to how the field may develop in the forthcoming years. This article is part of the theme issue 'Synergistic tomographic image reconstruction: part 1'.

Vector-valued image processing by parallel level sets

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.

Application of the extremum stack to neurological MRI

The extremum stack, as proposed by Koenderink, is a multiresolution image description and segmentation scheme which examines intensity extrema (minima and maxima) as they move and merge through a series of progressively isotropically diffused images known as scale space. Such a data-driven approach is attractive because it is claimed to be a generally applicable and natural method of image segmentation. The performance of the extremum stack is evaluated here using the case of neurological magnetic resonance imaging data as a specific example, and means of improving its performance proposed. It is confirmed experimentally that the extremum stack has the desirable property of being shift-, scale-, and rotation-invariant, and produces natural results for many compact regions of anatomy. It handles elongated objects poorly, however, and subsections of regions may merge prematurely before each region is represented as a single node. It is shown that this premature merging can often be avoided by the application of either a variable conductance-diffusing preprocessing step, or more effectively, the use of an adaptive variable conductance diffusion method within the extremum stack itself in place of the isotropic Gaussian diffusion proposed by Koenderink.