Shape Transformation of Multidimensional Density Functions using Distribution Interpolation of the Radon Transforms

Márton József Tóth, Balázs Csébfavi

2014

Abstract

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 Implicit Functions (IF). First, we perform distribution interpolation on the precalculated Radon transforms of two different density functions, and then an intermediate density function is obtained by an inverse Radon transform. This approach guarantees a smooth transition along all the directions the Radon transform is calculated for. Unlike the IF 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.

Paper Citation

in Harvard Style

Tóth M. and Csébfavi B. (2014). Shape Transformation of Multidimensional Density Functions using Distribution Interpolation of the Radon Transforms . In Proceedings of the 9th International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2014) ISBN 978-989-758-002-4, pages 5-12. DOI: 10.5220/0004640800050012

in Bibtex Style

@conference{grapp14,
author={Márton József Tóth and Balázs Csébfavi},
title={Shape Transformation of Multidimensional Density Functions using Distribution Interpolation of the Radon Transforms},
booktitle={Proceedings of the 9th International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2014)},
year={2014},
pages={5-12},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0004640800050012},
isbn={978-989-758-002-4},
}

in EndNote Style

TY - CONF
JO - Proceedings of the 9th International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2014)
TI - Shape Transformation of Multidimensional Density Functions using Distribution Interpolation of the Radon Transforms
SN - 978-989-758-002-4
AU - Tóth M.
AU - Csébfavi B.
PY - 2014
SP - 5
EP - 12
DO - 10.5220/0004640800050012