Affine Transformation from Fundamental Matrix and Two Directions

Nghia Le Minh; Levente Hajder

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Paper

Affine Transformation from Fundamental Matrix and Two Directions

Topics: Features Extraction; Image-Based Modeling and 3D Reconstruction; Stereo Vision and Structure from Motion

In Proceedings of the 15th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 4: VISAPP, 819-826, 2020 , Valletta, Malta

Authors: Nghia Le Minh and Levente Hajder

Affiliation: Department of Algorithms and Their Applications, Eötvös Loránd University, Pázmány Péter stny. 1/C, H-1117, Budapest, Hungary

Keyword(s): Affine Transformation, Epipolar Geometry, Surface Normal Reconstruction, 3D Reconstruction.

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.

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Paper citation in several formats:

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; ISSN 2184-4321, SciTePress, pages 819-826. DOI: 10.5220/0009154408190826

@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},
issn={2184-4321},
}

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
IS - 2184-4321
AU - Minh, N.
AU - Hajder, L.
PY - 2020
SP - 819
EP - 826
DO - 10.5220/0009154408190826
PB - SciTePress