Homotopies: A Panacea or Just Another Method?

Abstract

A general framework is presented for the solving of non-linear equations. Also, a discussion about its potential applications in the field of computer vision is made and illustrated by an example that shows how one can relate the solutions to the shape-from-shading problem through scale space. The methods presented seem to have been known since the 19th century; however, it was not until 1953 that the first practical applications of the relevant idea appeared. Keywords: Non-linear equations, Shape-from-shading, Scale space, Homotopies, Path following, Hilbert space, Continuation methods.

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1986
Accession Number
ADA189568

Entities

People

  • Isidore Rigoutsos

Organizations

  • University of Rochester

Tags

Communities of Interest

  • Air Platforms
  • Energy and Power Technologies
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Abstracts
  • Algorithms
  • Artificial Intelligence
  • Boundary Value Problems
  • Computational Fluid Dynamics
  • Computational Science
  • Computer Science
  • Computer Vision
  • Computers
  • Differential Equations
  • Equations
  • Functional Analysis
  • Geometry
  • Hilbert Space
  • Linear Systems
  • Nonlinear Systems
  • Universities

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Prostate Cancer Biology.
  • Strategic Security Studies

Technology Areas

  • AI & ML
  • AI & ML - Machine Learning Algorithms
  • Space