Flat Refractive Geometry

1. Flat Refractive Geometry Tali Treibitz, Yoav Y. Schechner Technion, Israel Hanumant Singh Woods Hole Oceanographic Institute

2. /192 Into Water Through Flat Window

3. /193 Geometrical Applications Size measurements Underwater stereo Harvey & Shortis Brandou et al.

4. /194 Prior Art- a Single Viewpoint Model Just a magnification effect: B. Skerry and H. Hall, ‘02 Webster, ‘98 Lavest et al, ECCV ‘00 scubageek.com Other diving and underwater photography literature Treibitz, Schechner & Singh, Flat Refractive Geometry

5. /195 Prior Art- a Single Viewpoint Model radial distortion, e.g. 3D distortion Harvey & Sortis, MTS J. ’02 Bryant et al, ACRA ’00 Pessel et al., WSCG ’03 Kwon & Casebolt, Sports Biomechanics ‘06 Negahdaripour & Firoozfan, IEEE J. Oceanic Eng. ’05 in a water tank Treibitz, Schechner & Singh, Flat Refractive Geometry

6. /196 Other non-single viewpoint systems: Sturm et al., Imaging beyond the pinhole camera,’06 Swaminathan et al., IJCV’06 Grossberg & Nayar, IJCV’05 Pajdla, IJCV’02 Peleg et al., PAMI’01 Single Viewpoint? No! interface physical lens position apparent viewpoint? apparent viewpoint? Treibitz, Schechner & Singh, Flat Refractive Geometry

7. /197 A Radial Distortion? No! interface single viewpoint model error distortion cannot be corrected lens visible objects are occluded errors can reach dozens of pixels Treibitz, Schechner & Singh, Flat Refractive Geometry

9. /199 air water Treibitz, Schechner & Singh, Flat Refractive Geometry

10. /1910 Prior Light Field Calibration: non-parametric • General • Used in Aquaria • Requires a few frames • Difficult outside the lab Grossberg & Nayar, IJCV ’05 Sturm & Ramalingam, ECCV ’04 Zongker et al., SIGGRAPH ’99 Fuchs et al., EGSR ’08 Kutulakos & Steger, IJCV ’07 Narashiman et al., ICCV ’05

11. Parameter Fitting /1911 known size known distance   lens measured projection Treibitz, Schechner & Singh, Flat Refractive Geometry

12. /1912 Our Calibration Method Known inputs: An underwater experiment size , distance Constraint:

13. /1913 Result- a Ray Map • Applications: • Stereo • Measurements • Geometrical applications Imaging System

14. Size Measurement From Known Distances /1914 our method ground truth single viewpoint  underestimation * not at the calibration distances Treibitz, Schechner & Singh, Flat Refractive Geometry

15. /1915 Rays in the Imaging System iris Treibitz, Schechner & Singh, Flat Refractive Geometry

16. /1916 Rays in the Imaging System iris a caustic surface Treibitz, Schechner & Singh, Flat Refractive Geometry

17. Caustics of the Flat Interface System /1917 interface a camera with a full FOV of 100° in air lens Treibitz, Schechner & Singh, Flat Refractive Geometry

18. /1918 Caustics of the Flat Interface System A closed-form solution: the system has a single viewpoint Treibitz, Schechner & Singh, Flat Refractive Geometry

19. Flat Refractive Geometry • Non-single viewpoint system • Old models  significant errors • Correct physics-based model & caustics • Calibration of true geometry: accurate, practical, in-situ Tali Treibitz, Yoav Y. Schechner & Hanumant Singh