Wavelet Local Extrema Applied to Image Processing

Abstract

The research project had two components. In the first part, we developed a numerical method, based on the wavelet transform, for the solution of partial differential equations. Singularities and sharp transitions in solutions of partial differential equations model important physical phenomena, which are hard to simulate with conventional numerical methods. In collaboration with Pfr. Papanicolaou and Bacry, we introduced a numerical scheme based on the orthogonal wavelet transform, that adapts the computational resolution in space and time to the regularity of the solution. This scheme saves computations by concentrating the computational effort in regions where singularities or sharp transitions occur. it has been tested on the Burgers equation.

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1992
Accession Number
ADA262362

Entities

People

  • Stephane Mallat

Organizations

  • New York University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Artificial Intelligence
  • Coding
  • Computations
  • Computer Programming
  • Computer Vision
  • Detection
  • Differential Equations
  • Equations
  • Image Processing
  • Information Theory
  • Mathematical Analysis
  • Numerical Analysis
  • Partial Differential Equations
  • Pattern Recognition
  • Signal Processing
  • Theorems
  • Wavelet Transforms

Readers

  • Computer Vision.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)

Technology Areas

  • Space