The conjugate of the difference of convex functions
Journal of Optimization Theory and Applications
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
On the convergence of the proximal point algorithm for convex minimization
SIAM Journal on Control and Optimization
Towards minimal assumptions for the infimal convolution regularization
Journal of Approximation Theory
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Entropic proximal mappings with applications to nonlinear programming
Mathematics of Operations Research
Nonlinear proximal point algorithms using Bregman functions, with applications to convex programming
Mathematics of Operations Research
Morphology neural networks: an introduction with applications
Circuits, Systems, and Signal Processing - Special issue: networks for neural processing
Approximated convex envelope of a function
SIAM Journal on Numerical Analysis
A fast algorithm for Euclidean distance maps of a 2-D binary image
Information Processing Letters
Entropy-like proximal methods in convex programming
Mathematics of Operations Research
Morphological systems: slope transforms and max-min difference and differential equations
Signal Processing - Special issue on mathematical morphology and its applications to signal processing
Morphological signal processing and the slope transform
Signal Processing - Special issue on mathematical morphology and its applications to signal processing
A fast Legendre transform algorithm and applications to the adhesion model
Journal of Scientific Computing
A quasi-second-order proximal bundle algorithm.
Mathematical Programming: Series A and B
SIAM Journal on Numerical Analysis
A fast computational algorithm for the Legendre-Fenchel transform
Computational Optimization and Applications
Regular Article: The Regular Shorted Matrix and the Hybrid Sum
Advances in Applied Mathematics
Variable metric bundle methods: from conceptual to implementable forms
Mathematical Programming: Series A and B - Special issue on computational nonsmooth optimization
Convex Set Symmetry Measurement via Minkowski Addition
Journal of Mathematical Imaging and Vision
Fast computation of morphological operations with arbitrary structuring elements
Pattern Recognition Letters
Lattice calculus of the morphological slope transform
Signal Processing
Multidimensional alignment using the Euclidean distance transform
Graphical Models and Image Processing
Morphology on Convolution Lattices with Applications to the Slope Transform and Random Set Theory
Journal of Mathematical Imaging and Vision
Journal of Approximation Theory
Hopf-type estimates and formulas for nonconvex nonconcave Hamilton-Jacobi equations
SIAM Journal on Mathematical Analysis
Sequential Operations in Digital Picture Processing
Journal of the ACM (JACM)
SIAM Review
The Moore--Penrose Generalized Inverse for Sums of Matrices
SIAM Journal on Matrix Analysis and Applications
Fundamenta Informaticae - Special issue on mathematical morphology
TCP is max-plus linear and what it tells us on its throughput
Proceedings of the conference on Applications, Technologies, Architectures, and Protocols for Computer Communication
Nonlinear image processing
Journal of Computational Physics
Convexity in Hamilton--Jacobi Theory II: Envelope Representations
SIAM Journal on Control and Optimization
On $\mathcalVU$-theory for Functions with Primal-Dual Gradient Structure
SIAM Journal on Optimization
Generalized Hessian Properties of Regularized Nonsmooth Functions
SIAM Journal on Optimization
Practical Aspects of the Moreau--Yosida Regularization: Theoretical Preliminaries
SIAM Journal on Optimization
A Generic Global Optimization Algorithmfor the Chemical and Phase EquilibriumProblem
Journal of Global Optimization
International Journal of Computer Vision
Fast visualization of plane-like structures in voxel data
Proceedings of the conference on Visualization '02
Enlargements and sums of monotone operators
Nonlinear Analysis: Theory, Methods & Applications
Linear Time Euclidean Distance Algorithms
IEEE Transactions on Pattern Analysis and Machine Intelligence
Efficient Dilation, Erosion, Opening, and Closing Algorithms
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
Distance Transformation and Skeletonization of 3D Pictures and Their Applications to Medical Images
Digital and Image Geometry, Advanced Lectures [based on a winter school held at Dagstuhl Castle, Germany in December 2000]
From max-plus algebra to nonexpansive mappings: a nonlinear theory for discrete event systems
Theoretical Computer Science
An Introduction to Morphological Neural Networks
ICPR '96 Proceedings of the International Conference on Pattern Recognition (ICPR '96) Volume IV-Volume 7472 - Volume 7472
