# Generalized fast marching method: applications to image segmentation

@article{Forcadel2008GeneralizedFM, title={Generalized fast marching method: applications to image segmentation}, author={Nicolas Forcadel and Carole Le Guyader and Christian Gout}, journal={Numerical Algorithms}, year={2008}, volume={48}, pages={189-211} }

In this paper, we propose a segmentation method based on the generalized fast marching method (GFMM) developed by Carlini et al. (submitted). The classical fast marching method (FMM) is a very efficient method for front evolution problems with normal velocity (see also Epstein and Gage, The curve shortening flow. In: Chorin, A., Majda, A. (eds.) Wave Motion: Theory, Modelling and Computation, 1997) of constant sign. The GFMM is an extension of the FMM and removes this sign constraint by…

## 63 Citations

Extrapolation of Vector Fields Using the Infinity Laplacian and with Applications to Image Segmentation

- MathematicsSSVM
- 2009

A new Gradient-Vector-Flow (GVF)-inspired static external force field for active contour models, deriving from the edge map of a given image and allowing to increase the capture range is investigated.

Variational models and numerical algorithms for selective image segmentation

- Computer Science
- 2013

The development of a restarted homotopy analysis method which has been designed to be easily adaptable to various types of image processing problems and introduced to introduce automatic segmentation of the object of interest as a contribution not only to the way doctors and surgeons diagnose and operate but to other fields as well.

Selective Segmentation of Piecewise Homogeneous Regions

- Computer Science
- 2019

A novel method for the interactive segmentation of the object and background which has multiple piecewise homogeneous intensities has been introduced and results are compared with state of the art methods using Jaccard's similarity index.

Fuzzy generalized fast marching method for 3D segmentation of brain structures

- Computer ScienceInt. J. Imaging Syst. Technol.
- 2017

This study proposes a robust and accurate brain structures segmentation method based on a combination of fuzzy model and deformable model and achieves significant improvements with respect to several state‐of‐the‐art methods and with the three practical segmentation techniques widely used in neuroimaging studies, namely SPM, FSL, and Freesurfer.

Image Segmentation with a Priori Conditions: Applications to Medical and Geophysical Imaging

- Computer ScienceMathematical and Computational Applications
- 2022

The main novelty of the proposed method is the initialization of the segmentation process, which is performed with a polynomial approximation of a user defined initialization (for instance, a set of points or a curve to be interpolated).

A local information based variational model for selective image segmentation

- Computer Science
- 2014

An improved selective segmentation model is presented, without `balloon' force, combining geometrical constraints and local image intensity information around zero level set, aiming to overcome the weakness of getting spurious solutions by Badshah and Chen's model.

A geodesic-active-contour-based variational model for short-axis cardiac MR image segmentation

- Computer ScienceInt. J. Comput. Math.
- 2013

A new edge detection function is developed that relaxes this restriction on the location of initial contours, and an iterative method that uses a sequence of edge detection functions to minimize the energy of the model successively is proposed.

Fast Marching Methods for Indefinite and Anisotropic Metrics

- Computer Science
- 2011

Two different variants of the Fast-Marching-Method (FMM) are discussed and the usage of virtual triangles is a central concept and is responsible for numeric effects which do not occur using iterative solvers.

Fast-marching segmentation of three-dimensional intravascular ultrasound images: a pre- and post-intervention study.

- MedicineMedical physics
- 2010

This new IVUS segmentation method provides accurate results that correspond well to the experts' manually traced contours, but requires much less manual interactions and is faster.

Introduction to the Fast Marching Method

- Mathematics
- 2010

In these notes, we present an introduction to the classical Fast Marching Method (FMM). The FMM has been first introduced to find numerical approximations of the solutions to the stationary eikonal…

## References

SHOWING 1-10 OF 48 REFERENCES

Image segmentation using a multilayer level-set approach

- Computer Science
- 2003

An efficient multilayer segmentation method based on implicit curve evolution and on variational approach based on Euler–Lagrange equations of the proposed minimizations together with theoretical results of energy decrease, existence of minimizers and approximations is presented.

A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model

- Computer Science, MathematicsInternational Journal of Computer Vision
- 2004

A new multiphase level set framework for image segmentation using the Mumford and Shah model, for piecewise constant and piecewise smooth optimal approximations, and validated by numerical results for signal and image denoising and segmentation.

Using a level set approach for image segmentation under interpolation conditions

- Mathematics, Computer ScienceNumerical Algorithms
- 2004

A new 2D segmentation model including geometric constraints, namely interpolation conditions, to detect objects in a given image by applying deformable models to an explicit function using the level set approach to avoid the classical problem of parameterization of both segmentation representation and interpolation Conditions.

Energy Minimization Based Segmentation and Denoising Using a Multilayer Level Set Approach

- Computer ScienceEMMCVPR
- 2005

This paper represents here the set of boundaries of the segmentation implicitly, by a multilayer of level-lines of a continuous function, in the standard approach of front propagation, only one level line is used to represent the boundary.

Active contours without edges

- Computer Science, MathematicsIEEE Trans. Image Process.
- 2001

We propose 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. Our model can…

Nonparametric methods for image segmentation using information theory and curve evolution

- Computer Science, MathematicsProceedings. International Conference on Image Processing
- 2002

This work casts the segmentation problem as the maximization of the mutual information between the region labels and the image pixel intensities, subject to a constraint on the total length of the region boundaries, and forms the problem based on nonparametric density estimates.

A fast marching level set method for monotonically advancing fronts.

- Computer ScienceProceedings of the National Academy of Sciences of the United States of America
- 1996

A fast marching level set method is presented for monotonically advancing fronts, which leads to an extremely fast scheme for solving the Eikonal equation. Level set methods are numerical techniques…

Level set methods and dynamic implicit surfaces

- Computer ScienceApplied mathematical sciences
- 2003

A student or researcher working in mathematics, computer graphics, science, or engineering interested in any dynamic moving front, which might change its topology or develop singularities, will find this book interesting and useful.

Segmentation under geometrical conditions using geodesic active contours and interpolation using level set methods

- MathematicsNumerical Algorithms
- 2004

This paper combines the ideas of the geodesic active contour and interpolation of points in a level set approach developed by Osher and Sethian and presents modelling of the proposed method, both theoretical results (viscosity solution) and numerical results are given.