Tractable Algorithms for Robust Model Estimation

Enqvist, Olof; Ask, Erik; Kahl, Fredrik; Åström, Kalle

doi:10.1007/s11263-014-0760-2

Cited by 30 publications

(27 citation statements)

References 14 publications

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“…However, most of these deterministic fitting methods assume that there only exists a single structure in data, and they cannot provide solutions for multiplestructure data within a reasonable time (most of them does not be applied sequentially for multiple-structure data since they cannot handle high outlier percentages). Note that IMaxFS-ISE [16] and MS [7] can work for multiple-structure data, but they require to generate a number of model hypotheses repeatedly, which is computationally expensive. Compared to these deterministic sampling based fitting methods, the proposed SDF fitting method not only reserves the deterministic nature but also efficiently provides good solutions for fitting both single-structure and multiple-structure data.…”

Section: Deterministic Sampling Based Fitting Methodsmentioning

confidence: 99%

Superpixel-Guided Two-View Deterministic Geometric Model Fitting

et al. 2018

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Geometric model fitting is a fundamental research topic in computer vision and it aims to fit and segment multiple-structure data. In this paper, we propose a novel superpixel-guided two-view geometric model fitting method (called SDF), which can obtain reliable and consistent results for real images. Specifically, SDF includes three main parts: a deterministic sampling algorithm, a model hypothesis updating strategy and a novel model selection algorithm. The proposed deterministic sampling algorithm generates a set of initial model hypotheses according to the prior information of superpixels. Then the proposed updating strategy further improves the quality of model hypotheses. After that, by analyzing the properties of the updated model hypotheses, the proposed model selection algorithm extends the conventional "fit-and-remove" framework to estimate model instances in multiple-structure data. The three parts are tightly coupled to boost the performance of SDF in both speed and accuracy, and SDF has the deterministic nature. Experimental results show that the proposed SDF has significant advantages over several state-of-the-art fitting methods when it is applied to real images with single-structure and multiple-structure data.

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Section: Deterministic Sampling Based Fitting Methodsmentioning

confidence: 99%

Superpixel-Guided Two-View Deterministic Geometric Model Fitting

et al. 2018

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“…However, outliers are almost always present in the correspondence set. When this is the case, the inlier set can be retrieved using RANSAC [20] or robust global optimization [19,2,18,55]. Some of these approaches [20,19] can be applied when correspondences are not available by providing all possible permutations of the correspondence set.…”

Section: Related Workmentioning

confidence: 99%

The Alignment of the Spheres: Globally-Optimal Spherical Mixture Alignment for Camera Pose Estimation

Campbell

Kneip

et al. 2019

2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)

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Determining the position and orientation of a calibrated camera from a single image with respect to a 3D model is an essential task for many applications. When 2D-3D correspondences can be obtained reliably, perspective-n-point solvers can be used to recover the camera pose. However, without the pose it is non-trivial to find cross-modality correspondences between 2D images and 3D models, particularly when the latter only contains geometric information. Consequently, the problem becomes one of estimating pose and correspondences jointly. Since outliers and local optima are so prevalent, robust objective functions and global search strategies are desirable. Hence, we cast the problem as a 2D-3D mixture model alignment task and propose the first globally-optimal solution to this formulation under the robust L 2 distance between mixture distributions. We search the 6D camera pose space using branch-andbound, which requires novel bounds, to obviate the need for a pose estimate and guarantee global optimality. To accelerate convergence, we integrate local optimization, implement GPU bound computations, and provide an intuitive way to incorporate side information such as semantic labels. The algorithm is evaluated on challenging synthetic and real datasets, outperforming existing approaches and reliably converging to the global optimum.

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“…Although such formulations lead to challenging optimization problems, using recent advances in robust estimation it is sometimes possible to develop tractable methods. In [5], it was shown how the number of inliers can be maximized in polynomial time, for a fixed-dimensional model, where the computational complexity follows directly as a consequence of the theory of optimization. One requirement is that the parameter space is a differentiable manifold embedded in R m with a set of equality constraints.…”

Section: Maximizing the Number Of Inliersmentioning

confidence: 99%

“…We will here describe how these ideas can be applied to orthographic essential matrix estimation, resulting in an optimal method. The main theorem from [5] shows that one can find the optimal solution with respect to the number of inliers by enumerating a finite set of so called critical points, essentially being the Karush-Kuhn-Tucker (KKT) points. These critical points divide the solution space into regions that contain different combinations of inliers and outliers, and the optimal solution with respect to the number of inliers will be found in one of the critical points.…”

Section: Maximizing the Number Of Inliersmentioning

confidence: 99%

“…Using two matching MSER feature points, an approximate fundamental matrix could be estimated. Lately, methods that optimally find models that maximize the number of inliers, in polynomial time, have been developed, [5,25]. We will in this paper investigate a number of specific geometric problems that have received little or no attention earlier, related to orthographic projections of rigid scenes in two views.…”

Section: Introductionmentioning

confidence: 99%

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Two-View Orthographic Epipolar Geometry: Minimal and Optimal Solvers

Oskarsson

2017

J Math Imaging Vis

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We will in this paper present methods and algorithms for estimating two-view geometry based on an orthographic camera model. We use a previously neglected nonlinear criterion on rigidity to estimate the calibrated essential matrix. We give efficient algorithms for estimating it minimally (using only three point correspondences), in a least squares sense (using four or more point correspondences), and optimally with respect to the number of inliers. The inlier-optimal algorithm is based on a three-point solver and gives a fourth-order polynomial time algorithm. These methods can be used as building blocks to robustly find inlier correspondences in the presence of high degrees of outliers. We show experimentally that our methods can be used in many instances, where the orthographic camera model isn't generally used. A case of special interest is situations with repetitive structures, which give high amounts of outliers in the initial feature point matching.

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Tractable Algorithms for Robust Model Estimation

Cited by 30 publications

References 14 publications

Superpixel-Guided Two-View Deterministic Geometric Model Fitting

Superpixel-Guided Two-View Deterministic Geometric Model Fitting

The Alignment of the Spheres: Globally-Optimal Spherical Mixture Alignment for Camera Pose Estimation

Two-View Orthographic Epipolar Geometry: Minimal and Optimal Solvers

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