MIT 6 891 - Computer Vision and Applications (107 pages)

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Computer Vision and Applications



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Computer Vision and Applications

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Lecture Notes


Pages:
107
School:
Massachusetts Institute of Technology
Course:
6 891 - Advanced Topics in Theoretical Computer Science

Unformatted text preview:

6 891 Computer Vision and Applications Prof Trevor Darrell Lecture 2 Linear Filters and Convolution review Fourier Transform review Sampling and Aliasing review Readings F P Chapter 7 1 7 6 1 Recap Cameras lenses and calibration Last time Camera models Projection equations Calibration methods Images are projections of the 3 D world onto a 2 D plane 2 Recap pinhole perspective Pinole camera model box with a small hole in it Perspective projection x y Forsyth Ponce x z y f z f 3 Recap Intrinsic parameters x y cot 6 u0 z z y v0 v sin 6 z u Using homogenous coordinates we can write this as u or v 1 1 p z 1 0 z 0 cot 6 u0 v0 sin 6 0 1 K 0 x 0 y 0 z 0 1 P4 Recap Combining extrinsic and intrinsic calibration parameters 1 p K z C P WC R W P C OW 1 p K z Forsyth Ponce Intrinsic 0 P C W R C OW 1 p P z Extrinsic P 5 Other ways to write the same equation pixel coordinates world coordinates 1 p MP z u v 1 m 1 m z m T 1 T 2 T 3 Wx W y Wz 1 z is in the camera coordinate system but we can solve for that since 1 m3 b P leading to z m1 b P u m3 b P m2 b P v m3 b P 6 m1 b P u m3 b P m2 b P v m3 b P Recap Camera calibration Stack all these measurements of i 1 n points m1 m2 ui m3 b Pi 0 vi m3 b Pi 0 into a big matrix P1T 0T u1 P1T T T T m 0 P1 v1 P1 1 m2 P T 0T u P T n n m3 n 0T P T v PT n n n 0 0 0 0 7 Today Review of early visual processing Linear Filters and Convolution Fourier Transform Sampling and Aliasing You should have been exposed to this material in previous courses this lecture is just a quick review Administrivia sign up sheet introductions 8 What is image filtering Modify the pixels in an image based on some function of a local neighborhood of the pixels 10 5 3 4 5 1 1 1 7 Local image data Some function 7 Modified image data 9 Linear functions Simplest linear filtering Replace each pixel by a linear combination of its neighbors The prescription for the linear combination is called the convolution kernel 10 5 3 4 5 1 1 1 7 Local image data 0 0 0 0 0 5 0 0 1 0 5 kernel 7



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