Image Registration using Mutual Information

1
Multi-Modal Image RegistrationGauge Co-ordinate
Mutual Information
Phil Legg School of Computer Science Cardiff
University
2
Contents

• Introduction
• Mutual Information
• Gauge Co-ordinates Feature Derivatives
• Incorporating Features with Mutual Information
• Results
• Future Work

3
Introduction

• My Aim Successfully register multi-modal images.
  (e.g. Retinal images)?

4
What is the problem?

• Images of different modalities may have little or
  no distinct intensity relationship.
• Many possible transformation to be considered
• Translation
• Rotation
• Scale

5
Introduction to Mutual Information

• A comparison of statistical dependence between
  two images by measuring the spread of data.
• Essentially a measure of how well one image
  predicts the other.
• Allows mapping of different intensities for
  feature representation.
• Ideal for Multi-Modal images.

6
Mutual Information Formula
I(A,B) H(A) H(B) - H(A,B)?

• H(A) entropy of template
• H(B) entropy of overlap ref. image
• H(A,B) joint entropy
• We wish to maximise I(A,B) to find the most
  suitable registration.

7
Problem?

• Mutual Information gives poor results for our
  data...
• Intensity relationship is too weak for MI to cope
  with
• Little spatial information considered by MI

8
Successful Results
9
Unsuccessful Results
10
Gauge Co-ordinates

• An alternate co-ordinate frame that is transform
  invariant.
• Each pixel now has gradient information that
  gives spatial relation

11
Gauge Co-ordinates

• We can take derivatives of an image using this
  new co-ordinate frame.
• Can take derivatives of w and/or v, at multiple
  scales.
• Higher order derivatives can be found by simple
  recursion

12
Gauge Co-ordinates
Lw
Original
Scale 2
Lwww
LwL2w
Scale 4
Scale 2
13
Incorporating Features with MI

• We adapt the method proposed by Russakoff for
  Regional MI.
• Generate intensity matrix P mxn
• m number of feature images
• n number of pixels
• Normalise P P mean(P)?
• Find Co-variance matrix C 1/N (PPT)?

14
Incorporating Features with MI

• Entropy H(c) log((2pi)d/2det(c)1/2)?
• d set of normally distributed points
• c covariance matrix
• MI H(CA) H(CB) H(C)?
• CA m/2 x m/2 sub matrix of C (top-left)?
• CB m/2 x m/2 sub matrix of C (bottom-right)?

15
Incorporating Features with MI

• Any number of feature images can be incorporated
  using this technique
• Neighbouring pixels can also be included (as
  proposed in original Regional MI)
• How do we know which features should be used?

16
Sequential Forward Search

• Determines a sub-set of elements, given a
  criteria to minimise (e.g. registration error)
• Start with empty set, select elements to add to
  set that minimise criteria

17
Sequential Forward Search
Lw
Original
Scale 2
Lwww
LwL2w
Scale 4
Scale 2
18
Transformation Search

• Image pyramid gives coarse-to-fine search
  approach
• Simplex algorithm used to find optimal
  translation
• Rotation and scale occur within fixed range
• search all possible values at coarse level then
  refine through each pyramid level.

19
Results
20
Results
21
Further Work

• Registration improvements
• High accuracy achieved for clinical use
• But... runtime issues, and the need for feature
  set training
• Segmentation of Optic Nerve Head
• Can multi-modal registration help aid
  segmentation?

22
Thank you for listening.Questions?