Journal ArticleDOI
A Fast Spectral Method for Active 3D Shape Reconstruction
Jia Li,Alfred O. Hero +1 more
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TLDR
In this paper, a spectral non-iterative solution of the Euler-Lagrange equation is proposed for 3D active surface reconstruction of star-shaped surfaces parameterized in polar coordinates.Abstract:
Variational energy minimization techniques for surface reconstruction are implemented by evolving an active surface according to the solutions of a sequence of elliptic partial differential equations (PDE's). For these techniques, most current approaches to solving the elliptic PDE are iterative involving the implementation of costly finite element methods (FEM) or finite difference methods (FDM). The heavy computational cost of these methods makes practical application to 3D surface reconstruction burdensome. In this paper, we develop a fast spectral method which is applied to 3D active surface reconstruction of star-shaped surfaces parameterized in polar coordinates. For this parameterization the Euler-Lagrange equation is a Helmholtz-type PDE governing a diffusion on the unit sphere. After linearization, we implement a spectral non-iterative solution of the Helmholtz equation by representing the active surface as a double Fourier series over angles in spherical coordinates. We show how this approach can be extended to include region-based penalization. A number of 3D examples and simulation results are presented to illustrate the performance of our fast spectral active surface algorithms.read more
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Posted Content
Proximal Splitting Methods in Signal Processing
Abstract: The proximity operator of a convex function is a natural extension of the notion of a projection operator onto a convex set. This tool, which plays a central role in the analysis and the numerical solution of convex optimization problems, has recently been introduced in the arena of signal processing, where it has become increasingly important. In this paper, we review the basic properties of proximity operators which are relevant to signal processing and present optimization methods based on these operators. These proximal splitting methods are shown to capture and extend several well-known algorithms in a unifying framework. Applications of proximal methods in signal recovery and synthesis are discussed.
Book ChapterDOI
Proximal Splitting Methods in Signal Processing
TL;DR: The basic properties of proximity operators which are relevant to signal processing and optimization methods based on these operators are reviewed and proximal splitting methods are shown to capture and extend several well-known algorithms in a unifying framework.
Journal ArticleDOI
Content-aware image restoration: pushing the limits of fluorescence microscopy.
Martin Weigert,Uwe Schmidt,Tobias Boothe,Andreas Müller,Alexandr Dibrov,Akanksha Jain,Benjamin Wilhelm,Deborah Schmidt,Coleman Broaddus,Siân Culley,Siân Culley,Mauricio Rocha-Martins,Fabián Segovia-Miranda,Caren Norden,Ricardo Henriques,Ricardo Henriques,Marino Zerial,Michele Solimena,Jochen C. Rink,Pavel Tomancak,Loic Royer,Florian Jug,Eugene W. Myers,Eugene W. Myers +23 more
TL;DR: This work shows how content-aware image restoration based on deep learning extends the range of biological phenomena observable by microscopy by bypassing the trade-offs between imaging speed, resolution, and maximal light exposure that limit fluorescence imaging to enable discovery.
Journal ArticleDOI
Structure-Texture Image Decomposition--Modeling, Algorithms, and Parameter Selection
TL;DR: The paper shows that the correlation graph between u and ρ may serve as an efficient tool to select the splitting parameter, and proposes a new fast algorithm to solve the TV − L1 minimization problem.
Journal ArticleDOI
An efficient augmented Lagrangian method with applications to total variation minimization
TL;DR: An algorithm for solving a class of equality-constrained non-smooth optimization problems (chiefly but not necessarily convex programs) with a particular structure that effectively combines an alternating direction technique with a nonmonotone line search to minimize the augmented Lagrangian function at each iteration is proposed.
References
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Journal ArticleDOI
Snakes : Active Contour Models
TL;DR: This work uses snakes for interactive interpretation, in which user-imposed constraint forces guide the snake near features of interest, and uses scale-space continuation to enlarge the capture region surrounding a feature.
Journal ArticleDOI
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Stanley Osher,James A. Sethian +1 more
TL;DR: The PSC algorithm as mentioned in this paper approximates the Hamilton-Jacobi equations with parabolic right-hand-sides by using techniques from the hyperbolic conservation laws, which can be used also for more general surface motion problems.
Journal ArticleDOI
Active contours without edges
Tony F. Chan,Luminita A. Vese +1 more
TL;DR: A new model for active contours to detect objects in a given image, based on techniques of curve evolution, Mumford-Shah (1989) functional for segmentation and level sets is proposed, which can detect objects whose boundaries are not necessarily defined by the gradient.
Journal ArticleDOI
Optimal approximations by piecewise smooth functions and associated variational problems
David Mumford,Jayant Shah +1 more
TL;DR: In this article, the authors introduce and study the most basic properties of three new variational problems which are suggested by applications to computer vision, and study their application in computer vision.
Journal ArticleDOI
Snakes, shapes, and gradient vector flow
Chenyang Xu,Jerry L. Prince +1 more
TL;DR: This paper presents a new external force for active contours, which is computed as a diffusion of the gradient vectors of a gray-level or binary edge map derived from the image, and has a large capture range and is able to move snakes into boundary concavities.