A minimal case solution to the calibrated relative pose problem for the case of two known orientation angles

Authors:
Friedrich Fraundorfer;Petri Tanskanen;Marc Pollefeys
Affiliations:
Computer Vision and Geometry Lab, Department of Computer Science, ETH Zürich, Switzerland;Computer Vision and Geometry Lab, Department of Computer Science, ETH Zürich, Switzerland;Computer Vision and Geometry Lab, Department of Computer Science, ETH Zürich, Switzerland
Venue:
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part IV
Year:
2010

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Abstract

It this paper we present a novel minimal case solution to the calibrated relative pose problemusing 3 point correspondences for the case of two known orientation angles. This case is relevant when a camera is coupled with an inertial measurement unit (IMU) and it recently gained importance with the omnipresence of Smartphones (iPhone, Nokia N900) that are equippedwith accelerometers tomeasure the gravity normal. Similar to the 5-point (6-point), 7-point, and 8-point algorithm for computing the essential matrix in the unconstrained case, we derive a 3-point, 4-point and, 5-point algorithm for the special case of two known orientation angles. We investigate degenerate conditions and show that the new 3-point algorithm can cope with planes and even collinear points. We will show a detailed analysis and comparison on synthetic data and present results on cell phone images. As an additional application we demonstrate the algorithm on relative pose estimation for a micro aerial vehicle's (MAV) camera-IMU system.