image formation ii chapter 2 (r. szelisky) · image formation ii chapter 2 (r. szelisky) guido...
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Image Formation IIChapter 2 (R. Szelisky)
Guido GerigCS 6320 Spring 2012
Acknowledgements: • Slides used/modified from Prof. Trevor Darrell
([email protected]) (http://www.eecs.berkeley.edu/~trevor/CS280.html)
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Recall, perspective effects…
• Far away objects appear smaller
Forsyth and Ponce
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Perspective effects
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Perspective effects
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Perspective effects
• Parallel lines in the scene intersect in the image
• Converge in image on horizon lineImage plane(virtual)
Scene
pinhole
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Projection properties
• Many-to-one: any points along same ray map to same point in image
• Points ? – points
• Lines ?– lines (collinearity preserved)
• Distances and angles are / are not ?preserved– are not
• Degenerate cases:– Line through focal point projects to a point.– Plane through focal point projects to line– Plane perpendicular to image plane projects to
part of the image.
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Weak perspective
• Approximation: treat magnification as constant
• Assumes scene depth << average distance to camera
World points:
Image plane
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Orthographic projection
• Given camera at constant distance from scene
• World points projected along rays parallel to optical access
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2D
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3D
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Other types of projection
• Lots of intriguing variants…• (I’ll just mention a few fun ones)
S. Seitz
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360 degree field of view…
• Basic approach– Take a photo of a parabolic mirror with an orthographic lens
(Nayar)– Or buy one a lens from a variety of omnicam manufacturers…
• See http://www.cis.upenn.edu/~kostas/omni.html
S. Seitz
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Tilt-shift
Titlt-shift images from Olivo Barbieriand Photoshop imitations
http://www.northlight-images.co.uk/article_pages/tilt_and_shift_ts-e.html
S. Seitz
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tilt, shift
http://en.wikipedia.org/wiki/Tilt-shift_photography
wikipedia http://www.luminous-landscape.com/tutorials/focusing-ts.shtml
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Tilt-shift perspective correction
http://en.wikipedia.org/wiki/Tilt-shift_photography
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normal lens tilt-shift lens
http://www.northlight-images.co.uk/article_pages/tilt_and_shift_ts-e.html
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Rollout Photographs © Justin Kerr http://research.famsi.org/kerrmaya.html
Rotating sensor (or object)
Also known as “cyclographs”, “peripheral images”S. Seitz