Multigrid Relaxation Methods and the Analysis of Lightness, Shading, and Flow

Abstract

Image analysis problems, posed mathematically as variational principles or as partial differential equations, are amenable to numerical solution by relaxation algorithms that are local, iterative, and often parallel. Although they are will suited structurally for implementation on massively parallel, locally-interconnected computational architectures, such distributed algorithms are seriously handicapped by an inherent inefficiency at propagating constraints between widely separated processing elements. Hence, they converge slowly when confronted by the large representations necessary for low-level vision. Application of multigrid methods can overcome this drawback, as we established in previous work on 3-D surface reconstruction. In this paper, we develop efficient multiresolution iterative algorithms fo computing lightness, shape-from-shading, and optical flow, and we evaluate the performance of these algorithms on synthetic images. This multigrid methodology is broadly applicable in low-level vision. Notably, it is an appealing strategy to use in conjunction with regularization analysis for the efficient solution of a wide range of ill- posed visual reconstruction problems. Keywords: Computer vision; Shape-from- shading; Variation principles; and Parallel algorithms.

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1984
Accession Number
ADA158173

Entities

People

  • D. Terzopoulos

Organizations

  • Massachusetts Institute of Technology

Tags

Communities of Interest

  • Energy and Power Technologies
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Algorithms
  • Artificial Intelligence
  • Boundary Value Problems
  • Computational Processes
  • Computational Science
  • Computations
  • Computer Graphics
  • Computer Vision
  • Differential Equations
  • Equations
  • Fluid Mechanics
  • Image Processing
  • Mathematics
  • New York
  • Partial Differential Equations
  • Three Dimensional
  • Variational Principles

Readers

  • Computational Fluid Dynamics (CFD)
  • Computer Vision.
  • Systems Analysis and Design

Technology Areas

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