Skip to content Skip to navigation

Connexions

You are here: Home » Content » Delaunay Triangulation for Image Processing

Navigation

Content Actions
  • Download module PDF
  • Add to ...
    Add the module to:
    • My Favorites
    • A lens
    • An external social bookmarking service
    • My Favorites (What is 'My Favorites'?)
      'My Favorites' is a special kind of lens which you can use to bookmark modules and collections directly in Connexions. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need a Connexions account to use 'My Favorites'.
    • A lens (What is a lens?)

      Definition of a lens

      Lenses

      A lens is a custom view of Connexions content. You can think of it as a fancy kind of list that will let you see Connexions through the eyes of organizations and people you trust.

      What is in a lens?

      Lens makers point to Connexions materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

      Who can create a lens?

      Any individual Connexions member, a community, or a respected organization.

      What are tags? tag icon

      Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

    • External bookmarks
  • E-mail the authors
  • Rate this module (How does the rating system work?)

    Rating system

    Ratings

    Ratings allow you to judge the quality of modules. If other users have ranked the module then its average rating is displayed below. Ratings are calculated on a scale from one star (Poor) to five stars (Excellent).

    How to rate a module

    Hover over the star that corresponds to the rating you wish to assign. Click on the star to add your rating. Your rating should be based on the quality of the content. You must have an account and be logged in to rate content.

    		(0 ratings)

Lenses

What is a lens?

Definition of a lens

Lenses

A lens is a custom view of Connexions content. You can think of it as a fancy kind of list that will let you see Connexions through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to Connexions materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual Connexions member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

This content is ...

Affiliated with (What does "Affiliated with" mean?)

This content is either by members of the organizations listed or about topics related to the organizations listed. Click each link to see a list of all content affiliated with the organization.
  • Rice University ELEC 301 Projects

    This module is included inLens: Rice University ELEC 301 Project Lens
    By: Rice University ELEC 301As a part of collection:"ELEC 301 Projects Fall 2006"

    Click the "Rice University ELEC 301 Projects" link to see all content affiliated with them.

Recently Viewed

This feature requires Javascript to be enabled.

Delaunay Triangulation for Image Processing

Module by: Jennifer Gillenwater, J. Ryan Stinnett, Elica Skorcheva

Summary: Triangulation is a tool that divide a surface into regions with certain common characteristics. The type of these characteristics depends on the type of triangulation. Delaunay triangulation can divide a surface into regions that are particularly well-suited for image processing applicaions.

Because of the inherent geometric qualities of image subjects, it is desirable that any algorithm for dividing an image into a set of regions should be able to model a wide variety of geometries. Triangles are the simplest building block for such models. As such, it is appropriate to use a triangulation to break down or build up an image.

Triangulation divides a surface into a set of triangles, with each triangle edge entirely shared by two triangles. Given a set of points P, the Delaunay triangulation of this set ensures that no point is in the circumcircle of any triangle formed.

Figure 1: The circumcircle of a triangle is the circle that passes through all of the triangle’s vertices (A, B, C).
Circumcircle
Circumcircle (circumcircle.bmp)

There are several methods for accomplishing this, such as incremental, divide and conquer, and sweepline. All of these can achieve O(nlogn) run time, where n is the number of points in P. The Delaunay triangulation for a set of points P(X,Y) can easily be accomplished in MATLAB via the command delaunay(X,Y).

The advantage of using Delaunay triangulation over other types is that it maximizes the minimum angles of the triangles. In this way, the triangles tend toward equiangularity, which avoids having triangles that are very long and thin. Therefore, the resulting triangulation looks geometrically balanced. Aside from equiangularity, Delaunay triangulation is particularly non-restrictive. Thus, it is ideal for interpolation algorithms, which attempt to avoid introducing distortions. (Other methods of triangulating might force unusual constraints on the triangle patches, which could result in really weird shapes on the surface. This would distort the pixel values of the final image, since pixel values over a region are directly related to the triangle that covers that region.)

The geometric versatility of triangulation as a tool for breaking down and building up images, combined with the particular geometric advantages of the Delaunay version in the interpolation realm, make Delaunay triangulation an ideal component of pixel interpolation algorithms.

Comments, questions, feedback, criticisms?

Send feedback