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

Quadric Surfaces01:28

Quadric Surfaces

Quadric surfaces are three-dimensional surfaces characterized by second-degree equations in the variables x, y, and z. These surfaces are smooth and continuous, and specific combinations of squared and linear terms define their shapes. The main types of quadric surfaces include ellipsoids, cones, paraboloids, and hyperboloids. Each type exhibits distinct geometric features depending on how the variables are arranged and related within the equation.Ellipsoids are closed surfaces formed when all...
Divergence Theorem in 3D Space01:20

Divergence Theorem in 3D Space

In vector calculus, flux measures the total flow of a vector field through a surface. For a closed surface in three-dimensional space, this means measuring how much of the field passes outward through every point on the boundary. Directly calculating this flux can be difficult when the surface has a complicated or irregular shape. The Divergence Theorem provides a powerful alternative by relating surface flux to behavior inside the enclosed region.The Divergence Theorem states that the outward...
Tangent Planes to Surfaces01:19

Tangent Planes to Surfaces

In multivariable calculus, the concept of a tangent plane plays a central role in approximating curved surfaces. When dealing with a surface defined by a function of two variables, such as z = f(x, y), the tangent plane at a given point provides the best linear approximation to the surface near that point. This local linearization allows complex, nonlinear geometries to be treated using simpler, planar models.The construction of the tangent plane involves taking vertical slices of the surface...
Parametric Surfaces01:30

Parametric Surfaces

A parametric surface in three-dimensional space is defined through a vector-valued function\begin{equation*}\mathbf{r}(u, v) = x(u, v)\mathbf{i} + y(u, v)\mathbf{j} + z(u, v)\mathbf{k}\end{equation*}where u and v are parameters within a specified domain D in the uv-plane. The functions x(u, v), y(u, v), and z(u, v) define the coordinates of points on the surface. As u and v vary over D, the position vector r(u, v) traces a continuous surface in space. This parametric representation is essential...
Tangent Planes to a Parametric Surface01:22

Tangent Planes to a Parametric Surface

A tangent plane provides a linear approximation to a curved surface at a specific point, capturing the local behavior of the surface. It can be understood as the plane that just touches the surface at that point and is defined by the tangent directions of curves lying on the surface. These tangent directions arise naturally when the surface is described parametrically, allowing systematic construction of the plane.For a surface expressed in parametric form, the position of any point is...
Oriented Surfaces01:30

Oriented Surfaces

A surface is called orientable if a consistent choice of unit normal vector can be made at every point on the surface. A thin soap film stretched across a wire loop provides a familiar example. The film separates the air on one side from the air on the other, so one side can be selected as positive and the opposite side as negative. Once this choice is made, a unit normal vector can be assigned smoothly across the entire surface.At each point on the soap film, a unit normal vector points...

You might also read

Related Articles

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

Sort by
Same author

Independent real-world application of a clinical-grade automated prostate cancer detection system.

The Journal of pathology·2021
Same author

Novel artificial intelligence system increases the detection of prostate cancer in whole slide images of core needle biopsies.

Modern pathology : an official journal of the United States and Canadian Academy of Pathology, Inc·2020
Same author

Precise measurement of coronary stenosis diameter with CCTA using CT number calibration.

Medical physics·2019
Same author

Generation of Patient-Specific Cardiac Vascular Networks: A Hybrid Image-Based and Synthetic Geometric Model.

IEEE transactions on bio-medical engineering·2018
Same author

Lumen boundaries extracted from coronary computed tomography angiography on computed fractional flow reserve (FFRCT): validation with optical coherence tomography.

EuroIntervention : journal of EuroPCR in collaboration with the Working Group on Interventional Cardiology of the European Society of Cardiology·2018
Same author

Automated estimation of image quality for coronary computed tomographic angiography using machine learning.

European radiology·2018
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 17, 2026

3D Scanning Technology Bridging Microcircuits and Macroscale Brain Images in 3D Novel Embedding Overlapping Protocol
10:14

3D Scanning Technology Bridging Microcircuits and Macroscale Brain Images in 3D Novel Embedding Overlapping Protocol

Published on: May 12, 2019

Minimal surfaces extend shortest path segmentation methods to 3D.

Leo Grady1

  • 1Siemens Corporate Research, Department of Imaging and Visualization, 755 College Rd., East Princeton, NJ 08540, USA. leo.grady@siemens.com

IEEE Transactions on Pattern Analysis and Machine Intelligence
|January 16, 2010
PubMed
Summary
This summary is machine-generated.

Shortest paths in 3D image segmentation are extended using minimal surfaces, not just paths. This approach correctly defines object boundaries as surfaces, improving segmentation accuracy.

More Related Videos

Extracting Metrics for Three-dimensional Root Systems: Volume and Surface Analysis from In-soil X-ray Computed Tomography Data
09:37

Extracting Metrics for Three-dimensional Root Systems: Volume and Surface Analysis from In-soil X-ray Computed Tomography Data

Published on: April 26, 2016

From Voxels to Knowledge: A Practical Guide to the Segmentation of Complex Electron Microscopy 3D-Data
12:08

From Voxels to Knowledge: A Practical Guide to the Segmentation of Complex Electron Microscopy 3D-Data

Published on: August 13, 2014

Related Experiment Videos

Last Updated: Jun 17, 2026

3D Scanning Technology Bridging Microcircuits and Macroscale Brain Images in 3D Novel Embedding Overlapping Protocol
10:14

3D Scanning Technology Bridging Microcircuits and Macroscale Brain Images in 3D Novel Embedding Overlapping Protocol

Published on: May 12, 2019

Extracting Metrics for Three-dimensional Root Systems: Volume and Surface Analysis from In-soil X-ray Computed Tomography Data
09:37

Extracting Metrics for Three-dimensional Root Systems: Volume and Surface Analysis from In-soil X-ray Computed Tomography Data

Published on: April 26, 2016

From Voxels to Knowledge: A Practical Guide to the Segmentation of Complex Electron Microscopy 3D-Data
12:08

From Voxels to Knowledge: A Practical Guide to the Segmentation of Complex Electron Microscopy 3D-Data

Published on: August 13, 2014

Area of Science:

  • Computer Vision
  • Image Processing
  • Computational Geometry

Background:

  • Shortest path algorithms are established for 2D object boundary segmentation.
  • Extending 2D shortest path methods to 3D fails to preserve the boundary as a surface.
  • Previous 3D segmentation methods using shortest paths lack guaranteed accuracy for minimal surfaces.

Purpose of the Study:

  • To demonstrate how minimal surfaces properly extend shortest paths for 3D object boundary segmentation.
  • To present an efficient method for computing minimal surfaces in 3D.
  • To apply minimal surface segmentation to real image data.

Main Methods:

  • Utilizing Sullivan's solution for computing discrete minimal surfaces on cellular complexes.
  • Formulating the minimal surface computation as a Minimum-cost Circulation Network Flow (MCNF) problem.
  • Applying the MCNF-based minimal surface computation to 3D image segmentation.

Main Results:

  • Minimal surfaces provide a mathematically sound extension of shortest paths for 3D boundaries.
  • The MCNF approach efficiently computes accurate discrete minimal surfaces.
  • Demonstrated successful application of minimal surface segmentation on image datasets.

Conclusions:

  • Minimal surfaces are the correct extension of shortest paths for 3D boundary segmentation.
  • Minimum-cost Circulation Network Flow offers an efficient and accurate method for computing these minimal surfaces.
  • This technique enhances the precision of 3D image segmentation.