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360 x 360 Mosaics

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. Goal. Easy Capture Process Use a Low Resolution CCD

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360 x 360 Mosaics

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

  4. Capturing 360 Degree Strips Fish Eye Lens : Catadioptric Imaging : 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. pixel image plane c mirror z (r) Resolution of Camera + Lens Resolution of Complete System viewpoint Resolution of a Catadioptric System ( Baker & Nayar 98 )

  6. Minimum Compression

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

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

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

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

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

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

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

  14. 360 Sheet Camera Rotation

  15. 360 x 360 Spherical Mosaic

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

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

  18. Left Panorama Right Panorama

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

  20. Stereoscopic Panorama

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

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