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High-resolution, High-speed, Three-dimensional Video Imaging with Digital Fringe Projection Techniques
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Digital convexity, straightness, and convex polygons.

C E Kim1

  • 1Department of Computer Science, University of Maryland, College Park, MD 20742; Department of Computer Science, Washington State University, Pullman, WA 99163.

IEEE Transactions on Pattern Analysis and Machine Intelligence
|April 14, 2012
PubMed
Summary

New digital geometry schemes establish the equivalence of Sklansky's digital convexity definition with others. A linear-time algorithm identifies the smallest integer n for digital convex n-gons from digital convex regions.

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Area of Science:

  • Computer Vision
  • Digital Geometry
  • Computational Geometry

Background:

  • Digital convexity is crucial for image analysis and pattern recognition.
  • Existing definitions of digital convexity lack unified characterization.
  • Efficient algorithms for analyzing digital shapes are needed.

Purpose of the Study:

  • Introduce novel schemes for digitizing regions and arcs.
  • Establish the equivalence of Sklansky's digital convexity definition with other existing definitions.
  • Define and characterize digital convex polygons and develop an algorithm for their identification.

Main Methods:

  • Development of new digitization schemes for geometric primitives.
  • Comparative analysis of Sklansky's digital convexity definition against alternative definitions.
  • Characterization of digital convex polygons using properties of digital line segments.
  • Design of a linear-time algorithm for determining the minimum number of vertices (n) for a digital convex region.

Main Results:

  • Demonstrated equivalence between Sklansky's digital convexity definition and others under the new schemes.
  • Defined digital convex polygons based on geometric properties of digital line segments.
  • Presented a linear-time algorithm capable of finding the smallest integer n for a digital convex n-gon.

Conclusions:

  • The proposed digitization schemes provide a consistent framework for digital convexity.
  • Digital convex polygons can be rigorously defined and characterized.
  • The developed algorithm efficiently determines the minimal polygonal representation for digital convex regions.