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 Concept Videos

Bernoulli's Equation for Flow Along a Streamline01:30

Bernoulli's Equation for Flow Along a Streamline

Bernoulli's equation relates the energy conservation in a fluid moving along a streamline. The equation applies to incompressible and inviscid fluids under steady flow. For such a flow, Newton's second law is applied to a small fluid element, which experiences forces due to pressure differences, gravity, and velocity variations. The force balance leads to the following form of Bernoulli's equation:
Bernoulli's Equation for Flow Normal to a Streamline01:16

Bernoulli's Equation for Flow Normal to a Streamline

Bernoulli's equation for flow normal to a streamline explains how pressure varies across curved streamlines due to the outward centrifugal forces induced by the fluid's curvature. The pressure is higher on the inner side of the curve, near the center of curvature, and decreases outward to balance these centrifugal forces.
The pressure difference depends on the fluid's velocity and radius of curvature. The pressure variation is minimal in flows with nearly straight streamlines. However, the...
Irrotational Flow01:28

Irrotational Flow

Irrotational flow is characterized by fluid motion where particles do not rotate around their axes, resulting in zero vorticity. For a flow to be irrotational, the curl of the velocity field must be zero. This imposes specific conditions on velocity gradients. For instance, to maintain zero rotation about the z-axis, the gradient condition:
Steady, Laminar Flow in Circular Tubes01:23

Steady, Laminar Flow in Circular Tubes

Hagen-Poiseuille flow describes a viscous fluid's steady, incompressible flow through a cylindrical tube with a constant radius R. This flow profile is often applied to understand fluid transport in narrow channels, such as capillaries. It serves as a foundational example of laminar flow. In this model, cylindrical coordinates (r,θ,z) are used to describe the radial (r), angular (θ), and axial (z) dimensions within the tube. For Hagen-Poiseuille flow, the velocity profile is purely axial,...
Fluid Pressure over Curved Plate of Constant Width01:12

Fluid Pressure over Curved Plate of Constant Width

When a curved plate of constant width is submerged in a liquid, the pressure acting normal to the plate varies continuously both in magnitude and direction. Calculating the magnitude and location of the resultant force at a point is often challenging for such cases. One of the methods to determine the resultant force and its location involves separately calculating the horizontal and vertical components of the resultant force. This complex calculation can be simplified by representing the...
Couette Flow01:22

Couette Flow

Couette flow represents the flow of fluid between two parallel plates, with one plate fixed and the other moving with a constant velocity. This configuration allows for a simplified analysis using the Navier-Stokes equations, which govern fluid motion under conditions of viscosity and incompressibility. For Couette flow, the assumptions include a steady, laminar, incompressible flow with a zero-pressure gradient in the flow direction. This flow type is beneficial for understanding shear-driven...

You might also read

Related Articles

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

Sort by
Same author

Topology-Aware Segmentation Using Discrete Morse Theory.

... International Conference on Learning Representations·2026
Same author

TOPODIFFUSIONNET: A TOPOLOGY-AWARE DIFFUSION MODEL.

... International Conference on Learning Representations·2026
Same author

Unifying Top-down and Bottom-up Scanpath Prediction Using Transformers.

Proceedings. IEEE Computer Society Conference on Computer Vision and Pattern Recognition·2026
Same author

Look Hear: Gaze Prediction for Speech-directed Human Attention.

Computer vision - ECCV ... : ... European Conference on Computer Vision : proceedings. European Conference on Computer Vision·2026
Same author

Measuring and predicting where and when pathologists focus their visual attention while grading whole slide images of cancer.

Medical image analysis·2025
Same author

Label-Efficient Deep Color Deconvolution of Brightfield Multiplex IHC Images.

IEEE transactions on medical imaging·2025
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

Related Experiment Video

Updated: Jun 15, 2026

Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow
13:02

Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow

Published on: February 27, 2016

Ricci flow for 3D shape analysis.

Wei Zeng1, Dimitris Samaras, Xianfeng David Gu

  • 1Department of Computer Science, Wayne State University, Detroit, MI 48202, USA. zeng@wayne.edu

IEEE Transactions on Pattern Analysis and Machine Intelligence
|March 13, 2010
PubMed
Summary
This summary is machine-generated.

Surface Ricci flow, a powerful geometric method, is now applied to computer vision for 3D shape analysis. This technique handles complex topologies and enables robust 3D shape matching, registration, and indexing.

More Related Videos

Determining 3D Flow Fields via Multi-camera Light Field Imaging
14:25

Determining 3D Flow Fields via Multi-camera Light Field Imaging

Published on: March 6, 2013

In vitro Assessment of Aortic Regurgitation Using Four-Dimensional Flow Magnetic Resonance Imaging
11:16

In vitro Assessment of Aortic Regurgitation Using Four-Dimensional Flow Magnetic Resonance Imaging

Published on: February 25, 2022

Related Experiment Videos

Last Updated: Jun 15, 2026

Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow
13:02

Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow

Published on: February 27, 2016

Determining 3D Flow Fields via Multi-camera Light Field Imaging
14:25

Determining 3D Flow Fields via Multi-camera Light Field Imaging

Published on: March 6, 2013

In vitro Assessment of Aortic Regurgitation Using Four-Dimensional Flow Magnetic Resonance Imaging
11:16

In vitro Assessment of Aortic Regurgitation Using Four-Dimensional Flow Magnetic Resonance Imaging

Published on: February 25, 2022

Area of Science:

  • Computer Vision
  • Differential Geometry
  • Computational Geometry

Background:

  • Surface Ricci flow is a curvature flow method invariant to rigid motion, scaling, and conformal deformations.
  • Existing conformal geometry methods are limited to simple 3D shape topologies.
  • Ricci flow offers a more general approach for surfaces with arbitrary topology.

Purpose of the Study:

  • To present the first application of surface Ricci flow in computer vision.
  • To develop a general framework for computing Ricci flow on discrete surfaces.
  • To demonstrate its utility in 3D shape analysis tasks.

Main Methods:

  • Developed a general framework for computing surface Ricci flow, allowing user-defined Riemannian metrics.
  • Implemented Ricci flow on discrete surfaces with Euclidean or hyperbolic background geometries.
  • Utilized conformal equivalence and Teichmüller space coordinates for shape indexing.

Main Results:

  • The Ricci flow-based method handles surfaces with arbitrary topology, subsuming previous conformal methods.
  • The method converts 3D problems into 2D domains, providing a general framework for 3D shape analysis.
  • Demonstrated successful 3D shape matching, registration, and indexing on facial and cardiac datasets, including non-rigid deformations.

Conclusions:

  • Surface Ricci flow provides a robust and generalizable framework for 3D shape analysis in computer vision.
  • The method is robust to noise and handles complex topologies effectively.
  • Applications include shape matching, registration, and indexing, with demonstrated success on challenging datasets.