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

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...
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...
Surface Integrals01:28

Surface Integrals

A curved roof has a surface area that is generally larger than its flat projection. To estimate the cost of painting it, the curved surface area must first be calculated. If the roof is represented parametrically by a vector-valued function r(u,v), then each point in a parameter domain D corresponds to a point on the surface S. This connection allows the curved surface to be studied through a two-dimensional parameter region.The parameter domain D is divided into many small rectangles. A...
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...
Calculus with Parametric Curves: Surface Areas01:30

Calculus with Parametric Curves: Surface Areas

A parametric curve is a description of a path in the plane where both the x and y coordinates are functions of a single parameter, typically denoted t. When such a curve is revolved about an external axis lying in the same plane, it generates a surface of revolution in three dimensions. The surface area of this rotated shape depends fundamentally on two aspects: the geometry of the original curve and how far it lies from the chosen axis of rotation.A torus is a classical surface of revolution...

You might also read

Related Articles

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

Sort by
Same author

An evaluation of brain volume and cortical thickness measurement at 0.55 T.

Magma (New York, N.Y.)·2026
Same author

Optimization of fetal brain MRI at 0.55 T with slice-to-volume reconstruction.

Magma (New York, N.Y.)·2026
Same author

Chronic Anemia Patients Demonstrate Diffuse Demyelination.

American journal of hematology·2026
Same author

A hierarchical brain MRI atlas of the coppery titi monkey (Plecturocebus cupreus).

NeuroImage·2026
Same author

Optimizing electrode placement and information capacity for local field potentials in cortex.

NeuroImage·2026
Same author

Clinical Manifestations.

Alzheimer's & dementia : the journal of the Alzheimer's Association·2025
Same journal

LEARNABLE HIERARCHICAL VISUAL CONTEXTS FOR TUMOR SEGMENTATION IN COMPUTED TOMOGRAPHY IMAGES.

Proceedings. IEEE International Symposium on Biomedical Imaging·2026
Same journal

DUAL CROSS-ATTENTION SIAMESE TRANSFORMER FOR RECTAL TUMOR REGROWTH ASSESSMENT IN WATCH-AND-WAIT ENDOSCOPY.

Proceedings. IEEE International Symposium on Biomedical Imaging·2026
Same journal

LUMEN: LONGITUDINAL MULTI-MODAL RADIOLOGY MODEL FOR PROGNOSIS AND DIAGNOSIS.

Proceedings. IEEE International Symposium on Biomedical Imaging·2026
Same journal

OVERVIEW OF THE CXR-LT 2026 CHALLENGE: MULTI-CENTER LONG-TAILED AND ZERO SHOT CHEST X-RAY CLASSIFICATION.

Proceedings. IEEE International Symposium on Biomedical Imaging·2026
Same journal

CROSS-MODAL FINE-TUNING OF 3D CONVOLUTIONAL FOUNDATION MODELS FOR ADHD CLASSIFICATION WITH LOW-RANK ADAPTATION.

Proceedings. IEEE International Symposium on Biomedical Imaging·2026
Same journal

AN IN SILICO STUDY OF LOW-INTENSITY FOCUSED ULTRASOUND DISPLACEMENT MAPPING WITH A 220 KHZ CLINICAL PHASED-ARRAY TRANSDUCER.

Proceedings. IEEE International Symposium on Biomedical Imaging·2026
See all related articles

Related Experiment Video

Updated: Jun 10, 2026

Cortical Bone Assessment Using Ultrasonic Guided Waves: A Reproducibility Study in a Healthy Population
09:02

Cortical Bone Assessment Using Ultrasonic Guided Waves: A Reproducibility Study in a Healthy Population

Published on: January 31, 2025

CORTICAL SURFACE PARAMETERIZATION BY P-HARMONIC ENERGY MINIMIZATION.

Anand A Joshi1, David W Shattuck, Paul M Thompson

  • 1SIGNAL AND IMAGE PROCESSING INSTITUTE, UNIVERSITY OF SOUTHERN CALIFORNIA, LOS ANGELES, CA90089.

Proceedings. IEEE International Symposium on Biomedical Imaging
|August 20, 2010
PubMed
Summary
This summary is machine-generated.

We developed a novel method for mapping brain surfaces into a common space. This technique enables detailed 3D spatial averaging of cortical surfaces for enhanced brain analysis.

Related Experiment Videos

Last Updated: Jun 10, 2026

Cortical Bone Assessment Using Ultrasonic Guided Waves: A Reproducibility Study in a Healthy Population
09:02

Cortical Bone Assessment Using Ultrasonic Guided Waves: A Reproducibility Study in a Healthy Population

Published on: January 31, 2025

Area of Science:

  • Neuroimaging
  • Computational Anatomy
  • Medical Image Analysis

Background:

  • Cortical surface parameterization is crucial for brain surface analysis and visualization.
  • Existing methods may lack robustness or efficiency for multi-subject studies.

Purpose of the Study:

  • To present a new scheme for parameterizing the cerebral cortex surface.
  • To enable consistent mapping of multiple brain surfaces into a common parameter space.

Main Methods:

  • Formulating parameterization as an energy functional minimization problem using the p-th norm.
  • Developing a numerical method to solve the minimization problem.
  • Establishing correspondences between brain surfaces via the common parameter space.

Main Results:

  • Successfully parameterized individual brain surfaces.
  • Demonstrated the ability to map brain surfaces from multiple subjects into a unified parameter space.
  • Generated 3D spatial averages of cortical surfaces utilizing the induced correspondences.

Conclusions:

  • The proposed parameterization scheme provides a robust method for aligning and averaging cortical surfaces.
  • This technique facilitates comparative analysis and enhances visualization of population brain data.