Optimal estimation of vanishing points in a Manhattan world

Mirzaei, Faraz M.; Roumeliotis, Stergios I.

doi:10.1109/iccv.2011.6126530

Cited by 87 publications

(66 citation statements)

References 19 publications

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“…This approach is used by Censi [13] for the global resolution of the 2D registration problem, reducing the problem to solving a 4-th order polynomial equation. However, this approach does not generalize well to the 3D case due to the higher complexity of the rotation space, which produces an explosion in the complexity of the resulting polynomial system [29,30].…”

Section: Global Optimizationmentioning

confidence: 99%

Convex Global 3D Registration with Lagrangian Duality

Briales

González-Jiménez

2017

2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)

138

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The registration of 3D models by a Euclidean transformation is a fundamental task at the core of many application in computer vision. This problem is non-convex due to the presence of rotational constraints, making traditional local optimization methods prone to getting stuck in local minima. This paper addresses finding the globally optimal transformation in various 3D registration problems by a unified formulation that integrates common geometric registration modalities (namely point-to-point, point-to-line and point-to-plane). This formulation renders the optimization problem independent of both the number and nature of the correspondences.The main novelty of our proposal is the introduction of a strengthened Lagrangian dual relaxation for this problem, which surpasses previous similar approaches [32] in effectiveness. In fact, even though with no theoretical guarantees, exhaustive empirical evaluation in both synthetic and real experiments always resulted on a tight relaxation that allowed to recover a guaranteed globally optimal solution by exploiting duality theory.Thus, our approach allows for effectively solving the 3D registration with global optimality guarantees while running at a fraction of the time for the state-of-the-art alternative [34], based on a more computationally intensive Branch and Bound method.

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Section: Global Optimizationmentioning

confidence: 99%

Convex Global 3D Registration with Lagrangian Duality

Briales

González-Jiménez

2017

2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)

138

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“…Column [9] should be omitted from fair comparison because the authors seem to apply the tolerance on individual angles (pitch, yaw, roll), not on the overall angular difference, which is the case of other works (and our evaluation). Column [15] should also be treated lightly because the authors feed the detector only with edges user-annotated as belonging to one of the vanishing points (no outliers), while other works are working with all the edges in the image, including clutter. evaluation was done on the complete set in order to be comparable with previous works.…”

Section: Vanishing Point Detection Accuracymentioning

confidence: 99%

“…evaluation was done on the complete set in order to be comparable with previous works. We used two means of evaluation popular in the literature: detection rate with 10 • angular error tolerance [9,10,15,16,17,18], Table 1, and cumulative histogram of the count of correctly recognized vanishing points based on the angular error tolerance [2,13,14], Figure 7.…”

Section: Vanishing Point Detection Accuracymentioning

confidence: 99%

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Real Projective Plane Mapping for Detection of Orthogonal Vanishing Points

Dubská

Herout

2013

Procedings of the British Machine Vision Conference 2013

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This paper deals with the detection of orthogonal vanishing points. The aim is to efficiently cope with the clutter edges in real-life images and to determine the camera orientation in the Manhattan world reliably. We are using a modified scheme of the Cascaded Hough Transform where only one Hough space is accumulated -the space of the vanishing points. The parameterization of the vanishing points -the "diamond space" -is based on the PClines line parameterization and it is defined as a mapping of the whole real projective plane to a finite space.Our algorithm for detection of vanishing points operates directly on edgelets detected by an edge detector, skipping the common step of grouping edges into straight lines or line segments. This decreases the number of configuration parameters and reduces the complexity of the algorithm. Evaluated on the York Urban DB, our algorithm yields 98.04 % success rate at 10 • angular error tolerance, which outperforms comparable existing solutions.Our parameterization of vanishing points is in all aspects linear; it involves no goniometric or other non-linear operations and thus it is suitable for implementation in embedded chips and circuitry. The iterative search scheme allows for finding orthogonal triplets of vanishing points with high accuracy and low computational costs. At the same time, our approach can be used without the orthogonality constraint.

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“…Firstly, we employ a RANSAC-based vanishing point estimator that uses triplets of lines for generating hypotheses of all three orthogonal vanishing points at once [13]. We prune these hypotheses, by keeping the one that corresponds to a rotational matrix with roll and pitch angles closest to those estimated by the filter.…”

Section: A Yaw Initializationmentioning

confidence: 99%

Exploiting Urban Scenes for Vision-aided Inertial Navigation

Kottas

Roumeliotis

2013

Robotics: Science and Systems IX

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Abstract-This paper addresses the problem of visual-inertial navigation when processing camera observations of both point and line features detected within a Manhattan world. First, we prove that the observations of: (i) a single point, and (ii) a single line of known direction perpendicular to gravity (e.g., a non-vertical structural line of a building), provide sufficient information for rendering all degrees of freedom of a visionaided inertial navigation system (VINS) observable, up to global translations. Next, we examine the observability properties of the linearized system employed by an extended Kalman filter (EKF) for processing line observations of known direction, and show that the rank of the corresponding observability matrix erroneously increases. To address this problem, we introduce an elegant modification which enforces that the linearized EKF system has the correct number of unobservable directions, thus improving its consistency. Finally, we validate our findings experimentally in urban scenes and demonstrate the superior performance of the proposed VINS over alternative approaches.

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Optimal estimation of vanishing points in a Manhattan world

Cited by 87 publications

References 19 publications

Convex Global 3D Registration with Lagrangian Duality

Convex Global 3D Registration with Lagrangian Duality

Real Projective Plane Mapping for Detection of Orthogonal Vanishing Points

Exploiting Urban Scenes for Vision-aided Inertial Navigation

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