1,057 research outputs found
PDEs for tensor image processing
Methods based on partial differential equations (PDEs) belong to those image processing techniques that can be extended in a particularly elegant way to tensor fields. In this survey paper the most important PDEs for discontinuity-preserving denoising of tensor fields are reviewed such that the underlying design principles becomes evident. We consider isotropic and anisotropic diffusion filters and their corresponding variational methods, mean curvature motion, and selfsnakes. These filters preserve positive semidefiniteness of any positive semidefinite initial tensor field. Finally we discuss geodesic active contours for segmenting tensor fields. Experiments are presented that illustrate the behaviour of all these methods
A flexible space-variant anisotropic regularisation for image restoration with automated parameter selection
We propose a new space-variant anisotropic regularisation term for
variational image restoration, based on the statistical assumption that the
gradients of the target image distribute locally according to a bivariate
generalised Gaussian distribution. The highly flexible variational structure of
the corresponding regulariser encodes several free parameters which hold the
potential for faithfully modelling the local geometry in the image and
describing local orientation preferences. For an automatic estimation of such
parameters, we design a robust maximum likelihood approach and report results
on its reliability on synthetic data and natural images. For the numerical
solution of the corresponding image restoration model, we use an iterative
algorithm based on the Alternating Direction Method of Multipliers (ADMM). A
suitable preliminary variable splitting together with a novel result in
multivariate non-convex proximal calculus yield a very efficient minimisation
algorithm. Several numerical results showing significant quality-improvement of
the proposed model with respect to some related state-of-the-art competitors
are reported, in particular in terms of texture and detail preservation
Double Diffusion Encoding Prevents Degeneracy in Parameter Estimation of Biophysical Models in Diffusion MRI
Purpose: Biophysical tissue models are increasingly used in the
interpretation of diffusion MRI (dMRI) data, with the potential to provide
specific biomarkers of brain microstructural changes. However, the general
Standard Model has recently shown that model parameter estimation from dMRI
data is ill-posed unless very strong magnetic gradients are used. We analyse
this issue for the Neurite Orientation Dispersion and Density Imaging with
Diffusivity Assessment (NODDIDA) model and demonstrate that its extension from
Single Diffusion Encoding (SDE) to Double Diffusion Encoding (DDE) solves the
ill-posedness and increases the accuracy of the parameter estimation. Methods:
We analyse theoretically the cumulant expansion up to fourth order in b of SDE
and DDE signals. Additionally, we perform in silico experiments to compare SDE
and DDE capabilities under similar noise conditions. Results: We prove
analytically that DDE provides invariant information non-accessible from SDE,
which makes the NODDIDA parameter estimation injective. The in silico
experiments show that DDE reduces the bias and mean square error of the
estimation along the whole feasible region of 5D model parameter space.
Conclusions: DDE adds additional information for estimating the model
parameters, unexplored by SDE, which is enough to solve the degeneracy in the
NODDIDA model parameter estimation.Comment: 22 pages, 7 figure
Anisotropy Across Fields and Scales
This open access book focuses on processing, modeling, and visualization of anisotropy information, which are often addressed by employing sophisticated mathematical constructs such as tensors and other higher-order descriptors. It also discusses adaptations of such constructs to problems encountered in seemingly dissimilar areas of medical imaging, physical sciences, and engineering. Featuring original research contributions as well as insightful reviews for scientists interested in handling anisotropy information, it covers topics such as pertinent geometric and algebraic properties of tensors and tensor fields, challenges faced in processing and visualizing different types of data, statistical techniques for data processing, and specific applications like mapping white-matter fiber tracts in the brain. The book helps readers grasp the current challenges in the field and provides information on the techniques devised to address them. Further, it facilitates the transfer of knowledge between different disciplines in order to advance the research frontiers in these areas. This multidisciplinary book presents, in part, the outcomes of the seventh in a series of Dagstuhl seminars devoted to visualization and processing of tensor fields and higher-order descriptors, which was held in Dagstuhl, Germany, on October 28–November 2, 2018
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