360 x 360 Mosaics Shree K. Nayar and Amruta Karmarkar Computer Science Department Columbia University IEEE CVPR Conference June 2000, Hilton Head Island,

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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 Compute a High Resolution Mosaic

Spherical Mosaics from Strips Unit Sphere : Spherical Panorama : x y z Strip Half - Strip Rotation from Correspondences: k k

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

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

Minimum Compression

Spherical Mosaic From Strips 700 pixels (8 pixels per deg.)

Spherical Mosaics from Slices Unit Sphere : Spherical Panorama : x y z Slice Half - Slice

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

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 :

Deriving Sheet Cameras : Formulation Differential Equation : Mirror Shape :

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

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

360 Sheet Camera Rotation

360 x 360 Spherical Mosaic

Reconstruction of Step Edge edge 1 Pixel Disc 4 Pixel Disc

360 x 360 Stereo Mosaics Slice Camera Rotation : b / 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

Left Panorama Right Panorama

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

Stereoscopic Panorama

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