Oriented-grid Encoder for 3D Implicit Representations

Encoding 3D points is one of the primary steps in learning-based implicit scene representation. Using features that gather information from neighbors with multi-resolution grids has proven to be the best geometric encoder for this task. However, prior techniques do not exploit some characteristics of most objects or scenes, such as surface normals and local smoothness. This paper is the first to exploit those 3D characteristics in 3D geometric encoders explicitly. In contrast to prior work on using multiple levels of details, regular cube grids, and trilinear interpolation, we propose 3D-oriented grids with a novel cylindrical volumetric interpolation for modeling local planar invariance. In addition, we explicitly include a local feature aggregation for feature regularization and smoothing of the cylindrical interpolation features. We evaluate our approach on ABC, Thingi10k, ShapeNet, and Matterport3D, for object and scene representation. Compared to the use of regular grids, our geometric encoder is shown to converge in fewer steps and obtain sharper 3D surfaces. When compared to the prior techniques, our method gets state-of-the-art results.

BANSAC: A dynamic BAyesian Network for adaptive SAmple Consensus

RANSAC-based algorithms are the standard techniques for robust estimation in computer vision. These algorithms are iterative and computationally expensive; they alternate between random sampling of data, computing hypotheses, and running inlier counting. Many authors tried different approaches to improve efficiency. One of the major improvements is having a guided sampling, letting the RANSAC cycle stop sooner. This paper presents a new adaptive sampling process for RANSAC. Previous methods either assume no prior information about the inlier/outlier classification of data points or use some previously computed scores in the sampling. In this paper, we derive a dynamic Bayesian network that updates individual data points' inlier scores while iterating RANSAC. At each iteration, we apply weighted sampling using the updated scores. Our method works with or without prior data point scorings. In addition, we use the updated inlier/outlier scoring for deriving a new stopping criterion for the RANSAC loop. We test our method in multiple real-world datasets for several applications and obtain state-of-the-art results. Our method outperforms the baselines in accuracy while needing less computational time.

Robust Frame-to-Frame Camera Rotation Estimation in Crowded Scenes

We present an approach to estimating camera rotation in crowded, real-world scenes from handheld monocular video. While camera rotation estimation is a well-studied problem, no previous methods exhibit both high accuracy and acceptable speed in this setting. Because the setting is not addressed well by other datasets, we provide a new dataset and benchmark, with high-accuracy, rigorously verified ground truth, on 17 video sequences. Methods developed for wide baseline stereo (e.g., 5-point methods) perform poorly on monocular video. On the other hand, methods used in autonomous driving (e.g., SLAM) leverage specific sensor setups, specific motion models, or local optimization strategies (lagging batch processing) and do not generalize well to handheld video. Finally, for dynamic scenes, commonly used robustification techniques like RANSAC require large numbers of iterations, and become prohibitively slow. We introduce a novel generalization of the Hough transform on SO(3) to efficiently and robustly find the camera rotation most compatible with optical flow. Among comparably fast methods, ours reduces error by almost 50\% over the next best, and is more accurate than any method, irrespective of speed. This represents a strong new performance point for crowded scenes, an important setting for computer vision. The code and the dataset are available at https://fabiendelattre.com/robust-rotation-estimation.

An observer cascade for velocity and multiple line estimation

Previous incremental estimation methods consider estimating a single line, requiring as many observers as the number of lines to be mapped. This leads to the need for having at least $4N$ state variables, with $N$ being the number of lines. This paper presents the first approach for multi-line incremental estimation. Since lines are common in structured environments, we aim to exploit that structure to reduce the state space. The modeling of structured environments proposed in this paper reduces the state space to $3N + 3$ and is also less susceptible to singular configurations. An assumption the previous methods make is that the camera velocity is available at all times. However, the velocity is usually retrieved from odometry, which is noisy. With this in mind, we propose coupling the camera with an Inertial Measurement Unit (IMU) and an observer cascade. A first observer retrieves the scale of the linear velocity and a second observer for the lines mapping. The stability of the entire system is analyzed. The cascade is shown to be asymptotically stable and shown to converge in experiments with simulated data.

