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Head mounted display calibration

1. Introduction

We present here our calibration method for Head Mounted Displays. Unlike other calibration methods, our technique:
  • Works for see-through and non-see-through HMDs.
  • Fully models both the intrinsic and extrinsic properties of each HMD display.
  • Support optional modelling of non-linear distortions in HMD display.
  • Is a fully automated procedure, requiring only a few discrete inputs from the operator. No need to wear the HMD and make difficult judgements with a 3D stylus!
  • Is quick and robust.
  • Requires no separate 3D calibration.
  • Delivers quantifiable results.
 This work has been published in Journal of Neuroscience Methods.


1.1 Background

When performing any visual task in a virtual reality system, it is essential that the display device (head mounted display, projector screen) is calibrated so that it represents real space. A virtual object drawn N metres from the observer's face should cause the observer to accomodate and converge on the virtual object in the same way they would for a real object N metres away from them (subject to limitations such as pixel resolution, and display focus). This needs to be true for all N, and also for all points in the display.

We show here a method to calibrate a head mounted display (HMD) so it can accurately represent real space.

Figure 1:The goals of calibration are: to find the relationship between the tracked centre and the pose of each frustum (extrinsic calibration) with respect to the tracked centre; and to ensure that each frustum has the correct width, height and focal length for the left- and right-displays (intrinsic calibration). image

What we have...

  1. We have a HMD with two video displays with unknown intrinsic parameters (display width and height, focal length, etc).
  2. The HMD is tracked by an accurate tracking system, but the tracked center (the coordinate reported by the tracking system) is at an arbitrary point on the HMD. The geometric transformation to move from this arbitrary tracked centre to the optic centre of each display are extrinsic parameters.
  3. We have a stream of HMD positions and orientations coming from the tracker.

What we want...

  1. We need to know the intrinsic parameters of each display, so that we can render appropriate images.
  2. We also need to know the extrinsic parameters (translation and rotation) that describe the spatial relationship between the tracked centre of the HMD and each of the video displays.
So, we wish to find values for all the italic terms in Figure 1. This essentially reduces to finding two matrices - the intrinsic and extrinsic matrices. These correspond directly to the the projection and modelview matrices used in OpenGL, which we use to render scenes.

We must be sure that whatever solution we find will work for any set of input coordinates - it is not acceptable to just improve the calibration for certain `veridical' HMD positions.

What we need...

Our technique is only applicable if:
  1. the tracking system can accurately measure position and orientation - such measures are the basis of the calibration, and errors here will produce poor results. The tracking system does not have to be real time (i.e. offline tracking could work).
  2. a small digital camera can be rigidly mounted inside the headset, and can be fitted with a lens suitable for capturing as much of the HMD image as possible (each display is calibrated independently). Higher resolution cameras will give better results.

Terminology

It may be useful to clarify some terms used in the following text.
  • Tracked marker - A marker that can be tracked by the tracking system. The tracking system needs to be able to accurately report the position of each of these.
  • Tracker transform - the position and orientation provided by the tracker for a tracked object.
  • Tracked centre - The point on a tracked object for which the tracker will provide a position and orientation. In the case of the Vicon optical tracker, this tracked center is (by default) the `centre of mass' of all the reflective markers defining the object.
  • Image plane - The rectangular area upon which pixels are drawn. Pixels are drawn according to how rays of light would pass through the image plane before reaching the optic centre (eye). Correctly determining the position and orientation of the image plane with respect to both the tracked centre and the optic centre is critical to a good calibration. See also this Wikipedia entry.
  • Calibration (verb) - Determining the intrinsic and extrinsic propeties of the HMD. These linear measurements can be augmented with measurements of the non-linearities in the image plane (e.g. radial and tangential distortions).
  • Projected points - The location (in 2D) of real points that have been projected onto an image plane.
  • Re-projected points - Given the 3D locations of the world points and models of the image plane and optic centre, these are where the 3D points would be projected onto the image plane. How these reprojected points differ from the original projected points is a measure of how good our model of the image plane and optic centre is (our "calibration").
  • Calibration (noun) - The result of performing a calibration on an HMD. A good calibration will have small differences between re-projected points and the original projected points.

We now describe our procedure which we have divided up into the following stages:

  1. Equipment and software setup.
  2. Preparation and data collection.
  3. Pre-processing.
  4. Calibration.
  5. Results.
  6. Conclusions, extensions and troubleshooting.
  7. Links.

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