Citation: Fang, X.; Li, Q.; Li, Q.; Ding,
K.; Zhu, J. Exploiting Graph and
Geodesic Distance Constraint for
Deep Learning-Based Visual
Odometry. Remote Sens. 2022, 14,
1854. https://doi.org/10.3390/
rs14081854
Academic Editors: Yangquan Chen,
Subhas Mukhopadhyay, Nunzio
Cennamo, M. Jamal Deen, Junseop
Lee and Simone Morais
Received: 2 March 2022
Accepted: 9 April 2022
Published: 12 April 2022
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Article
Exploiting Graph and Geodesic Distance Constraint for Deep
Learning-Based Visual Odometry
Xu Fang
1,2
, Qing Li
1,3
, Qingquan Li
1,3
, Kai Ding
4
and Jiasong Zhu
3,5,
*
1
Guangdong Key Laboratory of Urban Informatics, Shenzhen University, Shenzhen 518060, China;
fangxu2018@email.szu.edu.cn (X.F.); qingli@szu.edu.cn (Q.L.); liqq@szu.edu.cn (Q.L.)
2
College of Electronics and Information Engineering, Shenzhen University, Shenzhen 518060, China
3
College of Civil and Transportation Engineering, Shenzhen University, Shenzhen 518060, China
4
School of Computer Science and Technology, Dongguan University of Technology, Dongguan 523808, China;
dingkai@dgut.edu.cn
5
Shenzhen University Branch, Shenzhen Institute of Artificial Intelligence and Robotics for Society,
Shenzhen 518060, China
* Correspondence: zjsong@szu.edu.cn
Abstract:
Visual odometry is the task of estimating the trajectory of the moving agents from con-
secutive images. It is a hot research topic both in robotic and computer vision communities and
facilitates many applications, such as autonomous driving and virtual reality. The conventional
odometry methods predict the trajectory by utilizing the multiple view geometry between consecu-
tive overlapping images. However, these methods need to be carefully designed and fine-tuned to
work well in different environments. Deep learning has been explored to alleviate the challenge by
directly predicting the relative pose from the paired images. Deep learning-based methods usually
focus on the consecutive images that are feasible to propagate the error over time. In this paper,
graph loss and geodesic rotation loss are proposed to enhance deep learning-based visual odometry
methods based on graph constraints and geodesic distance, respectively. The graph loss not only
considers the relative pose loss of consecutive images, but also the relative pose of non-consecutive
images. The relative pose of non-consecutive images is not directly predicted but computed from
the relative pose of consecutive ones. The geodesic rotation loss is constructed by the geodesic
distance and the model regresses a Lie algebra so(3) (3D vector). This allows a robust and stable
convergence. To increase the efficiency, a random strategy is adopted to select the edges of the graph
instead of using all of the edges. This strategy provides additional regularization for training the
networks. Extensive experiments are conducted on visual odometry benchmarks, and the obtained
results demonstrate that the proposed method has comparable performance to other supervised
learning-based methods, as well as monocular camera-based methods. The source code and the
weight are made publicly available.
Keywords: deep learning; graph constraints; visual odometry; geodesic distance
1. Introduction
Visual odometry (VO) is the task of estimating the trajectory of mobile agents (e.g.,
robots, vehicles, and unmanned aerial vehicles (UAVs)) from image sequences. It is one
of the fundamental and important remote sensing methods in autonomous driving, pho-
togrammetry, and virtual/augmented reality (VR, AR) applications. In the past few decades,
visual odometry has attracted significant interest in both robotics and computer vision
communities [
1
]. Visual odometry was first proposed in 2004 by Nister [
2
] for the navi-
gation of autonomous ground vehicles. Later, monocular visual navigation was achieved
for autonomous micro helicopters [
3
]. Visual odometry is also a promising supplement to
other localization technologies, such as inertial measurement unit (IMU), global positioning
system (GPS), LiDAR and ultrasonic rangefinder especially in GPS-denied environments,
Remote Sens. 2022, 14, 1854. https://doi.org/10.3390/rs14081854 https://www.mdpi.com/journal/remotesensing
