SPPRA2010 Estimating a Rotation Matrix R by using higher-order Matrices R^n with Application to Supervised Pose Estimation
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Toru Tamaki, Bisser Raytchev, Kazufumi Kaneda, Toshiyuki Amano : "Wstimating a Rotation Matrix R by using higher-order Matrices R^n with Application to Supervised Pose Estimation," Proc. of SPPRA 2010: The Seventh IASTED International Conference on Signal Processing, Pattern Recognition and Applications, pp. 58-64 (2010 02). Innsbruck, Austria, 2010/February/17-19.
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SPPRA2010 Estimating a Rotation Matrix R by using higher-order Matrices R^n with Application to Supervised Pose Estimation
- 1. Estimating a rotation matrix R by using higher-order matrices Rn with application to supervised pose estimation Toru Tamaki Bisser Raytchev Kazufumi Kaneda Toshiyuki Amano
- 2. Estimating a rotation matrix R by using higher-order matrices Rn with application to supervised pose estimation Can Rnestimate R Toru Tamaki more accurately Bisser Raytchev than R ? Kazufumi Kaneda Toshiyuki Amano
- 3. To improve estimates… Average! t1 When measurement is only once… t2 t … … Average tn Lease-Squares How improve? Measure many times
- 4. To improve estimates… Average! t1 When measurement is only once… t2 t … … Average tn Lease-Squares Improve! Measure with many timers
- 5. To improve estimates… Average? t When measurement is only once… t2 t … … Average tn Lease-Squares How improve? Measure with many timers
- 6. To improve estimates… Average. t When measurement is only once… t2 t … … tn Improve! Measure with many timers But, What is it?
- 7. Our problem: Pose estimation Pose parameters R 3x3 rotation matrix t 3D translation Regression: image Appearance-based / Pose parameters View-based pose estimation R Parametric Eigenspace (Murase et al., 1995) linear regression (Okatani et al., 2000) kernel CCA (Melzer et al., 2003) SV regression (Ando et al., 2005) Manifold learning, and others R (Rothganger et al., 2006) (Lowe, 2004) (Ferrari et al., 2006) (Kushal et al., 2006) (Viksten, 2009)
- 8. Our concept Pose Rotation image vector matrix 1 p1 R ! axis µ angle Training 2 p2 R2 ! 2µ
- 9. Our concept New Pose Rotation image vector matrix axis angle 1 p1 R ! µ ! axis Polar Eigen Decomp. Decomp. µ angle 2 p2 R2 ! 2µ ! 2µ ! µ
- 10. Our concept New Pose Rotation image Examples vector matrix axis angle 1 p1 R ! µ 29 [deg] 210 [deg] ! axis Polar Eigen Decomp. Decomp. µ angle 62 [deg] 420 [deg] 2 p2 R2 ! 2µ =60 [deg] ! Div by 2 Div by 2 31 [deg] 30 [deg] 2µ ! µ 30 [deg] ? [deg]
- 11. Surveying Electronic Distance Measurement EDM Surveying – ARCHEOSCAN http://archeoscan.com/16.html
- 12. Principle of EDM Transmitter Receiver Dist ¸1 ¸2 µ2 µ1 device target Use •Longer wavelength ¸1 first, for a rough phase estimate µ1 •Shorter wavelength ¸2 next, for a fine phase estimate µ2
- 13. Our concept New Pose Rotation image Examples vector matrix axis angle 1 p1 R ! µ 29 [deg] 210 [deg] ! Polar Eigen Decomp. Decomp. µ 62 [deg] 420 [deg] 2 p2 R2 ! 2µ =60 [deg] ! Div by 2 Div by 2 31 [deg] 210 [deg] 2µ ! µ 30 [deg] 210 [deg]
- 14. Measurements Simulation 1 Pose Rotation vector matrix axis angle R R p1 +noise R !1 µ1 … Polar Eigen … … … … Decomp. Decomp. µ R8 p8 +noise R8 !8 µ8 ! R
- 15. Measurements Simulation 2 Pose Rotation vector matrix axis angle R +noise R p1 R !1 µ1 Polar Eigen … … … … … Decomp. Decomp. µ R8 p8 R8 !8 µ8 ! R Error doesn’t change… No free lunch!
- 16. •Linear regression Experimental results •Training with Pose Rotation images and poses vector matrix axis angle 1 p1 R !1 µ1 Polar Eigen … … … … Decomp. Decomp. µ 8 p8 R8 !8 µ8 images ! R
- 17. Summary • Improve estimates of a pose R with many measurements R1, R2, …, R8 • Simulations and experimental results shows that the concept works!