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The angular error-based triangulation method and the parallax path method are both high-performance methods for large-scale multi-view sequential reconstruction that can be parallelized on the GPU. We map parallax paths to the GPU and test its performance and accuracy as a triangulation method for the first time. To this end, we compare it with the angular method on the GPU for both performance and accuracy. Furthermore, we improve the recovery of path scales and perform more extensive analysis and testing compared with the original parallax paths method. Although parallax paths requires sequential and piecewise-planar camera positions, in such scenarios, we can achieve a speedup of up to 14x over angular triangulation, while maintaining comparable accuracy.

Structure-from-Motion (SfM) applications attempt to reconstruct the three-dimensional (3D) geometry of an underlying scene from a collection of images, taken from various camera viewpoints. Traditional optimization techniques in SfM, which compute and refine camera poses and 3D structure, rely only on feature tracks, or sets of corresponding pixels, generated from color (RGB) images. With the abundance of reliable depth sensor information, these optimization procedures can be augmented to increase the accuracy of reconstruction. This paper presents a general cost function, which evaluates the quality of a reconstruction based upon a previously established angular cost function and depth data estimates. The cost function takes into account two error measures: first, the angular error between each computed 3D scene point and its corresponding feature track location, and second, the difference between the sensor depth value and its computed estimate. A bundle adjustment parameter optimization is implemented using the proposed cost function and evaluated for accuracy and performance. As opposed to traditional bundle adjustment, in the event of feature tracking errors, a corrective routine is also present to detect and correct inaccurate feature tracks. The filtering algorithm involves clustering depth estimates of the same scene point and observing the difference between the depth point estimates and the triangulated 3D point. Results on both real and synthetic data are presented and show that reconstruction accuracy is improved.

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 pair wise 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 pair wise and multi-view triangulation, for varying numbers of cameras and configurations.

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 3–4× can be achieved on a 4-core CPU. On a GPU, large track numbers are favorable and an increase of up to 40× 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.

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 error-based L1 cost function which is more robust to outliers and less susceptible to local minima than cost functions such as L2 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 Grobner 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.

Analyzing sources and causes of error in multi-view scene reconstruction is difficult. In the absence of any ground-truth information, reprojection error is the only valid metric to assess error. Unfortunately, inspecting reprojection error values does not allow computer vision researchers to attribute a cause to the error. A visualization technique to analyze errors in sequential multi-view reconstruction is presented. By computing feature track summaries, researchers can easily observe the progression of feature tracks through a set of frames over time. These summaries easily isolate poor feature tracks and allow the observer to infer the cause of a delinquent track. This visualization technique allows computer vision researchers to analyze errors in ways previously unachieved. It allows for a visual performance analysis and comparison between feature trackers, a previously unachieved result in the computer vision literature. This framework also provides the foundation to a number of novel error detection and correction algorithms.

This paper presents a novel method for multi-view sequential scene reconstruction scenarios such as in aerial video, that exploits the constraints imposed by the path of a moving camera to allow for a new way of detecting and correcting inaccuracies in the feature tracking and structure computation processes. The main contribution of this paper is to show that for short, planar segments of a continuous camera trajectory, parallax movement corresponding to a viewed scene point should ideally form a scaled and translated version of this trajectory when projected onto a parallel plane. This creates two constraints, which differ from those of standard factorization, that allow for the detection and correction of inaccurate feature tracks and to improve scene structure. Results are shown for real and synthetic aerial video and turntable sequences, where the proposed method was shown to correct outlier tracks, detect and correct tracking drift, and allow for a novel improvement of scene structure, additionally resulting in an improved convergence for bundle adjustment optimization.

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 an interactive visualization system, based upon previous work, that allows for the analysis of scene structure uncertainty and its sensitivity to parameters in different multi-view scene reconstruction stages. Given a set of input cameras and feature tracks, the volume rendering-based approach creates a scalar field from reprojection error measurements. The obtained statistical, visual, and isosurface information provides insight into the sensitivity of scene structure at the stages leading up to structure computation, such as frame decimation, feature tracking, and self-calibration. Furthermore, user interaction allows for such an analysis in ways that have traditionally been achieved mathematically, without any visual aid. Results are shown for different types of camera configurations for real and synthetic data as well as compared to prior work.

This paper discusses the constraints imposed by the path of a moving camera in multi-view sequential scene reconstruction scenarios such as in aerial video, which allow for an efficient detection and correction of inaccuracies in the feature tracking and structure computation processes. The main insight is that for short, planar segments of a continuous camera trajectory, parallax movement corresponding to a viewed scene point should ideally form a scaled and translated version of this trajectory when projected onto a parallel plane. Two inter-camera and intra-camera constraints arise, which create a prediction of where all feature tracks should be located given the consensus information of all accurate tracks and cameras, which allows for the detection and correction of inaccurate feature tracks, as well as a very simple update of scene structure. This procedure differs from classical approaches such as factorization and RANSAC. In both aerial video and turntable sequences, the use of such constraints was proven to correct outlier tracks, detect and correct tracking drift, allow for a simple updating of scene structure, and improve bundle adjustment convergence.

