GOGMA: Globally-Optimal Gaussian Mixture Alignment

Campbell, Dylan; Petersson, Lars

doi:10.1109/cvpr.2016.613

Cited by 98 publications

(86 citation statements)

References 56 publications

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“…Go-ICP [14] provides a globally optimal solution to ICP in 3D Euclidean registration, which combines ICP with a branch-and-bound (BnB) scheme. Similarly, GOGMA [26] combines Gaussian mixture model (GMM) with a BnB scheme. These global optimal methods are sensitive to scale problem.…”

Section: A Direct Methodsmentioning

confidence: 99%

A Systematic Approach for Cross-Source Point Cloud Registration by Preserving Macro and Micro Structures

Huang

Zhang

et al. 2017

IEEE Trans. on Image Process.

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Abstract-We propose a systematic approach for registering cross-source point clouds. The compelling need for cross-source point cloud registration is motivated by the rapid development of a variety of 3D sensing techniques, but many existing registration methods face critical challenges as a result of the large variations in cross-source point clouds. This paper therefore illustrates a novel registration method which successfully aligns two crosssource point clouds in the presence of significant missing data, large variations in point density, scale difference and so on. The robustness of the method is attributed to the extraction of macro and micro structures. Our work has three main contributions: (1) a systematic pipeline to deal with cross-source point cloud registration; (2) a graph construction method to maintain macro and micro structures; (3) a new graph matching method is proposed which considers the global geometric constraint to robustly register these variable graphs. Compared to most of the related methods, the experiments show that the proposed method successfully registers in cross-source datasets, while other methods have difficulty achieving satisfactory results. The proposed method also shows great ability in same-source datasets.

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Section: A Direct Methodsmentioning

confidence: 99%

A Systematic Approach for Cross-Source Point Cloud Registration by Preserving Macro and Micro Structures

Huang

Zhang

et al. 2017

IEEE Trans. on Image Process.

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“…The alignment of mixture distributions to estimate relative sensor pose is a well-studied problem in R 2 , R 3 [15,57,27,10], and the sphere S 2 [54]. For 2D-3D camera pose estimation, we require a 3D positional and a 2D directional mixture distribution to model the input data.…”

Section: Spherical Mixture Alignmentmentioning

confidence: 99%

“…We also developed a local optimization algorithm denoted as Spherical Mixture Alignment (SMA), which was integrated into GOSMA (line 9). We use the quasi-Newton L-BFGS algorithm [8] to minimize (10), with the gradient derived in the appendix. SMA is run whenever the BB algorithm finds a sub-cube C ij that has an upper bound less than the best-so-far function value d * (line 9), initialized with the center transformation of C ij .…”

Section: The Gosma Algorithmmentioning

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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“…In contrast to the locally convergent algorithms and heuristics above, optimal algorithms have been developed for point cloud registration (Breuel, 2001;Yang et al, 2016;Campbell and Petersson, 2016;Parra Bustos et al, 2016). Their common theme is to set up a clear-cut, transparent objective function and then apply a suitable exact optimization scheme -often branch-and-bound type methods -to find the solution that maximises the objective function 5 .…”

Section: Introductionmentioning

confidence: 99%

Practical optimal registration of terrestrial LiDAR scan pairs

Cai

Chin

Parra

et al. 2019

ISPRS Journal of Photogrammetry and Remote Sensing

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Point cloud registration is a fundamental problem in 3D scanning. In this paper, we address the frequent special case of registering terrestrial LiDAR scans (or, more generally, levelled point clouds). Many current solutions still rely on the Iterative Closest Point (ICP) method or other heuristic procedures, which require good initializations to succeed and/or provide no guarantees of success. On the other hand, exact or optimal registration algorithms can compute the best possible solution without requiring initializations; however, they are currently too slow to be practical in realistic applications.Existing optimal approaches ignore the fact that in routine use the relative rotations between scans are constrained to the azimuth, via the built-in level compensation in LiDAR scanners. We propose a novel, optimal and computationally efficient registration method for this 4DOF scenario. Our approach operates on candidate 3D keypoint correspondences, and contains two main steps: (1) a deterministic selection scheme that significantly reduces the candidate correspondence set in a way that is guaranteed to preserve the optimal solution; and (2) a fast branch-and-bound (BnB) algorithm with a novel polynomial-time subroutine for 1D rotation search, that quickly finds the optimal alignment for the reduced set. We demonstrate the practicality of our method on realistic point clouds from multiple LiDAR surveys.

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GOGMA: Globally-Optimal Gaussian Mixture Alignment

Cited by 98 publications

References 56 publications

A Systematic Approach for Cross-Source Point Cloud Registration by Preserving Macro and Micro Structures

A Systematic Approach for Cross-Source Point Cloud Registration by Preserving Macro and Micro Structures

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

Practical optimal registration of terrestrial LiDAR scan pairs

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