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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...
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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...
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Calculus with Parametric Curves: Surface Areas

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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...

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Three-Dimensional Shape Modeling and Analysis of Brain Structures
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Three-Dimensional Shape Modeling and Analysis of Brain Structures

Published on: November 14, 2019

General multivariate linear modeling of surface shapes using SurfStat.

Moo K Chung1, Keith J Worsley, Brendon M Nacewicz

  • 1Department of Biostatistics and Medical Informatics, University of Wisconsin, Madison, WI 53705, USA. mkchung@wisc.edu

Neuroimage
|July 13, 2010
PubMed
Summary
This summary is machine-generated.

This study introduces a novel computational framework to analyze amygdala shape variations in individuals with autism. The method reveals localized shape abnormalities in the amygdala of high-functioning autistic subjects.

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Area of Science:

  • Neuroimaging
  • Computational Anatomy
  • Statistical Modeling

Background:

  • Limited research exists on modeling amygdala shape variations, despite numerous studies on amygdala volumetry.
  • Understanding amygdala shape is crucial for neurological and psychiatric research.

Purpose of the Study:

  • To present a unified computational and statistical framework for modeling amygdala shape variations.
  • To apply this framework to quantify shape abnormalities in a clinical population.

Main Methods:

  • Utilized weighted spherical harmonic representation for parameterizing, smoothing, and normalizing amygdala surfaces.
  • Employed multivariate linear models within the SurfStat package to analyze shape variations, controlling for covariates like age and brain size.
  • Applied the methodology to a cohort of 22 high-functioning autistic subjects.

Main Results:

  • Successfully quantified localized amygdala shape variations in high-functioning autistic subjects.
  • Demonstrated the framework's capability to identify subtle shape differences.

Conclusions:

  • The developed framework provides a robust method for analyzing amygdala shape variations.
  • This approach can aid in understanding the neuroanatomical underpinnings of autism spectrum disorder.