1. 360 x 360 Mosaics Shree K. Nayar and Amruta Karmarkar Computer Science Department Columbia University IEEE CVPR Conference June 2000, Hilton Head Island, USA Sponsors: ONR MURI, Packard Foundation

2. Goal Easy Capture Process Use a Low Resolution CCD Compute a High Resolution Mosaic

3. Spherical Mosaics from Strips Unit Sphere : Spherical Panorama : x y z Strip Half - Strip Rotation from Correspondences: k k+1 0 180 360

4. Capturing 360 Degree Strips Catadioptric Imaging : Fish Eye Lens : Examples: Rees 70, Rosendahl 83, Charles 87, Nayar 88, Yagi 90, Hong 91, Powell 95, Yamazawa 95, Bogner 95, Nalwa 96, Nayar 97, Chahl & Srinivasan 97 Examples: Wood 1906, Miyamoto 64, Hall 87, Zimmerman 93, Poelstra 96, Kuban et al. 94

5. Resolution of a Catadioptric System ( Baker & Nayar 98 ) Resolution of Complete System Resolution of Camera + Lens image plane pixel mirror z (r) viewpoint c

6. Minimum Compression

7. Spherical Mosaic From Strips 700 pixels (8 pixels per deg.) 0 180 360

8. Spherical Mosaics from Slices Unit Sphere : Spherical Panorama : x y z Slice Half - Slice 0 180 360

9. High Resolution Slices R 1 R 2 I i Image: 500 x 500 pixels Samples On Outer Ring: 1500 Pixels Samples In 6-Pixel Disc: 4500 Pixels Increase in Samples: 3 : 1 Example: d Slice Image Samples

10. Deriving Sheet Cameras : Formulation viewpoint pinhole normal image plane Mirror z(r) z r parallel sheet of rays c Perspective Projection : Local Mirror Slope : Specular Reflection :

11. Deriving Sheet Cameras : Formulation Differential Equation : Mirror Shape :

12. 360 Slice Cameras Image plane Hat mirror Parallel Sheet Rays Perspective Lens : Image plane Conical mirror Parallel Sheet Rays Telecentric Lens : Parabola

13. Variants : Folded Slice Cameras ellipsoidal mirror hat-shapped mirror camera parallel sheet paraboloid mirror conical mirror camera parallel sheet

14. 360 Sheet Camera Rotation

15. 360 x 360 Spherical Mosaic

16. Reconstruction of Step Edge edge 1 Pixel Disc 4 Pixel Disc

17. 360 x 360 Stereo Mosaics Slice Camera Rotation : b / 2 360 Slice b Left Right Left and Right Views : Stereo Panoramas: Ishiguro et al. 92, Huang and Hung 92 Peleg and Ben-Ezra 99, Shum et al. 99

18. Left Panorama Right Panorama

19. Smaller Fields of View ( Panoramas ) 0 deg. 45 deg -45 deg 640 pixels 480 pixels Increase in Resolution: 2:1

20. Stereoscopic Panorama

21. Summary 360 x 360 Spherical Mosaics Regular and Stereo High Resolution Slice Cameras Catadioptrics: Solid Angles to Image Areas