Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Videos

Algorithmic differentiation: application to variational problems in computer vision.

Thomas Pock1, Michael Pock, Horst Bischof

  • 1Institute for Computer Graphics and Vision, Graz University of Technology, Graz, Austria. pock@icg.tugraz.at

IEEE Transactions on Pattern Analysis and Machine Intelligence
|May 15, 2007
PubMed
Summary
This summary is machine-generated.

Related Concept Videos

You might also read

Related Articles

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

Sort by
Same author

Product-of-Gaussian-mixture diffusion models for joint nonlinear MRI reconstruction.

Journal of mathematical imaging and vision·2026
Same author

Total Variation-Based Image Decomposition and Denoising for Microscopy Images.

Microscopy and microanalysis : the official journal of Microscopy Society of America, Microbeam Analysis Society, Microscopical Society of Canada·2026
Same author

Evaluating artificial intelligence-enabled medical tests in cardiology: Best practice.

International journal of cardiology. Heart & vasculature·2025
Same author

Machine-learning guided differentiation between photoplethysmography waveforms of supraventricular and ventricular origin.

Computer methods and programs in biomedicine·2025
Same author

Harnessing deep learning to detect bronchiolitis obliterans syndrome from chest CT.

Communications medicine·2025
Same author

PIEMAP: Personalized Inverse Eikonal Model from cardiac Electro-Anatomical Maps.

Statistical atlases and computational models of the heart. STACOM (Workshop)·2024
Same journal

Relation DETR+: Exploring Explicit Position Relation Prior for Dense Prediction.

IEEE transactions on pattern analysis and machine intelligence·2026
Same journal

RBF++: Quantifying and Optimizing Reasoning Boundaries across Measurable and Unmeasurable Capabilities for Chain-of-Thought Reasoning.

IEEE transactions on pattern analysis and machine intelligence·2026
Same journal

CAFE: Cross-View Adaptive Fusion and Cluster Center Enhancement for Robust Multi-View Clustering.

IEEE transactions on pattern analysis and machine intelligence·2026
Same journal

DIVER: Reinforced Diffusion Breaks Imitation Bottlenecks in End-to-End Autonomous Driving.

IEEE transactions on pattern analysis and machine intelligence·2026
Same journal

Ethics-Aware Safe Reinforcement Learning for Rare-Event Risk Control in Interactive Urban Driving.

IEEE transactions on pattern analysis and machine intelligence·2026
Same journal

Learning Shape Anchors for Holistic Indoor Scene Understanding.

IEEE transactions on pattern analysis and machine intelligence·2026
See all related articles

This study introduces algorithmic differentiation to precisely compute derivatives for vision problems. This method simplifies implementing complex energy minimization tasks, yielding state-of-the-art results in denoising, segmentation, and stereo vision.

Area of Science:

  • Computer Vision
  • Computational Mathematics
  • Image Processing

Background:

  • Vision problems are often solved by minimizing energy functionals.
  • Traditional methods use calculus of variations (Euler-Lagrange equations), which are complex to discretize for computation.
  • Discretization of these equations can be error-prone and computationally intensive.

Purpose of the Study:

  • To present a novel, flexible alternative to traditional Euler-Lagrange equation discretization.
  • To leverage algorithmic differentiation for direct derivation of algorithms implementing energy functional derivatives.
  • To demonstrate the efficiency and accuracy of this new approach in computer vision tasks.

Main Methods:

  • Discretizing energy functionals directly.

Related Experiment Videos

  • Applying algorithmic differentiation to derive exact derivative algorithms.
  • Implementing and testing the approach on denoising, segmentation, and stereo vision problems.

    • Main Results:

    • Computed derivatives are exact with respect to the energy functional's implementation.
    • Second-order derivatives and Hessian matrices are straightforward to compute.
    • State-of-the-art results were achieved with minimal effort on benchmark vision tasks.

    Conclusions:

    • Algorithmic differentiation offers an automated and accurate method for implementing vision algorithms.
    • This approach simplifies the process of solving complex optimization problems in computer vision.
    • The method is versatile and effective across various vision applications.