# Optimal Surface Normal from Affine Transformation

### Barath Daniel, Jozsef Molnar, Levente Hajder

#### Abstract

This paper deals with surface normal estimation from calibrated stereo images. We show here how the affine transformation between two projections defines the surface normal of a 3D planar patch. We give a formula that describes the relationship of surface normals, camera projections, and affine transformations. This formula is general since it works for every kind of cameras. We propose novel methods for estimating the normal of a surface patch if the affine transformation is known between two perspective images. We show here that the normal vector can be optimally estimated if the projective depth of the patch is known. Other non-optimal methods are also introduced for the problem. The proposed methods are tested both on synthesized data and images of real-world 3D objects.

#### References

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#### Paper Citation

#### in Harvard Style

Daniel B., Molnar J. and Hajder L. (2015). **Optimal Surface Normal from Affine Transformation** . In *Proceedings of the 10th International Conference on Computer Vision Theory and Applications - Volume 3: VISAPP, (VISIGRAPP 2015)* ISBN 978-989-758-091-8, pages 305-316. DOI: 10.5220/0005303703050316

#### in Bibtex Style

@conference{visapp15,

author={Barath Daniel and Jozsef Molnar and Levente Hajder},

title={Optimal Surface Normal from Affine Transformation},

booktitle={Proceedings of the 10th International Conference on Computer Vision Theory and Applications - Volume 3: VISAPP, (VISIGRAPP 2015)},

year={2015},

pages={305-316},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0005303703050316},

isbn={978-989-758-091-8},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 10th International Conference on Computer Vision Theory and Applications - Volume 3: VISAPP, (VISIGRAPP 2015)

TI - Optimal Surface Normal from Affine Transformation

SN - 978-989-758-091-8

AU - Daniel B.

AU - Molnar J.

AU - Hajder L.

PY - 2015

SP - 305

EP - 316

DO - 10.5220/0005303703050316