Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Region of Convergence of Laplace Tarnsform

Region of Convergence of Laplace Tarnsform

The Region of Convergence (ROC) is a fundamental concept in signal processing and system analysis, particularly associated with the Laplace transform. The ROC represents an area in the complex plane where the Laplace transform of a given signal converges, determining the transform's applicability and utility.
Consider a decaying exponential signal that begins at a specific time. When deriving its Laplace transform, the time-domain variable is replaced with a complex variable. This substitution...

Mason's Rule

Mason's Rule

Mason's rule is a powerful tool in control systems and signal processing. It simplifies the calculation of transfer functions from signal-flow graphs. This method leverages various elements, including loop gains, forward-path gains, and non-touching loops, to determine the transfer function efficiently.
Loop gain is determined by identifying and tracing a path from a node back to itself. This involves computing the product of branch gains along the loop. Each loop's gain is crucial for further...

Linear Approximation in Frequency Domain

Linear Approximation in Frequency Domain

Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear.

Poisson's And Laplace's Equation

Poisson's And Laplace's Equation

The electric potential of the system can be calculated by relating it to the electric charge densities that give rise to the electric potential. The differential form of Gauss's law expresses the electric field's divergence in terms of the electric charge density.

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

Partial volume-aware assessment of multiple sclerosis lesions.

NeuroImage. Clinical·2018

Same author

Evaluating anorexia-related brain atrophy using MP2RAGE-based morphometry.

European radiology·2017

Same author

The impact of automated hippocampal volumetry on diagnostic confidence in patients with suspected Alzheimer's disease: A European Alzheimer's Disease Consortium study.

Alzheimer's & dementia : the journal of the Alzheimer's Association·2017

Same author

An Ultra-High Field Study of Cerebellar Pathology in Early Relapsing-Remitting Multiple Sclerosis Using MP2RAGE.

Investigative radiology·2016

Same author

Basic MR sequence parameters systematically bias automated brain volume estimation.

Neuroradiology·2016

Same author

A New Approach for Deep Gray Matter Analysis Using Partial-Volume Estimation.

PloS one·2016

Search research articles

Related Experiment Video

Updated: May 15, 2026

A Magnetic Resonance Imaging-based Computational Protocol for Analysis of Plaque Morphology and Hemodynamics in Patients with Carotid Artery Stenosis

A Magnetic Resonance Imaging-based Computational Protocol for Analysis of Plaque Morphology and Hemodynamics in Patients with Carotid Artery Stenosis

Published on: August 12, 2025

Closed-form relaxation for MRF-MAP tissue classification using discrete Laplace equations.

¹Siemens Research, CIBM, Lausanne, Switzerland. alexis.roche@epfl.ch

Medical Image Computing and Computer-Assisted Intervention : MICCAI ... International Conference on Medical Image Computing and Computer-Assisted Intervention

|January 5, 2013

Summary

A novel random walker algorithm variant offers a direct solution for Markov random field segmentation, overcoming local maxima issues common in iterative methods for medical image analysis.

More Related Videos

Quantitative Magnetic Resonance Imaging of Skeletal Muscle Disease

Quantitative Magnetic Resonance Imaging of Skeletal Muscle Disease

Published on: December 18, 2016

Patient-specific Modeling of the Heart: Estimation of Ventricular Fiber Orientations

Patient-specific Modeling of the Heart: Estimation of Ventricular Fiber Orientations

Published on: January 8, 2013

Related Experiment Videos

Last Updated: May 15, 2026

A Magnetic Resonance Imaging-based Computational Protocol for Analysis of Plaque Morphology and Hemodynamics in Patients with Carotid Artery Stenosis

A Magnetic Resonance Imaging-based Computational Protocol for Analysis of Plaque Morphology and Hemodynamics in Patients with Carotid Artery Stenosis

Published on: August 12, 2025

Quantitative Magnetic Resonance Imaging of Skeletal Muscle Disease

Quantitative Magnetic Resonance Imaging of Skeletal Muscle Disease

Published on: December 18, 2016

Patient-specific Modeling of the Heart: Estimation of Ventricular Fiber Orientations

Patient-specific Modeling of the Heart: Estimation of Ventricular Fiber Orientations

Published on: January 8, 2013

Area of Science:

Medical Image Processing
Computational Imaging
Computer Vision

Background:

Markov random fields (MRFs) are widely used for image segmentation.
Iterative methods for maximum a posteriori (MAP) estimation in MRFs often converge to local maxima, limiting segmentation accuracy.
Existing methods struggle with convergence and precision in complex medical images.

Purpose of the Study:

To present a new relaxation method for the MAP estimation problem in MRFs using a random walker algorithm variant.
To demonstrate that this method provides a unique, explicit solution, avoiding local maxima.
To enhance the quality of MAP estimation in medical image segmentation.

Main Methods:

Formulating the MAP estimation for MRFs under the Potts model as a relaxation problem.
Applying a variant of the random walker algorithm to solve this relaxed problem.
Solving the resulting sparse linear system to obtain an explicit solution.

Main Results:

The random walker variant effectively relaxes the MAP estimation problem.
The method yields a uniquely defined explicit solution, bypassing local maxima.
Experimental results show improved MAP estimation quality compared to classical mean-field algorithms.

Conclusions:

The proposed random walker-based approach offers a robust and accurate alternative for MRF-based medical image segmentation.
This method provides a significant improvement over traditional iterative techniques by guaranteeing convergence to a global optimum.
The explicit solution simplifies the estimation process and enhances segmentation performance.