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Image Registration by Information Theoretic criteria. 8002202 Digital Image Processing III Germán Gómez Herrero. Outline. What is image registration? Why is image registration important? Image registration steps Classification of image registration methods

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Image Registration by Information Theoretic criteria


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image registration by information theoretic criteria

Image Registration by Information Theoretic criteria

8002202 Digital Image Processing III

Germán Gómez Herrero

outline
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
what is image registration
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

why is it important
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
image registration steps
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

classification of image registration methods
Classification of image registration methods
  • By the nature of the images to register
    • Monomodal registration
    • Multimodal registration

Target Image: SPECT

Ref. Image: MRI

Registered: MRI + SPECT

classification of image registration methods1

Local

Original

Global

Rigid

Affine

Projective

Curved

Classification of image registration methods
  • By nature and domain of the transformation
classification of image registration methods2
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
traditional image registration criteria
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.
information theoretic criteria
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 u=R(x,y,z)

: pdf of v=T(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

information theoretic criteria1
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:
information theoretic criteria2
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.
information theoretic criteria3
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.

information theoretic criteria4
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.

information theoretic criteria5
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.

conclusions
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.
references
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.