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

Interpretations of Partial Derivatives01:14

Interpretations of Partial Derivatives

A surface defined by a function of two variables can be visualized as a vast, uneven terrain, where each point is identified using Cartesian coordinates. The elevation of the terrain at any point is determined by a function that assigns a height value to every pair of horizontal coordinates. This representation allows the surface to be studied in terms of how its height varies across different directions.At a specific point on this terrain, understanding how the height changes requires...
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...
Surface Area Calculations01:22

Surface Area Calculations

Surface area calculations for a graph z = f(x, y) are fundamental in engineering applications involving curved structures such as satellite dishes. A parabolic dish reflects communication signals efficiently, but engineers must determine its exact curved surface area to estimate coating materials, fabrication costs, and structural requirements. Since the rim of the dish forms a circular boundary, the surface area is calculated over a circular domain in the xy-plane.Parametric Representation of...
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...
Differential Leveling01:12

Differential Leveling

Differential leveling is a precise method in surveying used to determine the elevation difference between two points. Its primary goal is to establish accurate vertical measurements to create level surfaces or grade lines critical for designing and constructing infrastructures such as roads, bridges, and buildings.The procedure for differential leveling begins with setting up and leveling the instrument at a point where the benchmark can be seen. The level rod is held on the benchmark (BM), and...
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...

You might also read

Related Articles

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

Sort by
Same author

Calcium/calmodulin-dependent protein kinase II links ER stress with Fas and mitochondrial apoptosis pathways.

The Journal of clinical investigation·2009
Same author

Cripto-1 overexpression is involved in the tumorigenesis of nasopharyngeal carcinoma.

BMC cancer·2009
Same author

Range of motion and orientation of the lumbar facet joints in vivo.

Spine·2009
Same author

[Silencing of COX-2 in nasopharyngeal carcinoma cells with a shRNAmir lentivirus vector].

Nan fang yi ke da xue xue bao = Journal of Southern Medical University·2009
Same author

The risk of melamine-induced nephrolithiasis in young children starts at a lower intake level than recommended by the WHO.

Pediatric nephrology (Berlin, Germany)·2009
Same author

Adult scoliosis in patients over sixty-five years of age: outcomes of operative versus nonoperative treatment at a minimum two-year follow-up.

Spine·2009
Same journal

HardFlow: Hard-Constrained Sampling for Flow-Matching Models Via Trajectory Optimization.

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

Industrial Brain: Self-Evolving Neuro-Symbolic Autonomy with Causal Resilience for Cyber-Physical Systems.

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

Adaptive Hardness-Driven Dictionary Distillation for Incomplete Streaming View Clustering.

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

Mixture of Global and Local Experts with Diffusion Transformer for Controllable Face Generation.

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

Task-KV: Task-aware KV Cache Optimization via Semantic Differentiation of Attention Heads.

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

Achieving Text-based Person Retrieval with Any Granularity.

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

Related Experiment Video

Updated: Jun 18, 2026

Measuring Sensitivity to Viewpoint Change with and without Stereoscopic Cues
08:04

Measuring Sensitivity to Viewpoint Change with and without Stereoscopic Cues

Published on: December 4, 2013

Differential geometric inference in surface stereo.

Gang Li1, Steven W Zucker

  • 1Siemens Corporate Research, Princeton, NJ 08540, USA. gang-li@siemens.com

IEEE Transactions on Pattern Analysis and Machine Intelligence
|November 21, 2009
PubMed
Summary
This summary is machine-generated.

This study introduces a geometric approach to stereo reconstruction, moving beyond the frontal parallel plane assumption. By using Cartan's moving frame model, it improves accuracy for slanted surfaces and handles occlusions in 3D modeling.

More Related Videos

Robotized Testing of Camera Positions to Determine Ideal Configuration for Stereo 3D Visualization of Open-Heart Surgery
05:12

Robotized Testing of Camera Positions to Determine Ideal Configuration for Stereo 3D Visualization of Open-Heart Surgery

Published on: August 12, 2021

Quantification of Strain in a Porcine Model of Skin Expansion Using Multi-View Stereo and Isogeometric Kinematics
14:14

Quantification of Strain in a Porcine Model of Skin Expansion Using Multi-View Stereo and Isogeometric Kinematics

Published on: April 16, 2017

Related Experiment Videos

Last Updated: Jun 18, 2026

Measuring Sensitivity to Viewpoint Change with and without Stereoscopic Cues
08:04

Measuring Sensitivity to Viewpoint Change with and without Stereoscopic Cues

Published on: December 4, 2013

Robotized Testing of Camera Positions to Determine Ideal Configuration for Stereo 3D Visualization of Open-Heart Surgery
05:12

Robotized Testing of Camera Positions to Determine Ideal Configuration for Stereo 3D Visualization of Open-Heart Surgery

Published on: August 12, 2021

Quantification of Strain in a Porcine Model of Skin Expansion Using Multi-View Stereo and Isogeometric Kinematics
14:14

Quantification of Strain in a Porcine Model of Skin Expansion Using Multi-View Stereo and Isogeometric Kinematics

Published on: April 16, 2017

Area of Science:

  • Computer Vision
  • Geometric Modeling
  • Differential Geometry

Background:

  • Traditional stereo algorithms often assume frontal parallel planes, leading to errors in reconstructing slanted or curved surfaces.
  • These errors are significant for detailed 3D modeling of natural objects like human faces.
  • Existing methods struggle with accurate geometric representation beyond simple shapes.

Purpose of the Study:

  • To develop a novel stereo reconstruction method that overcomes the limitations of the frontal parallel plane assumption.
  • To improve the accuracy of 3D geometric modeling for complex surfaces.
  • To provide a geometrically consistent framework for depth and surface normal estimation.

Main Methods:

  • Utilized differential geometry and Cartan's moving frame model for contextual information encoding.
  • Applied local quadratic approximations to represent surface geometry.
  • Developed a framework for geometric consistency in stereo reconstruction.

Main Results:

  • Demonstrated the ability to avoid systematic errors common in traditional stereo algorithms.
  • Achieved accurate reconstructions of depth and surface normals for non-planar surfaces.
  • Showcased the sufficiency of local quadratic approximations within the Cartan model.

Conclusions:

  • Cartan's moving frame model offers a robust geometric constraint, enabling stereo reconstruction beyond the frontal parallel plane assumption.
  • The proposed method enhances the geometric accuracy of 3D models, particularly for complex natural objects.
  • The geometric framework can extend surfaces to address partial occlusion issues.