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Technical University of Munich

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Informatik IX
Chair of Computer Vision & Artificial Intelligence

Boltzmannstrasse 3
85748 Garching info@vision.in.tum.de

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02.10.2020

We have five papers accepted to 3DV 2020!

30.09.2020

Our effcient deep network architectures form the AI engine of the project Slow Down COVID-19 at Harvard.

24.07.2020

Our practical course "Vision-based Navigation" (WS18, SS19) by Dr. Vladyslav Usenko and Nikolaus Demmel was honored as best practical course in the academic year 2018/2019 by the department for Informatics.

07.05.2020

We are organizing a workshop on Map-based Localization for Autonomous Driving at ECCV 2020, Glasgow, UK.

13.04.2020

Daniel Cremers received an ERC Advanced Grant (3.5 Mio Euro) for pioneering frontier research from the European Research Council. This constitutes his fifth ERC grant.

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Efficient Derivative Computation for Cumulative B-Splines on Lie Groups

Abstract

Continuous-time trajectory representation has recently gained popularity for tasks where the fusion of high-frame-rate sensors and multiple unsynchronized devices is required. Lie group cumulative B-splines are a popular way of representing continuous trajectories without singularities. They have been used in near real-time SLAM and odometry systems with IMU, LiDAR, regular, RGB-D and event cameras, as well as for offline calibration.

These applications require efficient computation of time derivatives (velocity, acceleration), but all prior works rely on a computationally suboptimal formulation. In this work we present an alternative derivation of time derivatives based on recurrence relations that needs O(k) instead of O(k^2) matrix operations (for a spline of order k) and results in simple and elegant expressions. While producing the same result, the proposed approach significantly speeds up the trajectory optimization and allows for computing simple analytic derivatives with respect to spline knots. The results presented in this paper pave the way for incorporating continuous-time trajectory representations into more applications where real-time performance is required.

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Poster

Open-Source Code

The code for the experiments presented in the paper is available at https://gitlab.com/tum-vision/lie-spline-experiments.

If you are planning to use the code in your project check the 'include/basalt/spline' folder of the headers-only library. ( Documentation)

For a calibration tool based on the proposed B-spline trajectory representation check the dataset and device calibration tutorials of the basalt project.


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Conference and Workshop Papers
2020
[]Efficient Derivative Computation for Cumulative B-Splines on Lie Groups (C. Sommer, V. Usenko, D. Schubert, N. Demmel and D. Cremers), In IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2020.  [bibtex] [doi] [arXiv:1911.08860] [pdf]Oral Presentation
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Informatik IX
Chair of Computer Vision & Artificial Intelligence

Boltzmannstrasse 3
85748 Garching info@vision.in.tum.de

Follow us on:
CVG Group DVL Group

News

02.10.2020

We have five papers accepted to 3DV 2020!

30.09.2020

Our effcient deep network architectures form the AI engine of the project Slow Down COVID-19 at Harvard.

24.07.2020

Our practical course "Vision-based Navigation" (WS18, SS19) by Dr. Vladyslav Usenko and Nikolaus Demmel was honored as best practical course in the academic year 2018/2019 by the department for Informatics.

07.05.2020

We are organizing a workshop on Map-based Localization for Autonomous Driving at ECCV 2020, Glasgow, UK.

13.04.2020

Daniel Cremers received an ERC Advanced Grant (3.5 Mio Euro) for pioneering frontier research from the European Research Council. This constitutes his fifth ERC grant.

More