83,440 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
Gradient waveform design for tensor-valued encoding in diffusion MRI
Diffusion encoding along multiple spatial directions per signal acquisition
can be described in terms of a b-tensor. The benefit of tensor-valued diffusion
encoding is that it unlocks the "shape of the b-tensor" as a new encoding
dimension. By modulating the b-tensor shape, we can control the sensitivity to
microscopic diffusion anisotropy which can be used as a contrast mechanism; a
feature that is inaccessible by conventional diffusion encoding. Since imaging
methods based on tensor-valued diffusion encoding are finding an increasing
number of applications we are prompted to highlight the challenge of designing
the optimal gradient waveforms for any given application. In this review, we
first establish the basic design objectives in creating field gradient
waveforms for tensor-valued diffusion MRI. We also survey additional design
considerations related to limitations imposed by hardware and physiology,
potential confounding effects that cannot be captured by the b-tensor, and
artifacts related to the diffusion encoding waveform. Throughout, we discuss
the expected compromises and tradeoffs with an aim to establish a more complete
understanding of gradient waveform design and its impact on accurate
measurements and interpretations of data.Comment: Invited review, submitted in May 2020 to the Journal of Neuroscience
Methods. 46 pages, 9 figures, 35 equation
- …