Date post: | 21-Dec-2015 |
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Active Appearance Models
• Suppose we have a statistical appearance model– Trained from sets of examples
• How do we use it to interpret new images?
• Use an “Active Appearance Model”
• Iterative method of matching model to image
Quality of Match
• Residual difference:
• p : all parameters, eg
• Ideally find and optimise p(p|r)
• Cannot usually know p(r)
)()()( pIpIpr imm
)()()( prprp TE
),,,,( sYX cccp
)(
)()|()|( :rule Bayes
r
pprrp
p
ppp
Quality of Match
• Usually attempt to maximise
• This is equivalent to maximising
• Which is equivalent to minimising
)()|( ppr pp
)(log)|)((log pppr pp
)(log))((log)( pprp ppE
Quality of Match
• Assuming independent gaussian noise:
22
)()(exp))((
r
T
p
prprpr
constpr
T
22
)()())((log
prpr
pr
constpEr
)(log2
|)(|)(
2
2
ppr
p
Quality of Match
• If we assume all parameters equally likely (within certain limits)
• Thus we need to find the parameters which minimise the sum of squares of residuals,
constEr
2
2
2
|)(|)(
pr
p
constp )(p
2|)(|)( prp E
Quality of Match
• If we assume parameters have a gaussian distribution,
• We must then minimise
)5.0exp()( 1pSpp Tp
pSppr
p 12
2
5.02
|)(|)( T
r
E
Optimising the Match
• We must find p to minimise E(p)
• p may have many (100’s) of dimensions
• Can put into a multi-dimensional optimiser– Likely to be rather slow
• We can use some cunning approximations to find good solution rapidly
Learning the Relationship
• For each of a training set
– find best fit given landmarks, p
– randomly perturb p by p and measure
(in model frame)
• Multivariate regression to learn R in
)()()( ppIpIppr imm
)( ppRrp
AAM Algorithm
• Initial estimate Im(p)
• Start at coarse resolution
• At each resolution
– Measure residual error, r(p)
– predict correction p = Rr
– p p - p
– repeat to convergence
Search Accuracy (Brain images)
• Leave-1-out search experiments– For each image in training set:
• Train model on all current image,
• test on that image
– average results over all images
0
10
20
30
40
50
0 1 2 3 4 5
Point-Curve Error (pixels)
Fre
qu
en
cy
(%
)
Examples of Failure
• Poor initialisation can lead to failure
• Only samples current region– may not cover full extent of target
Higher Dimensional Images
• 3D
• 2D+time
• 3D+time
• ASM relatively straightforward
• AAM – problems with size of models
Problems
• Automatic Model Building– Require correspondences across a set– Hard to achieve reliably– Human interaction can impart expert
knowledge
Problems
• Reliable measure of quality of fit– Necessary for good matching– Essential for detection (eg is object present at
all?)– RMS of residual too sensitive to positional
errors
• Model initialisation– Getting good initial estimate can be hard