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Selection for Feature-Based Image Registration F. Brunet 1,2 , A. - PowerPoint PPT Presentation

Aug 07, 2023 •97 likes •371 views

Pixel-Based Hyperparameter Selection for Feature-Based Image Registration F. Brunet 1,2 , A. Bartoli 1 , N. Navab 2 , and R. Malgouyres 3 1 ISIT, Universit dAuvergne, Clermont -Ferrand, France 2 CAMPAR, Technische Universitt Mnchen,

  1. Pixel-Based Hyperparameter Selection for Feature-Based Image Registration F. Brunet 1,2 , A. Bartoli 1 , N. Navab 2 , and R. Malgouyres 3 1 ISIT, Université d’Auvergne, Clermont -Ferrand, France 2 CAMPAR, Technische Universität München, Munich, Germany 3 LIMOS, Université d’Auvergne, Clermont -Ferrand, France

  2. Outline • What is image registration? – General principle – Standard approaches • Problem: choice of the hyperparameters • Our approach • Experimental results F. Brunet, A. Bartoli, R. Malgouyres, and N. Navab

  3. What is image registration? Find the geometric transformation that aligns a source image and a target image ¯ nd p such that: W ( ¢ ; p ) Target image T Source image S F. Brunet, A. Bartoli, R. Malgouyres, and N. Navab

  4. Two standard approaches • The feature-based approach • The direct approach (photometric approach) F. Brunet, A. Bartoli, R. Malgouyres, and N. Navab

  5. The feature-based approach Source image S Target image T F. Brunet, A. Bartoli, R. Malgouyres, and N. Navab

  6. The feature-based approach Extracting point correspondences f q i $ q 0 i g n i =1 q i q 0 i [ Methods : SIFT, SURF, … ] F. Brunet, A. Bartoli, R. Malgouyres, and N. Navab

  7. The feature-based approach The parameters p * of the transformation are computed from the point correspondences n X p ¤ = arg min i k 2 kW ( q i ; p ) ¡ q 0 p i =1 W ( ¢ ; p ¤ ) F. Brunet, A. Bartoli, R. Malgouyres, and N. Navab

  8. The feature-based approach Response • Variants Response – Robustness Error Error n X ½ ( W ( q i ; p ) ¡ q 0 min i ; ° ) p i =1 – Regularization ° ° Z n 2 2 X X ° ° @ 2 W i ° ° ½ ( W ( q i ; p ) ¡ q 0 min i ; ° ) + ¸ @ q 2 ( q ; p ) d q ° ° p Ð i =1 i =1 F. Brunet, A. Bartoli, R. Malgouyres, and N. Navab

  9. The direct approach X p ¤ = arg min k S ( q ) ¡ T ( W ( q ; p )) k 2 p q 2 R Color S ( q ) Color T ( W ( q ; p )) F. Brunet, A. Bartoli, R. Malgouyres, and N. Navab

  10. Problem: the hyperparameters • What are the hyperparameters? n X ½ ( W ( q i ; p ) ¡ q 0 min i ; ° ) + ¸ R ( p ) p i =1 F. Brunet, A. Bartoli, R. Malgouyres, and N. Navab

  11. The hyperparameters Determining the hyperparameters is mandatory! Source image Not enough Number of Target image control points Too much F. Brunet, A. Bartoli, R. Malgouyres, and N. Navab

  12. The hyperparameters Determining the hyperparameters is mandatory! Source image Too low M-estimator Target image threshold Too high F. Brunet, A. Bartoli, R. Malgouyres, and N. Navab

  13. The hyperparameters Determining the hyperparameters is mandatory! Source image Too low Regularization Target image parameter Too high F. Brunet, A. Bartoli, R. Malgouyres, and N. Navab

  14. Determining the hyperparameters • How can we determine the hyperparameters? n X ½ ( W ( q i ; p ) ¡ q 0 min i ; ° ) + ¸ R ( p ) p ; ¸ ; ° ;::: i =1 F. Brunet, A. Bartoli, R. Malgouyres, and N. Navab

  15. Determining the hyperparameters • Classical approach ¸ ? ; ° ? ; : : : = arg min ¸ ; ° ;::: C ( ¸ ; ° ; : : : ) n X ½ ( W ( q i ; p ) ¡ q 0 i ; ° ? ) + ¸ ? R ( p ) min p i =1 F. Brunet, A. Bartoli, R. Malgouyres, and N. Navab

  16. Cross Validation • A common approach : Cross Validation – Measures the ability of « generalizing the data » – Divide the dataset into a training set and test set • Drawbacks – Computation time – Only use the data of the problem (here, the point correspondences) F. Brunet, A. Bartoli, R. Malgouyres, and N. Navab

  17. Other criteria • Mallow’s Cp • Akaike Information Criterion (AIC) • Bayesian Information Criterion (BIC) • Minimum Description Length (MDL) • … • Always the same problem: only use the point correspondences F. Brunet, A. Bartoli, R. Malgouyres, and N. Navab

  18. Our approach • Use all the available information: – The point correspondences – And the pixel colors • Point correspondences: training set • Colors: test set F. Brunet, A. Bartoli, R. Malgouyres, and N. Navab

  19. Our approach n X 1 kS ( q ) ¡ T ( W ( q ; p ¸ ; ° ;::: )) k 2 C ( ¸ ; ° ; : : : ) = j R j i =1 X p ¤ = arg min k S ( q ) ¡ T ( W ( q ; p )) k 2 p q 2 R F. Brunet, A. Bartoli, R. Malgouyres, and N. Navab

  20. Experimental results F. Brunet, A. Bartoli, R. Malgouyres, and N. Navab

  21. Experimental results Geometric error (with respect to the ground truth) Geometric error Geometric error F. Brunet, A. Bartoli, R. Malgouyres, and N. Navab

  22. Experimental results

  23. Experimental results Criterion Geometric error VCV 1,852% VCV (robust) 0,675% Our criterion 0,190% Our criterion (robust) 0,197% F. Brunet, A. Bartoli, R. Malgouyres, and N. Navab

  24. Experimental results

  25. Conclusion • Importance of the hyperparameters and of their selection • New criterion that uses all the available information – May be seen as a combination of the feature-based and the direct approaches to image registration • What’s next? – How can we optimize the proposed criterion? F. Brunet, A. Bartoli, R. Malgouyres, and N. Navab

  26. Thank you!

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