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2D matching part 2. Review of alignment methods and errors in using them Introduction to more 2D matching methods. Review of roadmap: algorithms to control matching. Rigid transformation review. Affine includes scaling and shear. Problems with error.

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2d matching part 2

2D matching part 2

  • Review of alignment methods and
  • errors in using them
  • Introduction to more 2D matching
  • methods

CSE 803 Fall 2009

problems with error
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

sources of error
Sources of error

* Wrong matching in the pair of points yields outlier

CSE 803 Fall 2009

2 point alignment error due to error in locations of q1 q2
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

remove outlier and refit
Remove outlier and refit

Plastic slides show concept better.

CSE 803 Fall 2009

sometimes a halucination
Sometimes a halucination

6 points match, but the objects do not. Can verify using more model points.

CSE 803 Fall 2009

local focus feature matching
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

pose clustering generalized hough transform
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

slide14

Pose clustering

CSE 803 Fall 2009

abstract vectors subtending detected junctions
“Abstract vectors” subtending detected junctions

MAP

IMAGE

Abstract vector with tail at T and tip at Y, or tail at L and tip at X

CSE 803 Fall 2009

parameter space resulting from 10 vector matches
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

parts labels relations
Parts, labels, relations

CSE 803 Fall 2009

partial interpretation tree to find a distance consistent labeling
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

detailed it algorithm
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

discrete relaxation labeling constrains possible labels
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

relaxation labeling
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.

CSE 803 Fall 2009