The Generalized Map Makers Problem: Optimal Flattening of Polyhedral Surfaces

Abstract

The authors' concern is to 'unfold' and flatten the curved, convoluted surfaces of the brain in order to study the functional architectures and neural maps embedded in them. In order to do this, it is necessary to solve the general map makers problem for representing curved surfaces by quasi- isometric planar models. This algorithm has applications in areas other than computer aided neuroanatomy, such as robotics motion planning and geophysics. The algorithm the author has written maximizes the goodness of fit of distances in these surfaces, to those in a planar configuration of points. He illustrates this algorithm with a flattening of monkey visual cortex, which is an extremely complex, folded surface. Found are distance errors in the range of several percent, with isolated regions of larger error, for the class of cortical surfaces so far studied.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1987
Accession Number
ADA210013

Entities

People

  • Eric M. Schwartz

Organizations

  • New York University

Tags

Communities of Interest

  • Air Platforms
  • Biomedical

DTIC Thesaurus Topics

  • Abstracts
  • Algorithms
  • Brain
  • Computational Neuroscience
  • Computer Science
  • Computers
  • Curvature
  • Equations
  • Geometric Forms
  • Geometry
  • Gray Scale
  • Hemispherical Shells
  • Motion Picture Cameras
  • Motion Planning
  • Neurosciences
  • New York
  • Visual Cortex

Readers

  • Graph Algorithms and Convex Optimization.
  • Robotics and Automation.
  • Space Exploration and Orbital Mechanics.

Technology Areas

  • AI & ML
  • AI & ML - Bayesian Inference
  • AI & ML - Machine Learning Algorithms
  • Autonomy