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Lipu Zhou

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8 papers

2 author rows

ICRA Conference 2023 Conference Paper

Efficient Bundle Adjustment for Coplanar Points and Lines

Lipu Zhou
Jiacheng Liu 0008
Fengguang Zhai
Pan Ai
Kefei Ren
Yinian Mao
Guoquan Huang 0003
Ziyang Meng 0001

Bundle adjustment (BA) is a well-studied fundamental problem in the robotics and vision community. In man-made environments, coplanar points and lines are ubiquitous. However, the number of works on bundle adjustment with coplanar points and lines is relatively small. This paper focuses on this special BA problem, referred to as $\pi-\mathbf{BA}$. For a point or a line on a plane, we derive a new constraint to describe the relationship among two poses and the plane, called $\pi$ -constraint. We distribute $\pi$ -constraints into different groups. Each group is called a $\pi$ -factor. We prove that, with some simple preprocessing, the computational complexity associated with a $\pi$ -factor in the Levenberg-Marquardt (LM) algorithm is $O(1)$, independent of the number of $\pi$ -constraints packed into the $\pi$ -factor. In $\pi-\mathbf{BA}, \pi$ -factors replace original reprojection errors. One problem is how to divide $\pi$ -constraints into $\pi$ -factors. Different strategies may result in different numbers of $\pi$ -factors, which in turn affects the efficiency. It is difficult to get the optimal division. We present a greedy algorithm to overcome this problem. Experimental results verify that our algorithm can significantly accelerate the computation.

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ICRA Conference 2023 Conference Paper

Efficient Visual-Inertial Navigation with Point-Plane Map

Jiaxin Hu
Kefei Ren
Xiaoyu Xu
Lipu Zhou
Xiaoming Lang
Yinian Mao
Guoquan Huang 0003

Accurate and real-time global pose estimation relative to a global prior map is indispensable in many applications, such as logistics with micro aerial vehicles and Augmented Reality. Supposed that a pure sparse 3D point map can provide a structureless representation of the environment, then generating a point-plane prior map can further model the environment topology and offer global constraints for an accurate localization. To implement this, we propose a filter-based, large-scale visual-inertial odometry system, termed PPM-VIO, which utilizes a point-plane map to correct the cumulative drift. Our system, detecting coplanar information from sparse point clouds with semantic information, achieves accurate online plane matching via geometric constraints, semantic constraints, and descriptor constraints. To improve the localization performance, we effectively integrate and formulate the global planar measurements and points measurements in a filter-based estimator. The effectiveness of the proposed method is extensively validated on real-world datasets collected in different scenarios. Experimental results demonstrate that, rather than using the point map alone, leveraging the plane information in the prior map can yield better trajectory estimates and broaden the effective scope of the prior map in different scenes.

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ICRA Conference 2022 Conference Paper

EDPLVO: Efficient Direct Point-Line Visual Odometry

Lipu Zhou
Guoquan Huang 0003
Yinian Mao
Shengze Wang 0002
Michael Kaess

This paper introduces an efficient direct visual odometry (VO) algorithm using points and lines. Pixels on lines are generally adopted in direct methods. However, the original photometric error is only defined for points. It seems difficult to extend it to lines. In previous works, the collinear constraints for points on lines are either ignored [1] or introduce heavy computational load into the resulting optimization system [2]. This paper extends the photometric error for lines. We prove that the 3D points of the points on a 2D line are determined by the inverse depths of the endpoints of the 2D line, and derive a closed-form solution for this problem. This property can significantly reduce the number of variables to speed up the optimization, and can make the collinear constraint exactly satisfied. Furthermore, we introduce a two-step method to further accelerate the optimization, and prove the convergence of this method. The experimental results show that our algorithm outperforms the state-of-the-art direct VO algorithms.

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ICRA Conference 2021 Conference Paper

π-LSAM: LiDAR Smoothing and Mapping With Planes

Lipu Zhou
Shengze Wang 0002
Michael Kaess

This paper introduces a real-time dense planar LiDAR SLAM system, named π-LSAM, for the indoor environment. The widely used LiDAR odometry and mapping (LOAM) framework [1] does not include bundle adjustment (BA) and generates a low fidelity tracking pose. This paper seeks to overcome these drawbacks for the indoor environment. Specifically, we use the plane as the landmark, and introduce plane adjustment (PA) as our back-end to jointly optimize planes and keyframe poses. We present the π-factor to significantly reduce the computational complexity of PA. In addition, we introduce an efficient loop detection algorithm based on the RANSAC framework using planes. In the front-end, our algorithm performs global registration in real time. To achieve this performance, we maintain the local-to-global point-to-plane correspondences scan by scan, so that we only need a small local KD-tree to establish the data association between a LiDAR scan and the global planes, rather than a large global KD-tree used in previous works. With this local-to-global data association, our algorithm directly identifies planes in a LiDAR scan, and yields an accurate and globally consistent pose. Experimental results show that our algorithm significantly outperforms the state-of-the-art LOAM variant, LeGO-LOAM [2], and our algorithm achieves real time.

