Transcript week10-matching2.ppt

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
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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
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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)
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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
MAP
IMAGE
Abstract vector with tail at T and tip at Y, or tail at L and tip at X
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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
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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.
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