CSE 803 Fall 2009 1

2D matching part 2

• Review of alignment methods and

errors in using them

• Introduction to more 2D matching

methods

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Review of roadmap: algorithms to control matching

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Rigid transformation review

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Affine includes scaling and shear

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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

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Sources of error

* Wrong matching in the pair of points yields outlier

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2-Point alignment error due to error in locations of Q1, Q2

Plastic slides can actually be overlaid for better viewing.

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Remove outlier and refit

Plastic slides show concept better.

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Sometimes a halucination

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

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Local Feature Focus Method (Bolles)

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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

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Focus features matching attempts

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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]

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Pose clustering

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Line segment junctions for matching

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“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

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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.

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Detecting airplanes on airfield

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Airplane model of abstract vectors; detected image features

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Relational matching method

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Some relations between parts

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Recognition via consistent labeling

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Parts, labels, relations

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In a consistent labeling “image” parts relate as do “model” parts

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Distance relation often used

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What model labels apply to detected holes H1, H2, H3?

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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.

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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).

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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.

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Discrete relaxation labeling constrains possible labels

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Kleep matching via relaxation

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Removing a possible label for one part affects labels for related parts

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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.