# Fast Fourier Transform based Force Histogram Computation for 3D Raster Data

### Jaspinder Kaur, Tyler Laforet, Pascal Matsakis

#### Abstract

The force histogram is a quantitative representation of the relative position between two objects. Two practical algorithms have been previously introduced to compute the force histogram between objects: the line-based algorithm (which works well with 2D data, but is computationally unstable in the case of 3D data), and the Fast Fourier Transform (FFT)-based algorithm (which is inefficient in the case of 2D data, but has not been implemented for 3D data). In this paper, an efficient FFT-based algorithm for force histogram computation in the case of 3D raster data is introduced. Its computation time is compared against that of the 3D line-based algorithm; except in a few cases, the computation time for new FFT-based algorithm is less than that of 3D line-based algorithm. The experiments validate that the FFT-based algorithm is computationally efficient regardless of the number of directions, type of forces, and shape of the objects (convex, concave, disjoint or overlapping).

Download#### Paper Citation

#### in Harvard Style

Kaur J., Laforet T. and Matsakis P. (2020). **Fast Fourier Transform based Force Histogram Computation for 3D Raster Data**.In *Proceedings of the 9th International Conference on Pattern Recognition Applications and Methods - Volume 1: ICPRAM,* ISBN 978-989-758-397-1, pages 69-74. DOI: 10.5220/0008985100690074

#### in Bibtex Style

@conference{icpram20,

author={Jaspinder Kaur and Tyler Laforet and Pascal Matsakis},

title={Fast Fourier Transform based Force Histogram Computation for 3D Raster Data},

booktitle={Proceedings of the 9th International Conference on Pattern Recognition Applications and Methods - Volume 1: ICPRAM,},

year={2020},

pages={69-74},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0008985100690074},

isbn={978-989-758-397-1},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 9th International Conference on Pattern Recognition Applications and Methods - Volume 1: ICPRAM,

TI - Fast Fourier Transform based Force Histogram Computation for 3D Raster Data

SN - 978-989-758-397-1

AU - Kaur J.

AU - Laforet T.

AU - Matsakis P.

PY - 2020

SP - 69

EP - 74

DO - 10.5220/0008985100690074