Radially-Distorted Conjugate Translations

This paper introduces the first minimal solvers that jointly solve for affine-rectification and radial lens distortion from coplanar repeated patterns. Even with imagery from moderately distorted lenses, plane rectification using the pinhole camera model is inaccurate or invalid. The proposed solvers incorporate lens distortion into the camera model and extend accurate rectification to wide-angle imagery, which is now common from consumer cameras. The solvers are derived from constraints induced by the conjugate translations of an imaged scene plane, which are integrated with the division model for radial lens distortion. The hidden-variable trick with ideal saturation is used to reformulate the constraints so that the solvers generated by the Grobner-basis method are stable, small and fast. Rectification and lens distortion are recovered from either one conjugately translated affine-covariant feature or two independently translated similarity-covariant features. The proposed solvers are used in a \RANSAC-based estimator, which gives accurate rectifications after few iterations. The proposed solvers are evaluated against the state-of-the-art and demonstrate significantly better rectifications on noisy measurements. Qualitative results on diverse imagery demonstrate high-accuracy undistortions and rectifications. The source code is publicly available at https://github.com/prittjam/repeats

A Novel Method for the Absolute Pose Problem with Pairwise Constraints

Absolute pose estimation is a fundamental problem in computer vision, and it is a typical parameter estimation problem, meaning that efforts to solve it will always suffer from outlier-contaminated data. Conventionally, for a fixed dimensionality d and the number of measurements N, a robust estimation problem cannot be solved faster than O(N^d). Furthermore, it is almost impossible to remove d from the exponent of the runtime of a globally optimal algorithm. However, absolute pose estimation is a geometric parameter estimation problem, and thus has special constraints. In this paper, we consider pairwise constraints and propose a globally optimal algorithm for solving the absolute pose estimation problem. The proposed algorithm has a linear complexity in the number of correspondences at a given outlier ratio. Concretely, we first decouple the rotation and the translation subproblems by utilizing the pairwise constraints, and then we solve the rotation subproblem using the branch-and-bound algorithm. Lastly, we estimate the translation based on the known rotation by using another branch-and-bound algorithm. The advantages of our method are demonstrated via thorough testing on both synthetic and real-world dataComment: 10 pages, 7figure

Efficient Many-to-Many RANSAC

V této bakalářské práci se věnujeme problému robustního odhadu dvoupohledové geometrie z mnohonásobných korespondencí. Způsoby, kterými se standardně získávají tentativní korespondence, zajištují, že se každý zájmový bod uplatní pouze v jediné potenciální korespondenci. Tyto konstrukce množiny potenciálních korespondencí, obvykle založené na testu poměru vzdáleností~\cite{Lowe2004}, nebo na vzájemné blízkosti~\cite{Matas2002} příznaků, přirozeně vyřazují potenciálně víceznačné korespondence. Ukazujeme, že v některých typech scén, například ve scénách obsahujících opakované struktury, nesou mnohonásobné korespondence cenné informace, které mohou být využity pro vylepšení odhadu geometrie. Navrhujeme čtyři nové varianty algoritmu \loransac, z nichž všechny využívají mnohonásobných korespondencí k tomu, aby v určitých situacích poskytly lepší výsledky než standardní \loransac. Shromáždili jsme přes 50 dvojic fotografií ze standardních testovacích datových sad obohacených o naše vlastní snímky a využili je k otestování navrhovaných algoritmů a jejich porovnání se standardním algoritmem \loransac. Na základě výsledků těchto testů jsme potvrdili, že jeden z námi navrhovaných algoritmů překonává standardní \loransac a přitom v případech, které zvládá původní algoritmus řešit dobře, není výpočetně náročnější.In this bachelor thesis, we investigate the problem of robust two-view geometry estimation from many-to-many correspondences. In standard approaches, the construction of tentative correspondences ensures that each feature point participates in at most one potential correspondence. Such constructions, typically based on a distance ratio~\cite{Lowe2004} test or mutually nearest property~\cite{Matas2002}, naturally drops potentially ambiguous correspondences. We show, that for certain types of scenes, such as those containing repeated structures, many-to-many correspondences contain valuable information that can be utilized in order to improve the geometry estimation. Four new variants of the \loransac algorithm are proposed, each of them using the additional many-to-many correspondences in order to get better results than the standard algorithm in some scenarios. We have collected more than 50 image pairs from standard benchmark datasets and our own photos and used them to test all of our proposed algorithms against the state-of-the-art \loransac. Based on the experimental results, we have concluded, that one of our proposed algorithms outperforms the standard \loransac, while not introducing any additional computational cost in the cases, when the original algorithm works well

Model-free Consensus Maximization for Non-Rigid Shapes

Many computer vision methods use consensus maximization to relate measurements containing outliers with the correct transformation model. In the context of rigid shapes, this is typically done using Random Sampling and Consensus (RANSAC) by estimating an analytical model that agrees with the largest number of measurements (inliers). However, small parameter models may not be always available. In this paper, we formulate the model-free consensus maximization as an Integer Program in a graph using `rules' on measurements. We then provide a method to solve it optimally using the Branch and Bound (BnB) paradigm. We focus its application on non-rigid shapes, where we apply the method to remove outlier 3D correspondences and achieve performance superior to the state of the art. Our method works with outlier ratio as high as 80\%. We further derive a similar formulation for 3D template to image matching, achieving similar or better performance compared to the state of the art.Comment: ECCV1