ODF Maxima Extraction in Spherical Harmonic Representation via Analytical Search Space Reduction

Abstract

By revealing complex fiber structure through the orientation distribution function (ODF), q-ball imaging has recently become a popular reconstruction technique in diffusion-weighted MRI. In this paper, we propose an analytical dimension reduction approach to ODF maxima extraction. We show that by expressing the ODF, or any antipodally symmetric spherical function, in the common fourth order real and symmetric spherical harmonic basis, the maxima of the two-dimensional ODF lie on an analytically derived one-dimensional space, from which we can detect the ODF maxima. This method reduces the computational complexity of the maxima detection, without compromising the accuracy. We demonstrate the performance of our technique on both artificial and human brain data.

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Document Details

Document Type
Technical Report
Publication Date
May 01, 2010
Accession Number
ADA540656

Entities

People

  • Christophe Lenglet
  • Guillermo Sapiro
  • Iman Aganj

Organizations

  • University of Minnesota

Tags

DTIC Thesaurus Topics

  • Accuracy
  • Algorithms
  • Computational Complexity
  • Diffusion
  • Equations
  • Extraction
  • Geometry
  • Inequalities
  • Legendre Functions
  • Magnetic Resonance
  • Mathematical Analysis
  • Mathematics
  • Minnesota
  • Orientation (Direction)
  • Polynomials
  • Two Dimensional

Readers

  • Approximation Theory.
  • Graph Algorithms and Convex Optimization.
  • Medical Imaging.

Technology Areas

  • Space