1. Computer Vision : CISC 4/689 Going Back a little Cameras.ppt

2. Computer Vision : CISC 4/689 Applications of RANSAC: Solution for affine parameters Affine transform of [x,y] to [u,v]: Rewrite to solve for transform parameters:

3. Computer Vision : CISC 4/689 Assignment Program-1 info-Link-Link Data

4. Computer Vision : CISC 4/689 Another app. : Automatic Homography H Estimation How to get correct correspondences without human intervention? from Hartley & Zisserman

5. Computer Vision : CISC 4/689 Computing a Homography 8 degrees of freedom in 3 x 3 matrix H, so at least n = 4 pairs of 2-D points are sufficient to determine it Use same basic algorithm for P (aka Direct Linear Transformation, or DLT) to compute H –Now stacked matrix A is 2 n x 9 vs. 2 n x 12 for camera matrix P estimation because all points are 2-D 3 collinear points in either image is a degenerate configuration preventing a unique solution Lets Side-track

6. Computer Vision : CISC 4/689 Estimating H : DLT Algorithm x 0 i = Hx i is an equation involving homogeneous vectors, so Hx i and x 0 i need only be in the same direction, not strictly equal We can specify “same directionality” by using a cross product formulation: See Hartley & Zisserman, Chapter 3.1-3.1.1 (linked on course page) for details

7. Computer Vision : CISC 4/689 Texture Mapping Needed for nice display when applying transformations (like a homography H ) to a whole image Simple approach: Iterate over source image coordinates and apply x 0 = H x to get destination pixel location –Problem: Some destination pixels may not be “hit”, leaving holes Easy solution: Iterate over destination image and apply inverse transform x = H -1 x 0 –Round off H -1 x 0 to address “nearest” source pixel value –This ensures every destination pixel is filled in

8. Computer Vision : CISC 4/689 Automatic H Estimation: Feature Extraction Find features in pair of images using corner detection—e.g., eigenvalue threshold of: from Hartley & Zisserman ~500 features found

9. Computer Vision : CISC 4/689 Automatic H Estimation: Finding Feature Matches Best match over threshold within square search window (here §300 pixels) using SSD or normalized cross-correlation from Hartley & Zisserman

10. Computer Vision : CISC 4/689 Automatic H Estimation: Finding Feature Matches Best match over threshold within square search window (here §300 pixels) using SSD or normalized cross-correlation from Hartley & Zisserman

11. Computer Vision : CISC 4/689 Automatic H Estimation: Initial Match Hypotheses 268 matched features (over SSD threshold) in left image pointing to locations of corresponding right image features from Hartley & Zisserman

12. Computer Vision : CISC 4/689 Automatic H Estimation: Applying RANSAC Sampling –Size: Recall that 4 correspondences suffice to define homography, so sample size s = 4 –Choice Pick SSD threshold conservatively to minimize bad matches Disregard degenerate configurations Ensure points have good spatial distribution over image Distance measure –Obvious choice is symmetric transfer error:

13. Computer Vision : CISC 4/689 Automatic H Estimation: Outliers & Inliers after RANSAC 43 samples used with t = 1.25 pixels 117 outliers ( ² = 0.44 ) 151 inliers from Hartley & Zisserman

14. Computer Vision : CISC 4/689 A Short Review of Camera Calibration

15. Computer Vision : CISC 4/689 Pinhole Camera Terminology Camera center/ pinhole Principal point/ image center Image point Camera point Focal length Optical axis Image plane

16. Computer Vision : CISC 4/689 Calibration Slides (calibration.ppt)