# REPRESENTING DIRECTIONS FOR HOUGH TRANSFORMS

### Fabian Wenzel, Rolf-Rainer Grigat

#### 2006

#### Abstract

Many algorithms in computer vision operate with directions, i. e. with representations of 3D-points by ignoring their distance to the origin. Even though minimal parametrizations of directions may contain singularities, they can enhance convergence in optimization algorithms and are required e. g. for accumulator spaces in Hough transforms. There are numerous possibilities for parameterizing directions. However, many do not account for numerical stability when dealing with noisy data. This paper gives an overview of different parametrizations and shows their sensitivity with respect to noise. In addition to standard approaches in the field of computer vision, representations originating from the field of cartography are introduced. Experiments demonstrate their superior performance in computer vision applications in the presence of noise as they are suitable for Gaussian filtering.

#### References

- Barnard, S. T. (1983). Interpreting perspective images. Artificial Intell., 21:435-462.
- D. Fleet, M. Black, Y. and Jepson, A. (2000). Design and use of linear models for image motion analysis. International Journal of Computer Vision, 36(3):171-193.
- Faugeras, O. (1993). Three-Dimensional Computer Vision - A Geometric ViewPoint. MIT Press.
- Golub, G. H. and Loan, C. F. V. (1996). MATRIX Computations. John Hopkins University Press.
- Hartley, R. and Zissermann, A. (2003). Multiple View Geometry. Cambridge University Press, 2. edition.
- Lutton, Maitre, L.-K. (1994). Contribution to the determination of vanishing points using hough transforms. IEEE Transactions on Pattern Analysis and Machine Intelligence, 16(4):430-438.
- Medioni, G. and Kang, S. B., editors (2004). Emerging Topics in Computer Vision, chapter Robust techniques for computer vision. Prentice Hall.
- Morris, D. D. (2001). Gauge Freedoms and Uncertainty Modeling for 3D Computer Vision. PhD thesis, Robotics Institute, Carnegie Mellon University.
- Perona, P. (1992). Steerable-scalable kernels for edge detection and junction analysis. In European Conference on Computer Vision, pages 3-18.
- Quan, L. and Mohr, R. (1989). Determining perspective structures using hierarchical hough transform. Pattern Recognition Letters, 9:279-286.
- Snyder, J. P. (1987). Map Projections; A Working Manual. U.S. Geological Survey, supersedes bulletin 1532 edition.
- Stuelpnagel, J. (1964). On the parametrization of the threedimensional rotation group. SIAM Review, 6(4). 2 4 6 8 Gaussian filter kernel size g (pixels) (a) Angular errors for s = 8? 10 0 2 4 6 8 Gaussian filter kernel size g (pixels) (b) Angular errors for s = 20?

#### Paper Citation

#### in Harvard Style

Wenzel F. and Grigat R. (2006). **REPRESENTING DIRECTIONS FOR HOUGH TRANSFORMS** . In *Proceedings of the First International Conference on Computer Vision Theory and Applications - Volume 2: VISAPP,* ISBN 972-8865-40-6, pages 116-122. DOI: 10.5220/0001373301160122

#### in Bibtex Style

@conference{visapp06,

author={Fabian Wenzel and Rolf-Rainer Grigat},

title={REPRESENTING DIRECTIONS FOR HOUGH TRANSFORMS},

booktitle={Proceedings of the First International Conference on Computer Vision Theory and Applications - Volume 2: VISAPP,},

year={2006},

pages={116-122},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0001373301160122},

isbn={972-8865-40-6},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the First International Conference on Computer Vision Theory and Applications - Volume 2: VISAPP,

TI - REPRESENTING DIRECTIONS FOR HOUGH TRANSFORMS

SN - 972-8865-40-6

AU - Wenzel F.

AU - Grigat R.

PY - 2006

SP - 116

EP - 122

DO - 10.5220/0001373301160122