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

2. Into Water Through Flat Window /192

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

4. 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 /194

5. radial distortion, e.g. in a water tank Prior Art- a Single Viewpoint Model Treibitz, Schechner & Singh, Flat Refractive Geometry /195 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

6. interface apparent viewpoint? Single Viewpoint? No! Treibitz, Schechner & Singh, Flat Refractive Geometry physical lens position 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 /196

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

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

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

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

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

13. Result- a Ray Map fdCalibration Distance Session 26.4mm7.4cm37cm1 24.3mm7.9cm48cm2 58mm4.2cm78cm3 Applications: Stereo Measurements Geometrical applications Imaging System /1913

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

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

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

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

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

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