1. Associating 6 DoF sensor data to 3D scan view registration Joris Vergeest, Thomas Kroes, Wolf Song Delft University of Technology Delft, The Netherlands WSCG 2007 Plzen, January 29 - February 2, 2007

2. Overview of Presentation Motivation Problem Computation of transform X Robustness / accuracy Improvements

3. Making scan view registration easier - Too tedious process for occasional user - Dedicated to fixed scanner / small models - Not relying on landmarks, mechanical devices etc - Sufficiently robust /accurate - Use simple (pref. wireless) 6 DoF sensor fixed to object aa

4. Problem: Associate 6-dim placement of sensor to 6-dim placement of scan view (=point cloud) There is no 6-dim placement of scan view available – no classical calibration We can associate two 6D sensor placements to one scan registration transform Should deliver X = (T relative to S) = S T. Then we can predict placement of new scan views from 6D data, and no manual operations needed anymore.

5. Movement relative to T: N = T F(t 0 ) ( T F(t 1 ) ) -1 Movement relative to S: M = S F(t 0 ) ( S F(t 1 ) ) -1 M and N are similar matrices, or there exists X such that XNX  1 =M. How to find X? Minimize: This will not produce requested S T. Now focus on rotation axis a.

6. Rotation axis as measured in T should be transformed to rotation axis as measured in S, by X (necessary, not sufficient). Construction: Define frame L with origin in a and z-axis equals a. Origin and x- and y- axis not completely defined. Thus we associate T to S using the common frame L up to two unknown scalars. Y = S L ( T L) -1. However, there is a unique Y that works for multiple axes a ! (then we have X)

7. Then we search for the pair (  ',  ')    [0, 2  ] for which holds Y 1 (  ',  ') T a i = S a i, 2  i  n,. Although seemingly simple 2-par minimizations, some numerical problems remain

8. Multiple calibrations X, spread of intrinsic rotation angle (0.1 degree) and of location of origin (35mm). Initial evaluation: scanning process speeds up by factor 10. Still needed: - More stable calibration - Wireless 6 DoF sensor