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Related Concept Videos

Gradient and Del Operator01:14

Gradient and Del Operator

In mathematics and physics, the gradient and del operator are fundamental concepts used to describe the behavior of functions and fields in space. The gradient is a mathematical operator that gives both the magnitude and direction of the maximum spatial rate of change. Consider a person standing on a mountain. The slope of the mountain at any given point is not defined unless it is quantified in a particular direction. For this reason, a "directional derivative" is defined, which is a vector...
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Automated Midline Shift and Intracranial Pressure Estimation based on Brain CT Images
14:08

Automated Midline Shift and Intracranial Pressure Estimation based on Brain CT Images

Published on: April 13, 2013

Modified gradient search for level set based image segmentation.

Thord Andersson1, Gunnar Läthén, Reiner Lenz

  • 1Center for Medical Image Science and Visualization, Linköping University, Linköping, Sweden. thord.andersson@liu.se

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|September 28, 2012
PubMed
Summary
This summary is machine-generated.

This study introduces modified gradient descent methods for image segmentation using level set methods. These new approaches improve convergence speed and reduce sensitivity to local minima, enhancing segmentation accuracy.

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Last Updated: May 18, 2026

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Published on: April 13, 2013

Area of Science:

  • Computer Vision
  • Image Processing
  • Computational Mathematics

Background:

  • Level set methods are widely used for image segmentation.
  • Gradient descent is a common optimization technique for minimizing cost functionals in segmentation.
  • Standard gradient descent methods suffer from slow convergence and sensitivity to local minima.

Purpose of the Study:

  • To improve the performance of gradient descent in level set image segmentation.
  • To address the limitations of slow convergence and local minima sensitivity.
  • To introduce machine learning-inspired optimization techniques into level set methods.

Main Methods:

  • Proposed two modified gradient descent methods: one with a momentum term and another based on resilient propagation.
  • Applied these methods to level set-based image segmentation.
  • Conducted experiments on 2D/3D real and synthetic data with ground truth.

Main Results:

  • The modified gradient descent methods demonstrated reduced sensitivity to local optima.
  • Increased convergence rates were observed compared to standard gradient descent.
  • Parameter sensitivity of the proposed methods was investigated.

Conclusions:

  • Modified gradient descent methods enhance level set image segmentation by improving convergence and robustness.
  • These simple modifications are compatible with existing level set implementations.
  • The proposed methods offer a practical improvement for image segmentation tasks.