Improving Entropy Registration

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Improving Entropy Registration

• Theodor D. Richardson

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Preliminary Results
Original Rotation 12 Entropy Result
-11 Segmented Entropy Result -13
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The Basic Concepts of Entropy

• Each pixel (or voxel) has a probability of
  occurrence, pnlog(pn)
• These probabilities make up an entropy for the
  image, H(N) where n is the image
• H(N) -?pnlog(pn)

n ? N
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Comparing Entropies

• Two images with entropies H(M) and H(N) will have
  a mutual or joint entropy H(M, N) when they are
  overlaid
• H(M,N) - ??pm, nlog(pm,n)
• This is a volume of overlap

n ? N
m ? M
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Comparing Entropies

• The sum of marginal entropies for this is I(M,N)
  H(M) H(N) H(M,N)
• Maximizing the value of the marginal entropies is
  the goal of this algorithm this means that the
  two images will have the most features in common

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Problems with the Entropy Algorithm

• Noise changes probability of intensities, causing
  misread results
• Background of image may be a factor in alignment
  when it should be invariant to background

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Estimating Entropies

• The entropy of a pixel can be estimated by the
  histogram intensity over the total number of
  pixels in the image.
• A frequently occurring pixel has less likelihood
  of being aligned perfectly than a rarely
  occurring pixel
• These values can be weighted by 1 p(n) where n
  is the pixel intensity

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Simple Segmentation Algorithm

• The problems with entropy may be helped by
  segmenting the image first.
• This can remove background noise by eliminating
  the noisy region
• Watershed method was first attempted, but the
  gathered regions were too small

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Simple Segmentation Algorithm

• New segmentation algorithm based on
  region-growing from input parameters.

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Simple Segmentation Algorithm

• Find regions of image with desired intensity
  within tolerance bounds
• Create edges from connecting pixels to expand
  regions
• Select largest region
• Optionally enclose region
• Create mask over image

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Simple Segmentation Algorithm

• Mask examples

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Simple Segmentation Algorithm

• Regions outside of the mask are given a
  probability of 0 and are not counted in total
  pixels

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Simple Segmentation Algorithm

• Intensity shift can adapt this segmentation
  method to intensity comparison alignments

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Basic Entropy Algorithm

• The entropy (mutual information) alignment
  algorithm for this project makes the assumption
  that the image is centered already
• This alignment algorithm focuses only on
  maximizing global mutual information

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Basic Entropy Algorithm

• Create image mask of probabilities for template
  and comparison images
• Rotate comparison image through 360 degrees by
  Affine Transformation of rotation around
  z-axiscos T sin T 0 0- sin T cos T
  0 00 0 1 00 0 0 1
• If pixel probabilities are within tolerance, add
  to volume
• Maximum volume is maximum mutual information

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Results

• The following is a sample of the results of the
  entropy algorithm with and without segmentation

Original Rotation 29 Entropy Result
-25 Segmented Entropy -28
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Problems

• This entropy algorithm is not the most robust
  available some use local entropy within the
  global information and some normalize the
  registration volume
• The assumption of a centered image is not valid
  for most images
• This entropy algorithm does not involve
  normalizing the joint entropy with the overall
  entropy

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Possible Future Research

• Expand the application of the Simple Segmentation
  Algorithm to other registration techniques
• Experiment further with different mutual
  information algorithms and different segmentation
  algorithms