This article presents for the first time a global method for registering 3D curves with 3D surfaces without requiring an initialization. The algorithm works with 2-tuples point+vector that consist in pairs of points augmented with the information of their tangents or normals. A closed-form solution for determining the alignment transformation from a pair of matching 2-tuples is proposed. In addition, the set of necessary conditions for two 2-tuples to match is derived. This allows fast search of correspondences that are used in an hypothesise-and-test framework for accomplishing global registration. Comparative experiments demonstrate that the proposed algorithm is the first effective solution for curve vs surface registration, with the method achieving accurate alignment in situations of small overlap and large percentage of outliers in a fraction of a second. The proposed framework is extended to the cases of curve vs curve and surface vs surface registration, with the former being particularly relevant since it is also a largely unsolved problem.

The article describes a pipeline that receives as input a sequence of stereo images, and outputs the camera motion and a Piecewise-Planar Reconstruction (PPR) of the scene. The pipeline, named Piecewise-Planar StereoScan (PPSS), works as follows: the planes in the scene are detected for each stereo view using semi-dense depth estimation; the relative pose is computed by a new closed-form minimal algorithm that only uses point correspondences whenever plane detections do not fully constrain the motion; the camera motion and the PPR are jointly refined by alternating between discrete optimization and continuous bundle adjustment; and, finally, the detected 3D planes are segmented in images using a new framework that handles low texture and visibility issues. PPSS is extensively validated in indoor and outdoor datasets, and benchmarked against two popular point-based SfM pipelines. The experiments confirm that plane-based visual odometry is resilient to situations of small image overlap, poor texture, specularity, and perceptual aliasing where the fast LIBVISO2 [1] pipeline fails. The comparison against VisualSfM+CMVS/PMVS [2] , [3] shows that, for a similar computational complexity, PPSS is more accurate and provides much more compelling and visually pleasant 3D models. These results strongly suggest that plane primitives are an advantageous alternative to point correspondences for applications of SfM and 3D reconstruction in man-made environments.

Global 3D point cloud registration has been solved by finding putative matches between the point clouds for establishing alignment hypotheses. A naive approach would try to perform exhaustive search of triplets with a cubic runtime complexity in the number of data points. Super4PCS reduces this complexity to linear by making use of sets of 4 coplanar points. This paper proposes 2-Point-Normal Sets (2PNS), a new global 3D registration approach that advances Super4PCS by using 2 points and their normals for generating alignment hypotheses. The dramatic improvement in the complexity of 2PNS when compared to Super4PCS is demonstrated by the experiments that show speed-ups of two orders of magnitude in noise-free datasets and up to 5.2× in Kinect scans, while improving robustness and alignment accuracy, even in datasets with overlaps as low as 5%.

Affine Correspondences (ACs) are more informative than Point Correspondences (PCs) that are used as input in mainstream algorithms for Structure-from-Motion (SfM). Since ACs enable to estimate models from fewer correspondences, its use can dramatically reduce the number of combinations during the iterative step of sample-and-test that exists in most SfM pipelines. However, using ACs instead of PCs as input for SfM passes by fully understanding the relations between ACs and multi-view geometry, as well as by establishing practical, effective AC-based algorithms. This article is a step forward into this direction, by providing a clear account about how ACs constrain the two-view geometry, and by proposing new algorithms for plane segmentation and visual odometry that compare favourably with respect to methods relying in PCs.

The article describes a new algorithm for calibrating a Kinect sensor that achieves high accuracy using only 6 to 10 image-disparity pairs of a planar checkerboard pattern. The method estimates the projection parameters for both color and depth cameras, the relative pose between them, and the function that converts kinect disparity units (kdu) into metric depth. We build on the recent work of Herrera et. al [8] that uses a large number of input frames and multiple iterative minimization steps for obtaining very accurate calibration results. We propose several modifications to this estimation pipeline that dramatically improve stability, usability, and runtime. The modifications consist in: (i) initializing the relative pose using a new minimal, optimal solution for registering 3D planes across different reference frames, (ii) including a metric constraint during the iterative refinement to avoid a drift in the disparity to depth conversion, and (iii) estimating the parameters of the depth distortion model in an open-loop post-processing step. Comparative experiments show that our pipeline can achieve a calibration accuracy similar to [8] while using less than 1/6 of the input frames and running in 1/30 of the time.

Odometry consists in using data from a moving sensor to estimate change in position over time. It is a crucial step for several applications in robotics and computer vision. This paper presents a novel approach for estimating the relative motion between suc-cessive RGB-D frames that uses plane-primitives instead of point features. The planes in the scene are extracted and the motion estimation is cast as a plane-to-plane registra-tion problem with a closed-form solution. Point features are only extracted in the cases where the plane surface configuration is insufficient to determine motion with no ambi-guity. The initial estimate is refined in a photo-geometric optimization step that takes full advantage of the plane detection and simultaneous availability of depth and visual appearance cues. Extensive experiments show that our plane-based approach is as accu-rate as state-of-the-art point-based approaches when the camera displacement is small, and significantly outperforms them in case of wide-baseline and/or dynamic foreground. 1