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Updated: Jun 19, 2026

Operation of the Collaborative Composite Manufacturing (CCM) System
10:09

Operation of the Collaborative Composite Manufacturing (CCM) System

Published on: October 1, 2019

A path following algorithm for the graph matching problem.

Mikhail Zaslavskiy1, Francis Bach, Jean-Philippe Vert

  • 1Centre for Computational Biology and the Centre for Mathematical Morphology, Mines ParisTech, Fontainebleau Cedex, France. mikhail.zaslavskiy@ensmp.fr

IEEE Transactions on Pattern Analysis and Machine Intelligence
|October 17, 2009
PubMed
Summary
This summary is machine-generated.

We introduce a novel convex-concave programming method for labeled weighted graph matching. This approach offers competitive results against state-of-the-art algorithms on diverse datasets.

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Last Updated: Jun 19, 2026

Operation of the Collaborative Composite Manufacturing (CCM) System
10:09

Operation of the Collaborative Composite Manufacturing (CCM) System

Published on: October 1, 2019

Area of Science:

  • Computer Vision
  • Machine Learning
  • Optimization

Background:

  • Graph matching is crucial for pattern recognition and computer vision.
  • Existing methods struggle with labeled, weighted graph matching.
  • Combinatorial optimization problems are computationally intensive.

Purpose of the Study:

  • To develop an efficient convex-concave programming approach for labeled weighted graph matching.
  • To integrate label similarity information directly into the optimization framework.
  • To provide a competitive alternative to existing graph matching algorithms.

Main Methods:

  • Formulated labeled weighted graph matching as a least-squares problem on permutation matrices.
  • Relaxed the problem into quadratic convex and concave optimization problems on doubly stochastic matrices.
  • Employed a convex-concave programming approach by interpolating convex and concave relaxations.
  • Developed an approximation algorithm by following a solution path from the convex relaxation.

Main Results:

  • The proposed method effectively performs labeled weighted graph matching.
  • Achieved competitive results compared to state-of-the-art methods.
  • Demonstrated effectiveness on simulated graphs, QAPLib, retina vessel images, and handwritten Chinese characters.

Conclusions:

  • The convex-concave programming approach provides an effective solution for labeled weighted graph matching.
  • The method successfully integrates label information, enhancing matching accuracy.
  • Results indicate strong performance and competitiveness across various applications.