# Affine Transformation from Fundamental Matrix and Two Directions

### Nghia Le Minh, Levente Hajder

#### 2020

#### Abstract

Researchers have recently shown that affine transformations between corresponding patches of two images can be applied for 3D reconstruction, including the reconstruction of surface normals. However, the accurate estimation of affine transformations between image patches is very challenging. This paper mainly proposes a novel method to estimate affine transformations from two directions if epipolar geometry of the image pair is known. A reconstruction pipeline is also proposed here in short. As side effects, two proofs are also given. The first one is to determine the relationship between affine transformations and the fundamental matrix, the second one shows how optimal surface normal estimation can be obtained via the roots of a cubic polynomial. A visual debugger is also proposed to validate the estimated surface normals in real images.

Download#### Paper Citation

#### in Harvard Style

Minh N. and Hajder L. (2020). **Affine Transformation from Fundamental Matrix and Two Directions**. In *Proceedings of the 15th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2020) - Volume 4: VISAPP*; ISBN 978-989-758-402-2, SciTePress, pages 819-826. DOI: 10.5220/0009154408190826

#### in Bibtex Style

@conference{visapp20,

author={Nghia Le Minh and Levente Hajder},

title={Affine Transformation from Fundamental Matrix and Two Directions},

booktitle={Proceedings of the 15th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2020) - Volume 4: VISAPP},

year={2020},

pages={819-826},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0009154408190826},

isbn={978-989-758-402-2},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 15th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2020) - Volume 4: VISAPP

TI - Affine Transformation from Fundamental Matrix and Two Directions

SN - 978-989-758-402-2

AU - Minh N.

AU - Hajder L.

PY - 2020

SP - 819

EP - 826

DO - 10.5220/0009154408190826

PB - SciTePress