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Dear reviewers,

Many thanks for your time and thoughtful comments. Should the paper be accepted, we propose to make the following changes:

1. We will shoot the pictures again to make the examples clearer. Specifically, the cube will be removed and the pointer will be rendered with thicker lines.

2. We believe that colour images are important to convey the details of how the algorithm works. The information we are trying to display is inherently four dimensional (three for the spatial dimensions, one for the uncertainty). However, we understand the need that users must be able to understand the paper if it is in black and white and so, as part of the redesign of our images, we will ensure that the grey scale in the selection regions will provide the appropriate cues.

3. The Aron et al. paper, published at ISMAR 2004, is an example of an approach that combines multiple trackers to improve tracking. As explained in our paper "OSGAR: A Scene Graph with Uncertain Transformations" (also published at ISMAR 2004), our work assumes that a tracker (of some kind) exists and is capable of returning uncertainty information. In this context, Aron's algorithm would merely another example of a tracking system. We feel that a more appropriate reference would be Wayne's paper on ARToolkit (which analyses the error in different locations).

4. Because of the space constraints of a short paper, we wanted to provide a simple, understandable examples that illustrate the points and demonstrate how the system works, so that others can replicate it. A 'real-world' example can be included if the committee thinks it is necessary.

5. All typos will be corrected and the final draft will be thoroughly proofread