Image Registration by Information Theoretic criteria

1
Image Registration by Information Theoretic
criteria

• 8002202 Digital Image Processing III
• Germán Gómez Herrero

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Outline

• What is image registration?
• Why is image registration important?
• Image registration steps
• Classification of image registration methods
• Traditional criteria used in image registration
• Information Theoretic criteria for image
  registration
• Conclusions

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What is image registration?

• It can be defined as the integration of the
  useful information in a set of images by means of
  spatial alignment.

Reference Image
Target Image
Registered Images
4
Why is it important?

• Image registration is needed in many image
  processing applications, e.g.
• Target recognition and localization
• Change detection
• Depth perception
• Motion estimation
• Movement artifacts correction in image sequences
• Image fusion

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Image registration steps
Ref. Image

• Preprocessing
• Image smoothing
• Deblurring
• Edge sharpening
• Segmentation
• Edge detection

Feature selection
Matching criteria

Ref. Image
Registered Images
YES
Target Image
NO
Target Image
Image transform
Resampling
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Classification of image registration methods

• By the nature of the images to register
• Monomodal registration
• Multimodal registration

Ref. Image MRI
Target Image SPECT
Registered MRI SPECT
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Classification of image registration methods

• By nature and domain of the transformation

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Classification of image registration methods

• By the features that are used for registration
• Landmark based
• Segmentation based
• Voxel values based
• Reduction to scalars/vectors (moments, principal
  axes)
• Using full image content

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Traditional image registration criteria

• Criteria for estimating the set of parameters
  describing the spatial transformation that
  ''best'' match the images together.
• A simple choice is the mean of squared difference
  between the voxel values of the two images.
• Works well when the target and reference images
  are similar.
• Unsuitable for multimodal registration.

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Information Theoretic criteria

• Notation
• Voxel gray value at point (x,y,z) of the
  reference image R
• Voxel gray value at point (x,y,z) of the
  target image T
• pdf of uR(x,y,z)
• pdf of vT(x,y,z)
• Joint pdf of u and v when the two images
  are registered
• Joint pdf of u and v when the
  transformation given by the parameters
  is applied to the target image.
• Optimum registration parameters

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Information Theoretic criteria

• By defining a suitable similarity (distance)
  measure D between two pdfs we can achieve the
  registration by
• A suitable distance measure is the
  Kullback-Leibler divergence

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Information Theoretic criteria

• Thus, if we know the joint pdf of the
  images voxel values when they are registered
• However, most of the times is unknown.

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Information Theoretic criteria

• When a prior estimation of is not
  available, an alternative approach for image
  registration is to require that should
  be different from unexpected prior pdfs as much
  as possible in the Kullback-Leibler sense 3,
  i.e.
• where is the unexpected prior.

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Information Theoretic criteria

• It is very undesirable that is uniform,
  i.e.
  ,where is constant. This leads us to the
  following registration contrast
• which is equivalent to minimizing the joint
  entropy of the reference and target image.

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Information Theoretic criteria

• A second undesirable pdf relationship would be
  represented by the case in which the voxel values
  in two images are independent, i.e.
• which is equivalent to maximizing the mutual
  information between the reference and the target
  image.

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Conclusions

• Multimodal full-volume voxel-values based image
  registration requires similarity measures able to
  account for very subtle relationships between the
  reference and target images.
• Information Theory provides a flexible framework
  for defining such similarity measures.
• It is crucial to find fast, accurate, smooth
  estimators of information theoretic contrasts.

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References

• 1 J. B. A. Maintz and M. A. Viergever, A
  survey on medical image registration,'' Medical
  Image Analysis, vol. 2, pp. 1-36, 1998.
• 2 R. Frackowiak, K. Friston, C. Frith,
  R. Dolan, C. Price, J. Ashburner, W. Penny, and
  S. Zeki, Human Brain Function. Academic Press,
  2003.
• 3 Y.-M. Zhu, Volume image registration by
  cross-entropy optimization,'' IEEE Transactions
  on Medical Imaging, vol. 21, no. 2, pp. 174-180,
  2002.