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
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
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
Project 1 questions

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Last time: projection
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)
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?
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
Projection matrix ( t in book’s notation) translation rotation projection intrinsics

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Projection matrix 0 = (in homogeneous image coordinates)
Perspective distortion What does a sphere project to? Image source: F. Durand

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Perspective distortion What does a sphere project to?
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
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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