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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

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slide1

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

slide2
Goal
  • Easy Capture Process
  • Use a Low Resolution CCD
  • Compute a High Resolution Mosaic
spherical mosaics from strips

k+1

Rotation from Correspondences:

Spherical Mosaics from Strips

Spherical Panorama :

Unit Sphere :

z

Strip

Half - Strip

180

k

y

x

0

360

capturing 360 degree strips
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

resolution of a catadioptric system

pixel

image plane

c

mirror z (r)

Resolution of

Camera + Lens

Resolution of

Complete System

viewpoint

Resolution of a Catadioptric System

( Baker & Nayar 98 )

spherical mosaic from strips

180

700

pixels

(8 pixels

per deg.)

0

360

Spherical Mosaic From Strips
spherical mosaics from slices
Spherical Mosaics from Slices

Spherical Panorama :

Unit Sphere :

z

Slice

Half - Slice

180

y

x

0

360

high resolution slices

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

deriving sheet cameras formulation

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

360 slice cameras

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

variants folded slice cameras

paraboloid

mirror

ellipsoidal

mirror

parallel sheet

parallel sheet

hat-shapped

mirror

conical

mirror

camera

camera

Variants : Folded Slice Cameras
reconstruction of step edge
Reconstruction of Step Edge

1 Pixel Disc

4 Pixel Disc

edge

360 x 360 stereo mosaics

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 :

slide18

Left Panorama

Right Panorama

summary

Catadioptrics: Solid Angles to Image Areas

Summary
  • 360 x 360 Spherical Mosaics
  • Regular and Stereo
  • High Resolution Slice Cameras