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Novel Ways to Estimate Homography from Local Affine TransformationsTopics: Image-Based Modeling and 3D Reconstruction; Stereo Vision and Structure from Motion

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Subjects/Areas/Topics:Applications
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Computer Vision, Visualization and Computer Graphics
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Geometry and Modeling
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Image-Based Modeling
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Motion, Tracking and Stereo Vision
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Pattern Recognition
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Software Engineering
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Stereo Vision and Structure from Motion

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.(More)

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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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: VISAPP, (VISIGRAPP 2016) ISBN 978-989-758-175-5, ISSN 2184-4321, pages 432-443. DOI: 10.5220/0005674904320443

@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: VISAPP, (VISIGRAPP 2016)}, year={2016}, pages={432-443}, publisher={SciTePress}, organization={INSTICC}, doi={10.5220/0005674904320443}, isbn={978-989-758-175-5}, }

TY - CONF

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