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Mojette Transform on Densest Lattices in 2D and 3D

  • Vincent RicordelEmail author
  • Nicolas NormandEmail author
  • Jeanpierre GuédonEmail author
Conference paper
  • 584 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10502)

Abstract

The Mojette Transform (MT) is an exact discrete form of the Radon transform. It has been originally defined on the lattice \(Z^n\) (where n is the dimension). We propose to study this transform when using the densest lattices for the dimensions 2 and 3, namely the lattice \(A^2\) and the face-centered cubic lattice \(A^3\). In order to compare the legacy MT using \(Z^n\), versus the new MT using \(A^n\), we define a fair comparison methodology between the two MT schemes. In particular we detail how to generate the projection angles by exploiting the lattice symmetries and by reordering the Haros-Farey series. Statistic criteria have been also defined to analyse the information distribution on the projections. The experimental results study shows the specific nature of the information distribution on the MT projections due to the high compacity of the \(A^n\) lattices.

Keywords

Mojette Transform Discrete tomography Lattices Densest lattices Haros-Farey series 

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Université de Nantes, LS2N UMR CNRS 6004 Polytech NantesNantes Cedex 3France

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