computer vision : cisc 4/689 going back a little cameras.ppt
TRANSCRIPT
Computer Vision : CISC 4/689
Going Back a little
• Cameras.ppt
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:
Computer Vision : CISC 4/689
Assignment
• Program-1
• info-Link
• Data
Computer Vision : CISC 4/689
Another app. : Automatic Homography H Estimation
• How to get correct correspondences without human intervention?
from Hartley & Zisserman
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 2n x 9 vs. 2n 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
Computer Vision : CISC 4/689
Estimating H: DLT Algorithm
• x0i = Hxi is an equation involving homogeneous vectors, so Hxi
and x0i 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
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 x0 = 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
x0 – Round off H-1
x0 to address “nearest” source pixel value– This ensures every destination pixel is filled in
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
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
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
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
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:
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 inliersfrom Hartley & Zisserman
Computer Vision : CISC 4/689
A Short Review of Camera Calibration
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
Computer Vision : CISC 4/689
Calibration
• Slides (calibration.ppt)