lec05_projection - CS6670:ComputerVision NoahSnavely...

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Lecture 5: Projection CS6670: Computer Vision Noah Snavely
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Projection Reading: Szeliski 2.1
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Projection Reading: Szeliski 2.1
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Müller Lyer Illusion http://www.michaelbach.de/ot/sze_muelue/index.html
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Modeling projection The coordinate system We will use the pin hole model as an approximation Put the optical center ( C enter O f P rojection) at the origin Put the image plane ( P rojection P lane) in front of the COP Why? The camera looks down the negative z axis we need this if we want right handed coordinates
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Modeling projection Projection equations Compute intersection with PP of ray from (x,y,z) to COP Derived using similar triangles (on board) We get the projection by throwing out the last coordinate:
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Homogeneous coordinates Is this a linear transformation? Trick: add one more coordinate: homogeneous image coordinates homogeneous scene coordinates Converting from homogeneous coordinates no—division by z is nonlinear
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Perspective Projection Projection is a matrix multiply using homogeneous coordinates: divide by third coordinate This is known as perspective projection The matrix is the projection matrix Can also formulate as a 4x4 (today’s reading does this) divide by fourth coordinate
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Perspective Projection How does scaling the projection matrix change the transformation?
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This note was uploaded on 09/27/2010 for the course CS 667 at Cornell University (Engineering School).

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lec05_projection - CS6670:ComputerVision NoahSnavely...

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