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Relative Motion Analysis using Rotating Axes-Problem Solving01:29

Relative Motion Analysis using Rotating Axes-Problem Solving

Consider a crane whose telescopic boom rotates with an angular velocity of 0.04 rad/s and angular acceleration of 0.02 rad/s2. Along with the rotation, the boom also extends linearly with a uniform speed of 5 m/s. The extension of the boom is measured at point D, which is measured with respect to the fixed point C on the other end of the boom. For the given instant, the distance between points C and D is 60 meters.
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Curvilinear Motion: Rectangular Components

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Related Experiment Video

Updated: Jun 21, 2026

Three-dimensional Super Resolution Microscopy of F-actin Filaments by Interferometric PhotoActivated Localization Microscopy (iPALM)
11:57

Three-dimensional Super Resolution Microscopy of F-actin Filaments by Interferometric PhotoActivated Localization Microscopy (iPALM)

Published on: December 1, 2016

Optimal real-time Q-ball imaging using regularized Kalman filtering with incremental orientation sets.

Rachid Deriche1, Jeff Calder, Maxime Descoteaux

  • 1Odyssée Project Team, INRIA Sophia Antipolis - Méditerranée, 2004 route des Lucioles, BP 93, 06902 Sophia-Antipolis Cedex, France. Rachid.Deriche@sophia.inria.fr

Medical Image Analysis
|July 10, 2009
PubMed
Summary

This study optimizes real-time Q-ball imaging (QBI) reconstruction using an improved Kalman filter, enabling faster and more accurate diffusion MRI analysis for clinicians and researchers.

Related Experiment Videos

Last Updated: Jun 21, 2026

Three-dimensional Super Resolution Microscopy of F-actin Filaments by Interferometric PhotoActivated Localization Microscopy (iPALM)
11:57

Three-dimensional Super Resolution Microscopy of F-actin Filaments by Interferometric PhotoActivated Localization Microscopy (iPALM)

Published on: December 1, 2016

Area of Science:

  • Medical Imaging
  • Neuroimaging
  • Biophysics

Background:

  • Diffusion MRI, including DTI, DSI, and QBI, is crucial for studying tissue structure.
  • Acquiring and analyzing diffusion MRI data presents significant challenges due to its complexity.
  • Real-time Kalman filtering frameworks for DTI and QBI have been proposed but may be sub-optimal.

Purpose of the Study:

  • To analyze and identify limitations in existing real-time Kalman filtering for QBI.
  • To propose a novel, optimal real-time QBI reconstruction method using improved Laplace-Beltrami regularization.
  • To develop a fast algorithm for recursively computing gradient orientation sets.

Main Methods:

  • Revisiting and analyzing a prior Kalman filtering framework for DTI and QBI.
  • Developing a new real-time QBI reconstruction algorithm with optimized Laplace-Beltrami regularization.
  • Validating the proposed method with real QBI data and comparing it to offline techniques.

Main Results:

  • The existing Kalman filtering approach was found to be sub-optimal due to regularization issues.
  • The proposed real-time method achieves optimal QBI solutions recursively.
  • The new method demonstrates equivalent accuracy to offline processing and outperforms existing real-time solutions.

Conclusions:

  • The developed real-time QBI method provides optimal solutions and matches offline accuracy.
  • The recursive gradient orientation set algorithm aids in efficient data acquisition and ordering.
  • This work facilitates real-time feedback for clinicians and advances research in optimal diffusion MRI acquisition and analysis.