Groupwise Registration ECCV 2004paper: Groupwise Diffeomorphic Nonrigid Registration for Automatic M

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Groupwise Registration ECCV 2004-paper
Groupwise Diffeomorphic Non-rigid Registration
for Automatic Model Building by Cootes,
Marsland, Twining, Smith and Taylor

• Presented by Hans Henrik Thodberg, Nov 2004

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Outline

• Motivation
• MDL
• Intuitive basis, examples
• Three formulations of MDL principle
• The ECCV-2004 Approach
• Diffeomorphic warp scheme
• Pairwise registration
• Groupwise registration
• Results
• Explorations of the methods

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Motivation

• ASM and AAM have been successful since 1992 A
  new example is recognized by bringing it in
  accordance with a previously learned statistical
  model of shape and appearance maximize
  p(example model, shape, pose) wrt shape
  pose
• But the statistical model itself is the
  bottleneck Derived from annotated examples
• We seek a (statistical) method that generates the
  model from a set of examples of which only one is
  annotated

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DefinitionThe unsupervised vision problem

• Given a set of 100 images, e.g. X-rays of bones
• Given an annotation of one example
• Annotate the other 99!
• Relevant!
• Easy for humans!
• Why is computer vision research not ambitious?

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How do we organize dataExample 1 Homology of
arm

• We prefer Darwins theory to creationism because
  it is simpler

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Example 2 How do we learn to see?
We must learn how to manage the huge amount of
visual information We organize impressions into
models, e.g. a chair
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An unusual chair.
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Example 3 Growth of human hand Tanner stages for
the Radius

• Tanner stages for the Radius

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Conclusions

• Humans learn an awful lot by studying
  collections Although we look at samples
  individually or pairwise, our brain is constantly
  seeking global models
• Challenge Map this principle to mathematical
  modeling

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Basic philosophy Minimum Description Length
(MDL)

• First formulation (Davies 2001, IPMI)
• Minimize DL(tot) DL(model) DL(dataSet
  model)wrt warping parameters
• Abandonned because DL(model) is impractical for
  PCA model
• Second formulation (Davies 2002, IEEE TMI)
• Minimize DL(dataSet model) S ?j gt?cut
  (1log ?j ) S ?j lt?cut ?j /?cut wrt warping
  parameters
• Similar to compactness of Kotcheff and Taylor
  (1998)

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MDL continued

• Third formulation (Cootes 2004, ECCV)
• Loop over examples i Maximize p(example i
  model(D\i) ) wrt warping parameters of
  example i

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The ECCV approach

• Synopsis of paper
• New formulation of MDL mentioned above
• Diffeomorphism
• Pairwise registration
• Groupwise registration
• Applications

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Notation and Pairwise registration Warping I2
to I1 by mapping X1 to X2
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Optimization Regime for Pairwise Registration
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Groupwise Registration

• The pairwise approach described above is fairly
  standard
• Now align a set S of N images
• Base it on a statistical model of the shape and
  texture
• Credo If analogous parts are warped together,
  the statistical model is simpler.
• That is, seeking simplicity (compactness) leads
  to to correspondence.
• The importance is the change from pairwise to
  groupwise definition of optimality

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Application of the third MDL formulation
Decoupling of pdfs for s and X
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Cootes choice of pdfs
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Comments to choice of pdf

• Very simple, where is the good old PCA?
• Intensity-pdf is based on simple deviation from
  mean intensity
• Location pdf is based on deviation from affine
  warp
• The only groupwise aspect is a location
  dependent normalization factor The examples can
  agree on locations where larger deviations from
  mean/affine are allowed
• Note The bending has 4 (and not 3) terms the
  mixed term should be doubled (c.f. Ruckert)

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Application to 16 brain MRI-images

• 1500 pairwise and 3000 groupwise warps
• 15 minutes on PC

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Application to 51 face imagesCrispness of modes
implies accuracy The groupwise method gives
better agreement with manual annotation than
pairwise (sd, not mean)
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Discussion

• The pdfs are very simple PCA models are likely
  to increase the power of the method
• The factor ? chosen to 1/3, normalized to number
  of terms
• Cootes is extending the method to 3D

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Exploration of the third formulation of MDL

• The Matlab implementation of MDL shape analysis
  uses second formulation DL(dataSet model)
  S ?j gt?cut (1log ?j ) S ?j lt?cut ?j /?cut
• Extra terms added to control run-away and ensure
  curvature match
• Problem Impractical for more than 50 cases

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Solution Use third formulation

• Optimization regime
• Perform standard MDL shape analysis on 24
  examples
• Freeze PCA model
• For subsequent examples maximize p(example i
  model ) wrt warping parameters of example i
• - log p(example i model ) S ?j
  gt?cut bj2/?j f Spoints k (xk xk,pred) 2
  /?cut2
• Tune f so the first 24 examples align the same
  way with the two cost functions.
• There are 64 points, so 128 degrees of freedom in
  second term, but they are far from uncorrelated.
• There are typically 8 large eigenvalues (first
  term)
• Empirically f is tuned so that the second term is
  larger than the first, i.e. the second term is
  the most important
• Note The PCA could be re-estimated to close the
  loop