1. Image Primitives and Correspondence
Jana Kosecka
George Mason University

2. Image Primitives and Correspondence
Given an image point in left image, what is the (corresponding) point in the right
image, which is the projection of the same 3-D point
ICRA 2003

3. Matching - Correspondence
Lambertian assumption
Rigid body motion
Correspondence
ICRA 2003

4. Local Deformation Models
Translational model
Affine model
Transformation of the intensity values and occlusions
ICRA 2003

5. Feature Tracking and Optical Flow
Translational model
Small baseline
RHS approx. by first two terms of Taylor series
Brightness constancy constraint
ICRA 2003

6. Aperture Problem
Normal flow
ICRA 2003

7. Optical Flow
Integrate around over image patch
Solve
ICRA 2003

8. Optical Flow, Feature Tracking
Conceptually:
rank(G) = 0 blank wall problem
rank(G) = 1 aperture problem
rank(G) = 2 enough texture – good feature candidates
In reality: choice of threshold is involved
ICRA 2003

9. Optical Flow Previous method - assumption locally constant flow
Alternative regularization techniques (locally smooth flow fields,
integration along contours)
Qualitative properties of the motion fields
ICRA 2003

10. Feature Tracking
ICRA 2003

11. 3D Reconstruction - Preview
ICRA 2003

12. Point Feature Extraction
Compute eigenvalues of G
If smalest eigenvalue  of G is bigger than  - mark pixel as candidate
feature point
Alternatively feature quality function (Harris Corner Detector)
ICRA 2003

13. Harris Corner Detector - Example
ICRA 2003

14. Wide Baseline Matching
ICRA 2003

15. Region based Similarity Metric
Sum of squared differences
Normalize cross-correlation
Sum of absolute differences
ICRA 2003

16. Edge Detection Canny edge detector Compute image derivatives
original image
gradient magnitude
Canny edge detector
Compute image derivatives
if gradient magnitude >  and the value is a local maximum along gradient
direction – pixel is an edge candidate
ICRA 2003

17. Line fitting Edge detection, non-maximum suppression  x y
Non-max suppressed gradient magnitude
Edge detection, non-maximum suppression
(traditionally Hough Transform – issues of resolution, threshold
selection and search for peaks in Hough space)
Connected components on edge pixels with similar orientation
- group pixels with common orientation
ICRA 2003

18. Line Fitting second moment matrix associated with each
connected component
Line fitting Lines determined from eigenvalues and eigenvectors of A
Candidate line segments - associated line quality
ICRA 2003