Some Discrete Approximations to a Variational Method for Image Segmentation

Abstract

Variational formulations have been proposed for a number of tasks in early vision. Discrete versions of these problems are closely related to Markov random field models and are typically used in implementing such methods. In particular, discrete and continuous versions for the problem of image segmentation have received considerable attention from both theoretical and algorithmic perspectives. It has been previously pointed out that the usual discrete version of the segmentation problem does not properly approximate the continuous formulation in the sense that the discrete solutions may not converge to a solution of the continuous problem as the lattice spacing tends to zero. One method for modifying the discrete formulations to ensure such convergence has been previously discussed. Here we consider two other partially discrete formulations which also satisfy desirable convergence properties in the continuum limit, and we discuss some general ideas about digitized versions of the variational formulation of the segmentation problem.

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Document Details

Document Type
Technical Report
Publication Date
Jan 03, 1991
Accession Number
ADA459293

Entities

People

  • Sanjoy K. Mitter
  • Shrinivas Kulkarni

Organizations

  • Massachusetts Institute of Technology

Tags

Communities of Interest

  • C4I
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Abstracts
  • Artificial Intelligence
  • Boundaries
  • Calculus
  • Computations
  • Computer Vision
  • Convergence
  • Image Restoration
  • Image Segmentation
  • Information Operations
  • Mathematics
  • Sequences
  • Standards
  • Topology
  • Variational Methods
  • Variational Principles

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Neural Network Machine Learning.

Technology Areas

  • Space