Homographies, Affine Transformations

Multi-H: Efficient Recovery of Tangent Planes in Stereo Images

Overview: Multi-H - an efficient method for the recovery of the tangent planes of a set of point correspondences satisfying the epipolar constraint is proposed. The problem is formulated as a search for a labeling minimizing an energy that includes a data and spatial regularization terms. The number of planes is controlled by a combination of Mean-Shift and Alpha-expansion.

Since the widely-used AdelaideRMF dataset seems to be easy, we propose a more challenging dataset for multi-homography estimation.

Code: C++ code (Not available yet.)
Dataset: Annotated dataset

One-page abstract: PDF

Reference paper: Barath, D. and Matas, J. and Hajder, L., Multi-H: Efficient Recovery of Tangent Planes in Stereo Images. 27th British Machine Vision Conference, 2016. PDF


Accurate Closed-form Estimation of Local Affine Transformations Consistent with the Epipolar Geometry

Overview: For a pair of images satisfying the epipolar constraint, a method for accurate estimation of local affine transformations is proposed. The method returns the local affine transformation consistent with the epipolar geometry that is closest in the least squares sense to the initial estimate provided by an affine-covariant detector. The minimized L2 norm of the affine matrix elements is found in closed-form. We show that the used norm has an intuitive geometric interpretation.

The method, with negligible computational requirements, is validated on publicly available benchmarking datasets and on synthetic data. The accuracy of the local affine transformations is improved for all detectors and all image pairs. Implicitly, precision of the tested feature detectors was compared. The Hessian-Affine detector combined with ASIFT view synthesis was the most accurate.

Code: C++ code, Matlab code

One-page abstract: PDF

Reference paper: Barath, D. and Matas, J. and Hajder, L., Accurate Closed-form Estimation of Local Affine Transformations Consistent with the Epipolar Geometry. 27th British Machine Vision Conference, 2016. PDF


Novel Ways to Estimate Homography from Local Affine Transformations

Overview: In this paper, three novel methods for the estimation of homographies exploiting local affine transformations are proposed. The method called Homography from Affine transformation and Fundamental matrix (HAF) shows that there is a one-to-one relationship between homography and local affinity for known epipolar geometry.

Code: Matlab code

Reference paper: Barath, D. and Hajder, L., Novel Ways to Estimate Homography from Local Affine Transformations. 11th International Conference on Computer Vision Theory and Applications, 2016. PDF


Contact: Dániel Baráth.