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Mesh Analysis

Mesh Analysis

Mesh analysis is a valuable method for simplifying circuit analysis using mesh currents as key circuit variables. Unlike nodal analysis, which focuses on determining unknown voltages, mesh analysis applies Kirchhoff's voltage law (KVL) to find unknown currents within a circuit. This method is particularly convenient in reducing the number of simultaneous equations that need to be solved.
A fundamental concept in mesh analysis is the definition of meshes and mesh currents. A mesh is a closed...

Mesh Analysis with Current Sources

Mesh Analysis with Current Sources

Mesh analysis becomes simpler when analyzing circuits with current sources, whether independent or dependent. The presence of current sources reduces the number of equations required for analysis. Two cases illustrate this:
Current Source in One Mesh: The analysis process is straightforward when a current source is found in only one mesh within the circuit. Mesh currents are assigned as usual, with the mesh containing the current source excluded from the analysis. Kirchhoff's voltage law (KVL)...

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Related Experiment Video

Updated: Jul 15, 2026

Three-Dimensional Shape Modeling and Analysis of Brain Structures

Three-Dimensional Shape Modeling and Analysis of Brain Structures

Published on: November 14, 2019

GAMEs: growing and adaptive meshes for fully automatic shape modeling and analysis.

Luca Ferrarini¹, Hans Olofsen, Walter M Palm

¹LKEB - Division of Image Processing, Department of Radiology, Leiden University Medical Center, 2333 ZA Leiden, The Netherlands. L.Ferrarini@lumc.nl

Medical Image Analysis

|May 5, 2007

Summary

This study introduces Growing and Adaptive Meshes (GAMEs) for shape analysis, combining self-organizing networks and Kohonen maps. The novel framework accurately models shapes and adapts to variations, proving robust in synthetic and medical data analysis.

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Three-Dimensional Shape Modeling and Analysis of Brain Structures

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Area of Science:

Computer Science
Artificial Intelligence
Pattern Recognition

Background:

Shape modeling and analysis are crucial in various fields, including medical imaging.
Existing methods often struggle with noise and capturing subtle shape variations.

Purpose of the Study:

To present a novel framework for shape modeling and analysis using artificial neural networks.
To introduce Growing and Adaptive Meshes (GAMEs) for robust shape representation and adaptation.

Main Methods:

Utilizing pattern recognition theory and artificial neural networks.
Integrating the self-organizing networks which grow when require (SONGWR) algorithm for topology learning.
Employing Kohonen's self-organizing maps (SOMs) for topology-preserving adaptation and point correspondence.

Main Results:

The GAMEs framework successfully models surfaces as an unsupervised clustering problem.
Adaptation to similar shapes was achieved through a classification task using SOMs.
The method demonstrated reproducibility and robustness to noise and shape variations on synthetic datasets.

Conclusions:

The proposed GAMEs framework offers a powerful approach to shape modeling and analysis.
The method is effective in handling challenging datasets, including medical data.
GAMEs can capture real variations within and between shape groups, highlighting its utility in comparative studies.