Solving the Discrete Euler-Arnold Equations for the Generalized Rigid Body Motion

We propose three iterative methods for solving the Moser-Veselov equation, which arises in the discretization of the Euler-Arnold differential equations governing the motion of a generalized rigid body. We start by formulating the problem as an optimization problem with orthogonal constraints and proving that the objective function is convex. Then, using techniques from optimization on Riemannian manifolds, the three feasible algorithms are designed. The first one splits the orthogonal constraints using the Bregman method, whereas the other two methods are of the steepest-descent type. The second method uses the Cayley-transform to preserve the constraints and a Barzilai-Borwein step size, while the third one involves geodesics, with the step size computed by Armijo's rule. Finally, a set of numerical experiments are carried out to compare the performance of the proposed algorithms, suggesting that the first algorithm has the best performance in terms of accuracy and number of iterations. An essential advantage of these iterative methods is that they work even when the conditions for applicability of the direct methods available in the literature are not satisfied.

On Incremental Structure-from-Motion using Lines

Humans tend to build environments with structure, which consists of mainly planar surfaces. From the intersection of planar surfaces arise straight lines. Lines have more degrees-of-freedom than points. Thus, line-based Structure-from-Motion (SfM) provides more information about the environment. In this paper, we present solutions for SfM using lines, namely, incremental SfM. These approaches consist of designing state observers for a camera's dynamical visual system looking at a 3D line. We start by presenting a model that uses spherical coordinates for representing the line's moment vector. We show that this parameterization has singularities, and therefore we introduce a more suitable model that considers the line's moment and shortest viewing ray. Concerning the observers, we present two different methodologies. The first uses a memory-less state-of-the-art framework for dynamic visual systems. Since the previous states of the robotic agent are accessible -- while performing the 3D mapping of the environment -- the second approach aims at exploiting the use of memory to improve the estimation accuracy and convergence speed. The two models and the two observers are evaluated in simulation and real data, where mobile and manipulator robots are used.

Mapping of Sparse 3D Data using Alternating Projection

We propose a novel technique to register sparse 3D scans in the absence of texture. While existing methods such as KinectFusion or Iterative Closest Points (ICP) heavily rely on dense point clouds, this task is particularly challenging under sparse conditions without RGB data. Sparse texture-less data does not come with high-quality boundary signal, and this prohibits the use of correspondences from corners, junctions, or boundary lines. Moreover, in the case of sparse data, it is incorrect to assume that the same point will be captured in two consecutive scans. We take a different approach and first re-parameterize the point-cloud using a large number of line segments. In this re-parameterized data, there exists a large number of line intersection (and not correspondence) constraints that allow us to solve the registration task. We propose the use of a two-step alternating projection algorithm by formulating the registration as the simultaneous satisfaction of intersection and rigidity constraints. The proposed approach outperforms other top-scoring algorithms on both Kinect and LiDAR datasets. In Kinect, we can use 100X downsampled sparse data and still outperform competing methods operating on full-resolution data.

Active Depth Estimation: Stability Analysis and its Applications

Recovering the 3D structure of the surrounding environment is an essential task in any vision-controlled Structure-from-Motion (SfM) scheme. This paper focuses on the theoretical properties of the SfM, known as the incremental active depth estimation. The term incremental stands for estimating the 3D structure of the scene over a chronological sequence of image frames. Active means that the camera actuation is such that it improves estimation performance. Starting from a known depth estimation filter, this paper presents the stability analysis of the filter in terms of the control inputs of the camera. By analyzing the convergence of the estimator using the Lyapunov theory, we relax the constraints on the projection of the 3D point in the image plane when compared to previous results. Nonetheless, our method is capable of dealing with the cameras' limited field-of-view constraints. The main results are validated through experiments with simulated data.

A Framework for Depth Estimation and Relative Localization of Ground Robots using Computer Vision

The 3D depth estimation and relative pose estimation problem within a decentralized architecture is a challenging problem that arises in missions that require coordination among multiple vision-controlled robots. The depth estimation problem aims at recovering the 3D information of the environment. The relative localization problem consists of estimating the relative pose between two robots, by sensing each other's pose or sharing information about the perceived environment. Most solutions for these problems use a set of discrete data without taking into account the chronological order of the events. This paper builds on recent results on continuous estimation to propose a framework that estimates the depth and relative pose between two non-holonomic vehicles. The basic idea consists in estimating the depth of the points by explicitly considering the dynamics of the camera mounted on a ground robot, and feeding the estimates of 3D points observed by both cameras in a filter that computes the relative pose between the robots. We evaluate the convergence for a set of simulated scenarios and show experimental results validating the proposed framework.