# Novel Ways to Estimate Homography from Local Affine Transformations

### Daniel Barath, Levente Hajder

#### Abstract

State-of-the-art 3D reconstruction methods usually apply point correspondences in order to compute the 3D geometry of objects represented by dense point clouds. However, objects with relatively large and flat surfaces can be most accurately reconstructed if the homographies between the corresponding patches are known. Here we show how the homography between patches on a stereo image pair can be estimated. We discuss that these proposed estimators are more accurate than the widely used point correspondence-based techniques because the latter ones only consider the last column (the translation) of the affine transformations, whereas the new algorithms use all the affine parameters. Moreover, we prove that affine-invariance is equivalent to perspective-invariance in the case of known epipolar geometry. Three homography estimators are proposed. The first one calculates the homography if at least two point correspondences and the related affine transformations are known. The second one computes the homography from only one point pair, if the epipolar geometry is estimated beforehand. These methods are solved by linearization of the original equations, and the refinements can be carried out by numerical optimization. Finally, a hybrid homography estimator is proposed that uses both point correspondences and photo-consistency between the patches. The presented methods have been quantitatively validated on synthesized tests. We also show that the proposed methods are applicable to real-world images as well, and they perform better than the state-of-the-art point correspondence-based techniques.

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#### Paper Citation

#### in Harvard Style

Barath D. and Hajder L. (2016). **Novel Ways to Estimate Homography from Local Affine Transformations** . In *Proceedings of the 11th Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 3: VISAPP, (VISIGRAPP 2016)* ISBN 978-989-758-175-5, pages 432-443. DOI: 10.5220/0005674904320443

#### in Bibtex Style

@conference{visapp16,

author={Daniel Barath and Levente Hajder},

title={Novel Ways to Estimate Homography from Local Affine Transformations},

booktitle={Proceedings of the 11th Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 3: VISAPP, (VISIGRAPP 2016)},

year={2016},

pages={432-443},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0005674904320443},

isbn={978-989-758-175-5},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 11th Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications - Volume 3: VISAPP, (VISIGRAPP 2016)

TI - Novel Ways to Estimate Homography from Local Affine Transformations

SN - 978-989-758-175-5

AU - Barath D.

AU - Hajder L.

PY - 2016

SP - 432

EP - 443

DO - 10.5220/0005674904320443