Discretisation Schemes for Level Sets of Planar Gaussian Fields
Sign Up to like & getrecommendations! Published in 2017 at "Communications in Mathematical Physics"
DOI: 10.1007/s00220-018-3084-1
Abstract: Smooth random Gaussian functions play an important role in mathematical physics, a main example being the random plane wave model conjectured by Berry to give a universal description of high-energy eigenfunctions of the Laplacian on… read more here.
Keywords: sets planar; planar gaussian; gaussian fields; discretisation schemes ... See more keywords
The Two Hyperplane Conjecture
Sign Up to like & getrecommendations! Published in 2019 at "Acta Mathematica Sinica, English Series"
DOI: 10.1007/s10114-019-8241-8
Abstract: We introduce a conjecture that we call the Two Hyperplane Conjecture, saying that an isoperimetric surface that divides a convex body in half by volume is trapped between parallel hy-perplanes. The conjecture is motivated by… read more here.
Keywords: two hyperplane; level sets; hyperplane conjecture; conjecture ... See more keywords
Geometric properties for level sets of quadratic functions
Sign Up to like & getrecommendations! Published in 2019 at "Journal of Global Optimization"
DOI: 10.1007/s10898-018-0706-2
Abstract: In this paper, we study some fundamental geometrical properties related to the $${\mathcal {S}}$$S-procedure. Given a pair of quadratic functions (g, f), it asks when “$$g(x)=0 \Longrightarrow ~ f(x)\ge 0$$g(x)=0⟹f(x)≥0” can imply “($$\exists \lambda \in {\mathbb… read more here.
Keywords: properties level; mathcal procedure; quadratic functions; sets quadratic ... See more keywords
3-D segmentation of lung nodules using hybrid level sets
Sign Up to like & getrecommendations! Published in 2018 at "Computers in biology and medicine"
DOI: 10.1016/j.compbiomed.2018.03.015
Abstract: Lung nodule segmentation in CT images and its subsequent volume analysis can help determine the malignancy status of a lung nodule. While several efficient segmentation schemes have been proposed, only a few studies evaluated the… read more here.
Keywords: volume; segmentation; lung nodules; level sets ... See more keywords
The Hausdorff dimension of level sets described by Erdös–Rényi average
Sign Up to like & getrecommendations! Published in 2018 at "Journal of Mathematical Analysis and Applications"
DOI: 10.1016/j.jmaa.2017.09.018
Abstract: Abstract Let 0 ≤ α ≤ 1 and ϕ be an integer function defined on N ∖ { 0 } satisfying 1 ≤ ϕ ( n ) ≤ n . Define the level set E… read more here.
Keywords: dimension; hausdorff dimension; dimension level; sets described ... See more keywords
Reformulating Level Sets as Deep Recurrent Neural Network Approach to Semantic Segmentation
Sign Up to like & getrecommendations! Published in 2018 at "IEEE Transactions on Image Processing"
DOI: 10.1109/tip.2018.2794205
Abstract: Variational Level Set (LS) has been a widely used method in medical segmentation. However, it is limited when dealing with multi-instance objects in the real world. In addition, its segmentation results are quite sensitive to… read more here.
Keywords: segmentation; sup; semantic segmentation; reformulating level ... See more keywords
Evaluation of Parallel Level Sets and Bowsher’s Method as Segmentation-Free Anatomical Priors for Time-of-Flight PET Reconstruction
Sign Up to like & getrecommendations! Published in 2018 at "IEEE Transactions on Medical Imaging"
DOI: 10.1109/tmi.2017.2767940
Abstract: In this article, we evaluate Parallel Level Sets (PLS) and Bowsher’s method as segmentation-free anatomical priors for regularized brain positron emission tomography (PET) reconstruction. We derive the proximity operators for two PLS priors and use… read more here.
Keywords: pet reconstruction; parallel level; pet; anatomical priors ... See more keywords
Feature Level-Sets: Generalizing Iso-Surfaces to Multi-Variate Data
Sign Up to like & getrecommendations! Published in 2020 at "IEEE Transactions on Visualization and Computer Graphics"
DOI: 10.1109/tvcg.2018.2867488
Abstract: Iso-surfaces or level-sets provide an effective and frequently used means for feature visualization. However, they are restricted to simple features for uni-variate data. The approach does not scale when moving to multi-variate data or when… read more here.
Keywords: level sets; feature level; iso surfaces; multi variate ... See more keywords
Applied 3D salt body reconstruction using shape optimization with level sets
Sign Up to like & getrecommendations! Published in 2020 at "Geophysics"
DOI: 10.1190/geo2019-0352.1
Abstract: As oil and gas extraction becomes more advanced, deep-water exploration becomes increasingly focused on imaging near or under complex salt geology, which necessitates detailed velocity models with strong contrast interfaces. These interfaces can be elegantly… read more here.
Keywords: inversion; salt; implicit surface; applied salt ... See more keywords
Posterior contraction and credible regions for level sets
Sign Up to like & getrecommendations! Published in 2021 at "Electronic Journal of Statistics"
DOI: 10.1214/21-ejs1846
Abstract: For a given function f on a multivariate domain, the level sets, given by {x:f(x)=c} for different values of c, provide important geometrical insights about the underlying function of interest. The distance on level sets… read more here.
Keywords: level sets; contraction rates; posterior contraction; contraction ... See more keywords