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ICRA Conference 2020 Conference Paper

A Fast and Accurate Solution for Pose Estimation from 3D Correspondences

Lipu Zhou
Shengze Wang 0002
Michael Kaess

Estimating pose from given 3D correspondences, including point-to-point, point-to-line and point-to-plane correspondences, is a fundamental task in computer vision with many applications. We present a fast and accurate solution for the least-squares problem of this task. Previous works mainly focus on studying the way to find the global minimizer of the least-squares problem. However, existing works that show the ability to achieve the global minimizer are still unsuitable for real-time applications. Furthermore, as one of contributions of this paper, we prove that there exist ambiguous configurations for any number of lines and planes. These configurations have several solutions in theory, which makes the correct solution may come from a local minimizer when the data are with noise. Previous works based on convex optimization which is unable to find local minimizers do not work in the ambiguous configuration. Our algorithm is efficient and able to reveal local minimizers. We employ the Cayley-Gibbs-Rodriguez (CGR) parameterization of the rotation to derive a general rational cost for the three cases of 3D correspondences. The main contribution of this paper is to solve the first-order optimality conditions of the least-squares problem, which are of a complicated rational form. The central idea of our algorithm is to introduce some intermediate unknowns to simplify the problem. Extensive experimental results show that our algorithm is more stable than previous algorithms when the number N of correspondences is small. Besides, when N is large, our algorithm achieves the same accuracy as the state-of-the-art algorithm [1], but our algorithm is about 7 times faster than [1] in real applications.

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AAAI Conference 2019 Conference Paper

A Robust and Efficient Algorithm for the PnL Problem Using Algebraic Distance to Approximate the Reprojection Distance

Lipu Zhou
Yi Yang
Montiel Abello
Michael Kaess

This paper proposes a novel algorithm to solve the pose estimation problem from 2D/3D line correspondences, known as the Perspective-n-Line (PnL) problem. It is widely known that minimizing the geometric distance generally results in more accurate results than minimizing an algebraic distance. However, the rational form of the reprojection distance of the line yields a complicated cost function, which makes solving the first-order optimality conditions infeasible. Furthermore, iterative algorithms based on the reprojection distance are time-consuming for a large-scale problem. In contrast to previous works which minimize a cost function based on an algebraic distance that may not approximate the reprojection distance of the line, we design two simple algebraic distances to gradually approximate the reprojection distance. This speeds up the computation, and maintains the robustness of the geometric distance. The two algebraic distances result in two polynomial cost functions, which can be efficiently solved. We directly solve the first-order optimality conditions of the first problem with a novel hidden variable method. This algorithm makes use of the specific structure of the resulting polynomial system, therefore it is more stable than the general Gröbner basis polynomial solver. Then, we minimize the second polynomial cost function by the damped Newton iteration, starting from the solution of the first cost function. Experimental results show that the first step of our algorithm is already superior to the state-of-the-art algorithms in terms of accuracy and applicability, and faster than the algorithms based on Gröbner basis polynomial solver. The second step yields comparable results to the results from minimizing the reprojection distance, but is much more efficient. For speed, our algorithm is applicable to real-time applications.

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IROS Conference 2019 Conference Paper

An Efficient and Accurate Algorithm for the Perspecitve-n-Point Problem

Lipu Zhou
Michael Kaess

In this paper, we address the problem of pose estimation from N 2D/3D point correspondences, known as the Perspective-n-Point (PnP) problem. Although many solutions have been proposed, it is hard to optimize both computational complexity and accuracy at the same time. In this paper, we propose an accurate and simultaneously efficient solution to the PnP problem. Previous PnP algorithms generally involve two sets of unknowns including the depth of each pixel and the pose of the camera. Our formulation does not involve the depth of each pixel. By introducing some intermediate variables, this formulation leads to a fourth degree polynomial cost function with 3 unknowns that only involves the rotation. In contrast to previous works, we do not address this minimization problem by solving the first-order optimality conditions using the off-the-shelf Gröbner basis method, as the Gröbner basis method may encounter numeric problems. Instead, we present a method based on linear system null space analysis to provide a robust initial estimation for a Newton iteration. Experimental results demonstrate that our algorithm is comparable to the start-of-the-art algorithms in terms of accuracy, and the speed of our algorithm is among the fastest algorithms.

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IROS Conference 2018 Conference Paper

Automatic Extrinsic Calibration of a Camera and a 3D LiDAR Using Line and Plane Correspondences

Lipu Zhou
Zimo Li
Michael Kaess

In this paper, we address the problem of extrinsic calibration of a camera and a 3D Light Detection and Ranging (LiDAR) sensor using a checkerboard. Unlike previous works which require at least three checkerboard poses, our algorithm reduces the minimal number of poses to one by combining 3D line and plane correspondences. Besides, we prove that parallel planar targets with parallel boundaries provide the same constraints in our algorithm. This allows us to place the checkerboard close to the LiDAR so that the laser points better approximate the target boundary without loss of generality. Moreover, we present an algorithm to estimate the similarity transformation between the LiDAR and the camera for the applications where only the correspondences between laser points and pixels are concerned. Using a similarity transformation can simplify the calibration process since the physical size of the checkerboard is not needed. Meanwhile, estimating the scale can yield a more accurate result due to the inevitable measurement errors of the checkerboard size and the LiDAR intrinsic scale factor that transforms the LiDAR measurement to the metric measurement. Our algorithm is validated through simulations and experiments. Compared to the plane-only algorithms, our algorithm can obtain more accurate result by fewer number of poses. This is beneficial to the large-scale commercial application.

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