Upload
kelly-glenn
View
220
Download
0
Tags:
Embed Size (px)
Citation preview
CSE 803 Fall 2009 1
2D matching part 2
• Review of alignment methods and
errors in using them
• Introduction to more 2D matching
methods
CSE 803 Fall 2009 2
Review of roadmap: algorithms to control matching
CSE 803 Fall 2009 3
Rigid transformation review
CSE 803 Fall 2009 4
Affine includes scaling and shear
CSE 803 Fall 2009 5
Problems with error Least squares fitting uses n >> 3 point
pairs Significantly reduces error across field Will still be thrown off by outliers * can throw out pairs with high error and then refit * can set the “weight” of any pair to be inversely proportional to error squared
CSE 803 Fall 2009 6
Sources of error
* Wrong matching in the pair of points yields outlier
CSE 803 Fall 2009 7
2-Point alignment error due to error in locations of Q1, Q2
Plastic slides can actually be overlaid for better viewing.
CSE 803 Fall 2009 8
Remove outlier and refit
Plastic slides show concept better.
CSE 803 Fall 2009 9
Sometimes a halucination
6 points match, but the objects do not. Can verify using more model points.
CSE 803 Fall 2009 10
Local Feature Focus Method (Bolles)
CSE 803 Fall 2009 11
Local focus feature matching Local features tolerate occlusion
by other objects (binpicking problem)
Subgraph matching provides several features (distances, angles, connections, etc.)
Method can be used to support different higher level strategies and alignment parameters
CSE 803 Fall 2009 12
Focus features matching attempts
CSE 803 Fall 2009 13
Pose clustering (generalized Hough transform)
Use m minimal sets of matching features, each just enough to compute alignment
Vector of alignment parameters is put as evidence into “parameter space”
When all m units of evidence computed, examine parameter space for cluster[s]
CSE 803 Fall 2009 14
Pose clustering
CSE 803 Fall 2009 15
Line segment junctions for matching
CSE 803 Fall 2009 16
“Abstract vectors” subtending detected junctions
Abstract vector with tail at T and tip at Y, or tail at L and tip at X
MAP IMAGE
CSE 803 Fall 2009 17
Parameter space resulting from 10 vector matches
Rotation, scale, translation computed as in single match alignment. Use the cluster center to estimate best alignment parameters.
CSE 803 Fall 2009 18
Detecting airplanes on airfield
CSE 803 Fall 2009 19
Airplane model of abstract vectors; detected image features
CSE 803 Fall 2009 20
Relational matching method
CSE 803 Fall 2009 21
Some relations between parts
CSE 803 Fall 2009 22
Recognition via consistent labeling
CSE 803 Fall 2009 23
Parts, labels, relations
CSE 803 Fall 2009 24
In a consistent labeling “image” parts relate as do “model” parts
CSE 803 Fall 2009 25
Distance relation often used
CSE 803 Fall 2009 26
What model labels apply to detected holes H1, H2, H3?
CSE 803 Fall 2009 27
Partial Interpretation Tree to find a distance consistent labeling
The IT shows matching attempts that can be tried using a backtracking algorithm. If a relation fails the algorithm tries a different branch.
CSE 803 Fall 2009 28
Detailed IT algorithm
Current matching pairs can be stored in the recursive stack. If a new pair is consistent with the previous pairs, continue forward; if not, then back up (and retract the recent pairing).
CSE 803 Fall 2009 29
CSE 803 Fall 2009 30
Discrete relaxation labeling constrains possible labels
A sometimes useful method that once drew much interest (see pubs by Rosenfeld, Zucker, Hummel, etc.) The Marr-Poggio stereo matching algorithm has the character of relaxation.
CSE 803 Fall 2009 31
Discrete relaxation labeling constrains possible labels
CSE 803 Fall 2009 32
Kleep matching via relaxation
CSE 803 Fall 2009 33
Removing a possible label for one part affects labels for related parts
CSE 803 Fall 2009 34
Relaxation labeling Can work truly in parallel Pairwise constraints are weaker than
what the IT method can check, so sometimes the IT must follow the relaxation method
There is “probabalistic relaxation” which changes probability of labels rather than just keeping or deleting them
Relaxation was once thought to model human visual processes.