aam lecture

8/13/2019 Aam Lecture

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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


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Interpreting Images (1)

Place model

in imageMeasure

DifferenceUpdate Model

Iterate


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Quality of Match

Residual difference:

p: all parameters, eg

Ideally find and optimisep(p|r)

Cannot usually knowp(r)

)()()( pIpIpr imm

)()()( prprp

T

E

),,,,( sYX cccp

)(

)()|()|(:ruleBayes

r

pprrp

p

ppp


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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


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Quality of Match

Assuming independent gaussian noise:

22

)()(

exp))((r

T

p

prpr

pr

constpr

T

22

)()())((log

prprpr

constpEr

)(log2

|)(|)(

2

2

ppr

p


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Quality of Match

If we assume parameters have a gaussian

distribution,

We must then minimise

)5.0exp()( 1pSpp T

p

pSppr

p 1

2

2

5.02

|)(|)( T

r

E


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Optimising the Match

We must find pto minimiseE(p)

pmay have many (100s) 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


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Key Insight

Image error related to error in p


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Learning the Relationship

For each of a training set

find best fit given landmarks, p

randomly perturb pby p and measure

(in model frame)

Multivariate regression to learn Rin

)()()( ppIpIppr imm

)( ppRrp


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More Analytic Approach

pp

rprppr

)()(

rrEppT,minimizeTo )E(

TT

p

r

p

r

p

rR

1

)( pRrp


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How Good are the Predictions?

Predicted xvs. actual x over test set


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Multi-Resolution Predictions

Predicted xvs. actual x over test set


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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


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Search Example


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Search Example


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Search Example


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Search Example


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Sub-cortical Structures

Initial Position Converged


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Sub-cortical Structures

Initial Position Converged


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Brain search


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Examples of Failure

Poor initialisation can lead to failure

Only samples current region

may not cover full extent of target


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MR Knee Cartilage


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Higher Dimensional Images

3D

2D+time

3D+time

ASM relatively straightforward

AAMproblems with size of models


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Problems

Automatic Model Building

Require correspondences across a set

Hard to achieve reliably

Human interaction can impart expert

knowledge


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Correspondence Important

Manual Annotation Equally spaced points


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Problems

Reliable measure of quality of fit

Necessary for good matching

Essential for detection (eg is object present atall?)

RMS of residual too sensitive to positional

errors Model initialisation

Getting good initial estimate can be hard


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Problems

Failures to match at edges of model

Perhaps need some model of whole image

Multiple initialisations can help

Model explains region under itself very

well, but fails to explain all it could.

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