This paper presents a framework for N -view triangulation of scene points, which improves processing time and final reprojection error with respect to standard methods, such as linear triangulation. The framework introduces an angular error-based cost function, which is robust to outliers and inexpensive to compute, and designed such that simple adaptive gradient descent can be applied for convergence. Our method also presents a statistical sampling component based on confidence levels, that reduces the number of rays to be used for triangulation of a given feature track. It is shown how the statistical component yields a meaningful yet much reduced set of representative rays for triangulation, and how the application of the cost function on the reduced sample can efficiently yield faster and more accurate solutions. Results are demonstrated on real and synthetic data, where it is proven to significantly increase the speed of triangulation and optimize reprojection error in most cases. This makes it especially attractive for efficient triangulation of large scenes given the speed and low memory requirements.

This paper presents a novel framework for practical and accurate N -view triangulation of scene points. The algorithm is based on applying swarm optimization inside a robustly-computed bounding box, using an angular errorbased L 1 cost function which is more robust to outliers and less susceptible to local minima than cost functions such as L 2 on reprojection error. Extensive testing on synthetic data with ground-truth has determined an accurate position over 99.9% of the time, on thousands of camera configurations with varying degrees of feature tracking errors. Opposed to existing polynomial methods developed for a small number of cameras, the proposed algorithm is at best linear in the number of cameras and does not suffer from inaccuracies inherent in solving high-order polynomials or Gröbner bases. In the specific case of three views, there is a two to three order of magnitude performance increase with respect to such methods. Results are provided to highlight performance for arbitrary camera configurations, numbers of cameras and under noise, which has not been previously achieved in the triangulation literature. Results on real data also prove that reprojection error is improved with respect to other methods.

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This paper presents a framework for GPU-accelerated N -view triangulation in multi-view reconstruction that improves processing time and final reprojection error with respect to methods in the literature. The framework uses an algorithm based on optimizing an angular error-based L 1 cost function and it is shown how adaptive gradient descent can be applied for convergence. The triangulation algorithm is mapped onto the GPU and two approaches for parallelization are compared: one thread per track and one thread block per track. The better performing approach depends on the number of tracks and the lengths of the tracks in the dataset. Furthermore, the algorithm uses statistical sampling based on confidence levels to successfully reduce the quantity of feature track positions needed to triangulate an entire track. Sampling aids in load balancing for the GPU's SIMD architecture and for exploiting the GPU's memory hierarchy. When compared to a serial implementation, a typical performance increase of 3-4x can be achieved on a 4-core CPU. On a GPU, large track numbers are favorable and an increase of up to 40x can be achieved. Results on real and synthetic data prove that reprojection errors are similar to the best performing current triangulation methods but costing only a fraction of the computation time, allowing for efficient and accurate triangulation of large scenes.

A comprehensive uncertainty, baseline, and noise analysis in computing 3D points using a recent L1-based triangulation algorithm is presented. This method is shown to be not only faster and more accurate than its main competitor, linear triangulation, but also more stable under noise and baseline changes. A Monte Carlo analysis of covariance and a confidence ellipsoid analysis were performed over a large range of baselines and noise levels for different camera configurations, to compare performance between angular error-based and linear triangulation. Furthermore, the effect of baseline and noise was analyzed for true multi-view triangulation versus pairwise stereo fusion. Results on real and synthetic data show that L1 angular error-based triangulation has a positive effect on confidence ellipsoids, lowers covariance values and results in more-accurate pairwise and multi-view triangulation, for varying numbers of cameras and configurations.