Distribution Interpolation of the Radon Transforms for Shape Transformation of Gray-Scale Images and Volumes

  • Márton József Tóth
  • Balázs Csébfalvi
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 550)


In this paper, we extend 1D distribution interpolation to 2D and 3D by using the Radon transform. Our algorithm is fundamentally different from previous shape transformation techniques, since it considers the objects to be interpolated as density distributions rather than level sets of density functions. First, we perform distribution interpolation on the precalculated Radon transforms of two different density functions, and then an intermediate density function is obtained by a consistent inverse Radon transform. This approach guarantees a smooth transition along all the directions the Radon transform is calculated for. Unlike the previous methods, our technique is able to interpolate between features that do not even overlap and it does not require a one dimension higher object representation. We will demonstrate that these advantageous properties can be well exploited for 3D modeling and metamorphosis.


Shape-based interpolation Image/volume morphing Distribution interpolation Radon transform 



This work was supported by OTKA K-101527. The Heloderma data set is from the Digital Morphology data archive. Special thanks to Dr. Jessica A. Maisano for making this data set available to us.


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© Springer International Publishing Switzerland 2015

Open Access This chapter is distributed under the terms of the Creative Commons Attribution Noncommercial License, which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

Authors and Affiliations

  1. 1.Budapest University of Technology and EconomicsBudapestHungary

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