Danda Pani Paudel

Robust and Optimal Sum-of-Squares-Based Point-to-Plane Registration of Image Sets and Structured Scenes

This paper deals with the problem of registering a known structured 3D scene and its metric Structure-from-Motion (SfM) counterpart. The proposed work relies on a prior plane segmentation of the 3D scene and aligns the data obtained from both modalities by solving the point-to-plane assignment problem. An inliers-maximization approach within a Branch-and-Bound (BnB) search scheme is adopted. For the first time in this paper, a Sum-of-Squares optimization theory framework is employed for identifying point-to-plane mismatches (i.e. outliers) with certainty. This allows us to iteratively build potential inliers sets and converge to the solution satisfied by the largest number of point-to-plane assignments. Furthermore, our approach is boosted by new plane visibility conditions which are also introduced in this paper. Using this framework, we solve the registration problem in two cases: (i) a set of putative point-to-plane correspondences (with possibly overwhelmingly many outliers) is given as input and (ii) no initial correspondences are given. In both cases, our approach yields outstanding results in terms of robustness and optimality.

Efficient Pruning LMI Conditions for Branch-and-Prune Rank and Chirality-Constrained Estimation of the Dual Absolute Quadric

We present a new globally optimal algorithm for self-calibrating a moving camera with constant parameters. Our method aims at estimating the Dual Absolute Quadric (DAQ) under the rank-3 and, optionally, camera centers chirality constraints. We employ the Branch-and-Prune paradigm and explore the space of only 5 parameters. Pruning in our method relies on solving Linear Matrix Inequality (LMI) feasibility and Generalized Eigenvalue (GEV) problems that solely depend upon the entries of the DAQ. These LMI and GEV problems are used to rule out branches in the search tree in which a quadric not satisfying the rank and chirality conditions on camera centers is guaranteed not to exist. The chirality LMI conditions are obtained by relying on the mild assumption that the camera undergoes a rotation of no more than 90 between consecutive views. Furthermore, our method does not rely on calculating bounds on any particular cost function and hence can virtually optimize any objective while achieving global optimality in a very competitive running-time.

Consensus Maximization with Linear Matrix Inequality Constraints

Consensus maximization has proven to be a useful tool for robust estimation. While randomized methods like RANSAC are fast, they do not guarantee global optimality and fail to manage large amounts of outliers. On the other hand, global methods are commonly slow because they do not exploit the structure of the problem at hand. In this paper, we show that the solution space can be reduced by introducing Linear Matrix Inequality (LMI) constraints. This leads to significant speed ups of the optimization time even for large amounts of outliers, while maintaining global optimality. We study several cases in which the objective variables have a special structure, such as rotation, scaled-rotation, and essential matrices, which are posed as LMI constraints. This is very useful in several standard computer vision problems, such as estimating Similarity Transformations, Absolute Poses, and Relative Poses, for which we obtain compelling results on both synthetic and real datasets. With up to 90 percent outlier rate, where RANSAC often fails, our constrained approach is consistently faster than the non-constrained one - while finding the same global solution.

Robust and Optimal Registration of Image Sets and Structured Scenes via Sum-of-Squares Polynomials

This paper addresses the problem of registering a known structured 3D scene, typically a 3D scan, and its metric Structure-from-Motion (SfM) counterpart. The proposed registration method relies on a prior plane segmentation of the 3D scan. Alignment is carried out by solving either the point-to-plane assignment problem, should the SfM reconstruction be sparse, or the plane-to-plane one in case of dense SfM. A Polynomial Sum-of-Squares optimization theory framework is employed for identifying point-to-plane and plane-to-plane mismatches, i.e. outliers, with certainty. An inlier set maximization approach within a Branch-and-Bound search scheme is adopted to iteratively build potential inlier sets and converge to the solution satisfied by the largest number of assignments. Plane visibility conditions and vague camera locations may be incorporated for better efficiency without sacrificing optimality. The registration problem is solved in two cases: (i) putative correspondences (with possibly overwhelmingly many outliers) are provided as input and (ii) no initial correspondences are available. Our approach yields outstanding results in terms of robustness and optimality.

2D–3D synchronous/asynchronous camera fusion for visual odometry

We propose a robust and direct 2D–3D registration method for camera synchronization. Once the cameras are synchronized—or for synchronous setups—we also propose a visual odometry framework that benefits from both 2D and 3D acquisitions. Our method does not require a precise set of 2D-to-3D correspondences, handles occlusions and works when the scene is only partially known. It is carried out through a 2D–3D based initial motion estimation followed by a constrained nonlinear optimization for motion refinement. The problems of occlusion and that of missing scene parts are handled by comparing the image-based reconstruction and 3D sensor measurements. The results of our experiments demonstrate that the proposed framework allows to obtain a good initial motion estimate and a significant improvement through refinement.

High quality reconstruction of dynamic objects using 2D-3D camera fusion

In this paper, we propose a complete pipeline for high quality reconstruction of dynamic objects using 2D-3D camera setup attached to a moving vehicle. Starting from the segmented motion trajectories of individual objects, we compute their precise motion parameters, register multiple sparse point clouds to increase the density, and develop a smooth and textured surface from the dense (but scattered) point cloud. The success of our method relies on the proposed optimization framework for accurate motion estimation between two sparse point clouds. Our formulation for fusing closest-point and consensus based motion estimations, respectively in the absence and presence of motion trajectories, is the key to obtain such accuracy. Several experiments performed on both synthetic and real (KITTI) datasets show that the proposed framework is very robust and accurate.

VarCity - the video: the struggles and triumphs of leveraging fundamental research results in a graphics video production

VarCity - the Video is a short documentary-style CGI movie explaining the main outcomes of the 5-year Computer Vision research project VarCity. Besides a coarse overview of the research, we present the challenges that were faced in its production, induced by two factors: i) usage of imperfect research data produced by automatic algorithms, and ii) human factors, like federating researchers and a CG artist around a similar goal many had a different conception of, while no one had a detailed overview of all the content. Successive achievement was driven by some ad-hoc technical developments but more importantly of detailed and abundant communication and agreement on common best practices.