Properties of Minimal Ghosts

  • Imants Svalbe
  • Nicolas Normand
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6607)


A ghost image is an array of signed pixel values so positioned as to create zero-sums in all discrete projections taken across that image for a pre-defined set of angles. The discrete projection scheme used here is the finite Radon transform. Minimal ghosts employ just 2N pixels to generate zero-sum projections at N projection angles. We describe efficient methods to construct \(N^\text{th}\) order minimal ghost images on prime-sized 2D arrays. Ghost images or switching components are important in discrete image reconstruction. Ghosts usually grow larger as they are constrained by more projection angles. When ghosts become too large to be added to an image, image reconstruction from projections becomes unique and exact. Ghosts can be used to synthesize image/anti-image data that will also exhibit zero-sum projections at N pre-defined angles. We examine the remarkable symmetry, cross- and auto-correlation properties of minimal ghosts. The geometric properties of minimal ghost images may make them suitable to embed in data as watermarks.


Image Space Projection Angle Ghost Image Discrete Image Projected View 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Imants Svalbe
    • 1
  • Nicolas Normand
    • 1
    • 2
  1. 1.School of PhysicsMonash UniversityMelbourneAustralia
  2. 2.IRCCyNUniversity of NantesNantesFrance

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