Scene reconstruction from video sequences has become a prominent computer vision research area in recent years, due to its large number of applications in fields such as security, robotics and virtual reality. Despite recent progress in this field, there are still a number of issues that manifest as incomplete, incorrect or computationally-expensive reconstructions. The engine behind achieving reconstruction is the matching of features between images, where common conditions such as occlusions, lighting changes and texture-less regions can all affect matching accuracy. Subsequent processes that rely on matching accuracy, such as camera parameter estimation, structure computation and non-linear parameter optimization, are also vulnerable to additional sources of error, such as degeneracies and mathematical instability. Detection and correction of errors, along with robustness in parameter solvers, are a must in order to achieve a very accurate final scene reconstruction. However, error detection is in general difficult due to the lack of ground-truth information about the given scene, such as the absolute position of scene points or GPS/IMU coordinates for the camera(s) viewing the scene. In this dissertation, methods are presented for the detection, factorization and correction of error sources present in all stages of a scene reconstruction pipeline from video, in the absence of ground-truth knowledge. Two main applications are discussed. The first set of algorithms derive total structural error measurements after an initial scene structure computation and factorize errors into those related to the underlying feature matching process and those related to camera parameter estimation. A brute-force local correction of inaccurate feature matches is presented, as well as an improved conditioning scheme for non-linear parameter optimization which applies weights on input parameters in proportion to estimated camera parameter errors. Another application is in reconstruction pre-processing, where an algorithm detects and discards frames that would lead to inaccurate feature matching, camera pose estimation degeneracies or mathematical instability in structure computation based on a residual error comparison between two different match motion models. The presented algorithms were designed for aerial video but have been proven to work across different scene types and camera motions, and for both real and synthetic scenes.

An algorithm that shows how ray divergence in multi-view stereo scene reconstruction can be used towards improving bundle adjustment weighting and conditioning is presented. Starting with a set of feature tracks, ray divergence when attempting to compute scene structure for each track is first obtained. Assuming accurate feature matching, ray divergence reveals mainly camera parameter estimation inaccuracies. Due to its smooth variation across neighboring feature tracks, from its histogram a set of weights can be computed that can be used in bundle adjustment to improve its convergence properties. It is proven that this novel weighting scheme results in lower reprojection errors and faster processing times than others such as image feature covariances, making it very suitable in general for applications involving multi-view pose and structure estimation.

This paper introduces a non-parametric sequential frame decimation algorithm for image sequences in low-memory streaming environments. Frame decimation reduces the number of input frames to increase pose and structure robustness in Structure and Motion (SaM) applications. The main contribution of this paper is the introduction of a sequential low-memory work-flow for frame decimation in embedded systems where memory and memory traffic come at a premium. This approach acts as an online preprocessing filter by removing frames that are ill-posed for reconstruction before streaming. The introduced sequential approach reduces the number of needed frames in memory to three in contrast to global frame decimation approaches that use at least ten frames in memory and is therefore suitable for low-memory streaming environments. This is moreover important in emerging systems with large format cameras which acquire data over several hours and therefore render global approaches impossible. In this paper a new decimation metric is designed which facilitates sequential keyframe extraction fit for reconstruction purposes, based on factors such as a correspondence-to-feature ratio and residual error relationships between epipolar geometry and homography estimation. The specific design of the error metric allows a local sequential decimation metric evaluation and can therefore be used on the fly. The approach has been tested with various types of input sequences and results in reliable low-memory frame decimation robust to different frame sampling frequencies and independent of any thresholds, scene assumptions or global frame analysis.

A correspondence and camera error analysis for dense correspondence applications such as structure from motion is introduced. This provides error introspection, opening up the possibility of adaptively and progressively applying more expensive correspondence and camera parameter estimation methods to reduce these errors. The presented algorithm evaluates the given correspondences and camera parameters based on an error generated through simple triangulation. This triangulation is based on the given dense, non-epipolar constraint, correspondences and estimated camera parameters. This provides an error map without requiring any information about the perfect solution or making assumptions about the scene. The resulting error is a combination of correspondence and camera parameter errors. An simple, fast low/high pass filter error factorization is introduced, allowing for the separation of correspondence error and camera error. Further analysis of the resulting error maps is applied to allow efficient iterative improvement of correspondences and cameras.