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Three-dimensional digital planes.

C E Kim1

  • 1Department of Computer Science, Washington State University, Pullman, WA 99164.

IEEE Transactions on Pattern Analysis and Machine Intelligence
|August 27, 2011
PubMed
Summary
This summary is machine-generated.

This study defines 3-D digital surfaces and planes, exploring their geometric properties. It reveals digital convexity is not always sufficient for plane elements but is crucial for digital surfaces to be digital planes.

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Area of Science:

  • Digital Geometry
  • Computational Geometry
  • Computer Graphics

Background:

  • Understanding digital representations of geometric objects is crucial in computer graphics and image analysis.
  • Existing definitions of digital planes and surfaces lack comprehensive geometric property analysis.

Purpose of the Study:

  • To introduce precise definitions for 3-D digital surfaces and planes.
  • To investigate the geometric properties of these digital objects, particularly focusing on digital convexity.
  • To develop algorithms for identifying digital plane elements.

Main Methods:

  • Formal definition of 3-D digital surfaces and planes.
  • Analysis of geometric properties, including digital convexity.
  • Development and presentation of algorithms for digital plane element recognition.

Main Results:

  • Digital convexity is neither necessary nor sufficient for a digital surface element to be a convex digital plane element.
  • Digital convexity is both necessary and sufficient for a digital surface to be a digital plane.
  • Algorithms are provided to determine if a finite set of digital points constitutes a convex digital plane element.

Conclusions:

  • The relationship between digital convexity and digital planes is clarified.
  • The study provides a robust framework for analyzing digital planes and surfaces.
  • Algorithms enable practical identification of digital plane elements in discrete datasets.