1. CS 223b Assignment 2: Review Vaibhav Vaish Escher: Looking inside “Another World”

2. Harris Corner Detection: Demo

3. Harris Corner Detection If we shift the image, do the corners shift by the same amount ?

4. Camera Calibration: What is it ? Given a (3D) point, what is the location of its (2D) projection in the camera ? (X,Y,Z) (x,y)

5. Perspective Camera: 3x4 matrix Pixel coordinates: (x/w, y/w) This can be shown from the lecture notes You can refer to the text for more details … … but is not really needed for this homework.

6. Affine Camera Not as accurate as perspective model … … but much simpler!

7. Affine Camera No division involved … linear relation Proof: see Multiple View Geometry, Ch 5, by Hartley and Zisserman if interested

8. Step 1: Locate feature points Harris corners Stanford Calibration Grid Detector – For Linux (vine.stanford.edu) only!

9. Step 2: Get Correspondences Associate grid corners (x i, y i ) with 3D coordinates (X i, Y i, Z i ) – Mismatches can be fatal

10. Step 3: Set up system of equations Ax = b x : unknown entries of camera matrix A : depends on 3D coordinates b: depends on corner coordinates Question: What are the sizes of A, x, b ?

11. Step 4: Solve it Ax = b Find x * which minimizes the squared error ||Ax – b|| 2 In Matlab: x * = A \ b

12. Step 4.1: Debug it How do we check if the calibration parameters are “correct” ? – Look at the average error ||Ax – b|| – Test the camera matrix on some 3D points and compare with the actual images Common Bugs: – Mismatch between features and 3D points – Incorrect 3D coordinates

13. A Cube in Perspective Belvedere M. C. Escher, 1958