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Related Concept Videos

Properties of DTFT I01:24

Properties of DTFT I

In signal processing, Discrete-Time Fourier Transforms (DTFTs) play a critical role in analyzing discrete-time signals in the frequency domain. Various properties of the DTFTs such as linearity, time-shifting, frequency-shifting, time reversal, conjugation, and time scaling help understand and manipulate these signals for different applications.
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Properties of Laplace Transform-II01:16

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Time differentiation, convolution, integration, and periodicity are fundamental concepts in analyzing functions and signals over time. Each concept provides a unique perspective on how functions evolve, interact, and repeat, offering essential tools for various scientific and engineering applications.
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Properties of Fourier Transform II01:24

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Updated: Jun 27, 2026

Three-Dimensional Shape Modeling and Analysis of Brain Structures
05:33

Three-Dimensional Shape Modeling and Analysis of Brain Structures

Published on: November 14, 2019

Time sequence diffeomorphic metric mapping and parallel transport track time-dependent shape changes.

Anqi Qiu1, Marilyn Albert, Laurent Younes

  • 1Division of Bioengineering, National University of Singapore, Singapore. bieqa@nus.edu.sg

Neuroimage
|December 2, 2008
PubMed
Summary
This summary is machine-generated.

We developed a novel method for tracking brain shape changes over time using serial MRI scans. This technique helps analyze brain development and disease progression more accurately.

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Area of Science:

  • Medical imaging analysis
  • Computational anatomy
  • Neuroscience

Background:

  • Serial MRI scans are crucial for understanding brain development and diseases.
  • Tracking anatomical shape changes is essential for monitoring disease progression and drug effects.

Purpose of the Study:

  • To introduce a new point-based time sequence large deformation diffeomorphic metric mapping (TS-LDDMM) for inferring within-subject geometric shape changes.
  • To propose a diffeomorphic analysis framework for comparing shapes across subjects.

Main Methods:

  • Generalized Euler-Lagrange equation for point sets (landmarks, curves, surfaces).
  • Inferred time-dependent momentum from TS-LDDMM to encode shape changes.
  • Diffeomorphic framework using parallel transport for cross-subject comparison.

Main Results:

  • The TS-LDDMM method effectively infers time-dependent geometric shape changes from serial MRI data.
  • The proposed framework enables translation of within-subject deformations into a global template for cross-subject analysis.
  • This approach isolates anatomical variations from disease-specific changes.

Conclusions:

  • The developed TS-LDDMM and diffeomorphic analysis framework offer a robust method for analyzing longitudinal brain shape changes.
  • This technique can enhance the understanding of brain development, neurodegenerative diseases, and treatment efficacy.
  • It provides a powerful tool for clinical trials and neuroimaging research.