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
A Multiplicative Multifractal Model for TCP Traffic
ISCC '01 Proceedings of the Sixth IEEE Symposium on Computers and Communications
Fast Euclidean distance transformation in two scans using a 3 × 3 neighborhood
Computer Vision and Image Understanding
Pictorial Structures for Object Recognition
International Journal of Computer Vision
Fast Sweeping Methods for Static Hamilton--Jacobi Equations
SIAM Journal on Numerical Analysis
A Linear Euclidean Distance Transform Algorithm Based on the Linear-Time Legendre Transform
CRV '05 Proceedings of the 2nd Canadian conference on Computer and Robot Vision
An Explanation for the Logarithmic Connection between Linear and Morphological System Theory
International Journal of Computer Vision
Minimizing within Convex Bodies Using a Convex Hull Method
SIAM Journal on Optimization
Semismoothness of solutions to generalized equations and the Moreau-Yosida regularization
Mathematical Programming: Series A and B
A **-algorithm for convex minimization
Mathematical Programming: Series A and B
A Smoothing Method of Global Optimization that Preserves Global Minima
Journal of Global Optimization
Efficient Belief Propagation for Early Vision
International Journal of Computer Vision
Symbolic computation of Fenchel conjugates
ACM Communications in Computer Algebra
A linear-time algorithm for Euclidean feature transform sets
Information Processing Letters
Value Regularization and Fenchel Duality
The Journal of Machine Learning Research
Necklaces, convolutions, and X + Y
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
An alternative approach for non-linear optimal control problems based on the method of moments
Computational Optimization and Applications
2D Euclidean distance transform algorithms: A comparative survey
ACM Computing Surveys (CSUR)
Primal-Dual Symmetric Intrinsic Methods for Finding Antiderivatives of Cyclically Monotone Operators
SIAM Journal on Control and Optimization
Mathematical Programming: Series A and B - Nonlinear convex optimization and variational inequalities
New sequential exact Euclidean distance transform algorithms based on convex analysis
Image and Vision Computing
The piecewise linear-quadratic model for computational convex analysis
Computational Optimization and Applications
Conjugate network calculus: A dual approach applying the Legendre transform
Computer Networks: The International Journal of Computer and Telecommunications Networking - Selected papers from the 3rd international workshop on QoS in multiservice IP networks (QoS-IP 2005)
Network calculus: a theory of deterministic queuing systems for the internet
Network calculus: a theory of deterministic queuing systems for the internet
The multi-fractal nature of worm and normal traffic at individual source level
ISI'05 Proceedings of the 2005 IEEE international conference on Intelligence and Security Informatics
Slope transforms: theory and application to nonlinear signalprocessing
IEEE Transactions on Signal Processing
A novel broadcast scheduling strategy using factor graphs and the sum-product algorithm
IEEE Transactions on Wireless Communications
A multifractal wavelet model with application to network traffic
IEEE Transactions on Information Theory
The generalized distributive law
IEEE Transactions on Information Theory
Factor graphs and the sum-product algorithm
IEEE Transactions on Information Theory
Differential morphology and image processing
IEEE Transactions on Image Processing
A fast implementation of 3-D binary morphological transformations
IEEE Transactions on Image Processing
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Computational convex analysis algorithms have been rediscovered several times in the past by researchers from different fields. To further communications between practitioners, we review the field of computational convex analysis, which focuses on the numerical computation of fundamental transforms arising from convex analysis. Current models use symbolic, numeric, and hybrid symbolic-numeric algorithms. Our objective is to disseminate widely the most efficient numerical algorithms useful for applications in image processing (computing the distance transform, the generalized distance transform, and mathematical morphology operators), partial differential equations (solving Hamilton-Jacobi equations and using differential equations numerical schemes to compute the convex envelope), max-plus algebra (computing the equivalent of the fast Fourier transform), multifractal analysis, etc. The fields of applications include, among others, computer vision, robot navigation, thermodynamics, electrical networks, medical imaging, and network communication.