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Calibration of a Multi-Camera Rig from Non-Overlapping Views

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Abstract

This work describes a novel approach to estimate the relative poses of multiple cameras fixed inside a rig. In contrast to existing methods for

stereo and multi-camera rig calibration, overlapping views of the individual cameras are not required.

The proposed approach estimates the rig parameters, i.e. relative position and orientation of the fixed cameras with respect to each other, using timecorresponding

poses for each camera during an arbitrary motion of the rig. This estimation can be done by solving systems of linear equations. The corresponding poses are previously obtained using pose estimation techniques from a sequence of time-corresponding images for each camera individually. Afterwards the rig parameter estimates are refined by a

non-linear optimization. It is shown that the presented calibration method is comparable in accuracy and efficiency to common rig calibration techniques that require overlapping views.

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Goal

We are interesting in calibrating a rigidly coupled multi-camera system (“rig“) with known intrinsic parameters, i.e. to determine the relative poses of each camera fixed inside the rig with respect to the rig's coordinate frame. While various methods are proposed for calibrating a rig with strongly overlapping camera view fields, e.g. 3d stereo rigs used for scene reconstruction, there are only few approach for rigs without overlapping camera view fields, e.g. omni-directional camera systems consisting of front and rear cameras.

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Our Approach

We tie in with previous work in the field of hand-eye estimation which is in fact very similar to the proposed problem: estimate the fixed relation between different coordinate frames (e.g. between a sensor mounted onto a robot’s hand and the hand itself). Hand-eye calibration problems need to solve a homogeneous matrix equation of the form AX = XB where A, B describe local pose transformations of devices A and B during a motion of the system at a certain point of time, and X denotes the time-fixed relative pose transformation between the coordinate frames of devices A and B. We can interpret a camera rig as a hand-eye system consisting of camera devices only.Local pose transformations can be reconstructed from image sequences of each camera of the moving rig by common image-based pose estimation methods such as the Structure from Motion (SfM) approach. We present a linear approach to solve the equation system AX = XB in order to retrieve the relative pose transformations X between each pair of camera inside the rig even if the relative scale between the local camera coordinate frames obtained by SfM is unknown and possibly changing over time. We also investigate settings where our approach does not perform well (e.g. for purely translational rig motions) and propose alternative methods for such cases. Non-linear optimization methods are also considered in order to increase the accuracy of the calibration. |

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Results and Future Work

Within this work we showed that the calibration is similar in accuracy as Bouget's calibration approach for stereo rigs with overlapping camera views. We evaluated the approach both for synthetic images with ground-truth data available, and for real camera systems which have been calibrated offline. Future work could aim for integrating the calibration constraints directly into SfM approaches in order to stabilize the pose estimation.

**Tutor:** Felix Woelk

**Download:** Diploma thesis (PDF)

**Publication:** S. Esquivel, F. Woelk, R. Koch: Calibration of a Multi-Camera Rig from Non-Overlapping Views, in: Lecture Notes in Computer Science 4713 (DAGM 2007), pp. 82–91, Heidelberg, 2007

The original publication is available at www.springerlink.com

**BibTex:**

@MASTERSTHESIS{esquivel07:diplomathesis, author = {Sandro Esquivel}, title = {Calibration of a Multi-Camera Rig from Non-Overlapping Views}, type = {Diploma thesis}, school = {Christian-Albrechts-University, Kiel}, year = {2007} }