lec06_alignment

lec06_alignment - CS6670:ComputerVision NoahSnavely...

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Lecture 6: Image transformations and alignment CS6670: Computer Vision Noah Snavely
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Announcement New TA! Adarsh Kowdle Office hours: M 11 12, Ward Laboratory 112
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Announcements Project 1 out, due Thursday, 9/24, by 11:59pm Quiz on Thursday, first 10 minutes of class Next week: guest lecturer, Prof. Pedro Felzenszwalb, U. Chicago
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Announcements Project 2 will be released on Tuesday You can work in groups of two Send me your groups by Friday evening
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Readings Szeliski Chapter 3.5 (image warping), 9.1 (motion models)
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Announcements A total of 3 late days will be allowed for projects
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Project 1 questions
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Last time: projection
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Perspective projection Projection is a matrix multiply using homogeneous coordinates: divide by third coordinate Equivalent to:
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Perspective projection (intrinsics) in general, : aspect ratio (1 unless pixels are not square) : skew (0 unless pixels are shaped like rhombi/parallelograms) : principal point ((0,0) unless optical axis doesn’t intersect projection plane at origin) (upper triangular matrix) (converts from 3D rays in camera coordinate system to pixel coordinates)
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Extrinsics How do we get the camera to “canonical form”? (Center of projection at the origin, x axis points right, y axis points up, z axis points backwards) 0 Step 1: Translate by c
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Extrinsics How do we get the camera to “canonical form”? (Center of projection at the origin, x axis points right, y axis points up, z axis points backwards) 0 Step 1: Translate by c How do we represent translation as a matrix multiplication?
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Extrinsics How do we get the camera to “canonical form”? (Center of projection at the origin, x axis points right, y axis points up, z axis points backwards) 0 Step 1: Translate by c Step 2: Rotate by R 3x3 rotation matrix
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Extrinsics How do we get the camera to “canonical form”? (Center of projection at the origin, x axis points right, y axis points up, z axis points backwards) 0 Step 1: Translate by c Step 2: Rotate by R
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Projection matrix ( t in book’s notation) translation rotation projection intrinsics
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Projection matrix 0 = (in homogeneous image coordinates)
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Perspective distortion What does a sphere project to? Image source: F. Durand
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Perspective distortion What does a sphere project to?
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Distortion Radial distortion of the image Caused by imperfect lenses Deviations are most noticeable for rays that pass through the edge of the lens No distortion Pin cushion Barrel
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Correcting radial distortion from Helmut Dersch
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Modeling distortion To model lens distortion Use above projection operation instead of standard projection matrix multiplication Apply radial distortion Apply focal length translate image center Project to “normalized” image coordinates
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Other types of projection Lots of intriguing variants… (I’ll just mention a few fun ones)
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This note was uploaded on 09/27/2010 for the course CS 667 at Cornell.

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lec06_alignment - CS6670:ComputerVision NoahSnavely...

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