Wanlin Zhu, Tianzi Jiang, and Xiaobo Li

1
Segmentation of Brain MR Images Using J
Divergence Based Active Contour Models

• Wanlin Zhu, Tianzi Jiang, and Xiaobo Li
• Medical Imaging and Computing
• National Laboratory of Pattern Recognition
• Institute of Automation
• Chinese Academy of Sciences

2
Outline

• Introduction
• Variational Segmentation Model
• Experimental Results
• 3-Phase Brain MR Image Segmentation.
• Conclusion

3
Definition of Deformable Model
Move an contour towards object boundary within
an image under velocity field.
4
Introduction
5
Variational Model

• Energy functional is derived from quantifying
  segmentation criterion.

Minimum Description Length criterion Bayesian
Rule Maximum Likelihood
2. When arrived its minimum, an optimum
partitioning of image is obtained.
Calculus of variation. Shape gradients.
6
Image and Region

• The homogeneous means intensity/ feature of a
  region follow some distribution.
• A homogeneous region can be assumed to be sampled
  from the same distribution, which is decided by
  all voxels in the region. We note it global
  region.

m1 Intensity Image m3 Color Image m6
Tensor Image
7
Neighborhood Information
Combination of voxels neighborhood
information is crucial for image segmentation.
The neighbor region of a voxel is similar to the
global region to which the voxel belongs. It is
also called that their distance is the
shortest.
8
Assumptions

• The neighborhood of a voxel is sampled from the
  same distribution.

2. All global regions and neighborhood regions
follow Gaussian distribution. This is because for
most medical images, the noise can been assumed
to follow Gaussian distribution.
9
Measure of Dissimilarity of Distributions

• In order to measure the dissimilarity between two
  distribution, we use some measures in
  information theory.

2. In this paper, we assume that regions
intensities follow Gaussian distribution. So we
would like to choose the measure that can
simplify expression for Gaussian distribution.
10
Measure of Distributions
1. Symmetric Kullback-Leibler divergence
2. Bhattacharyya measure
3. Renyis measure
11
Energy Functional
Neighborhood of voxel x, following normal
distribution
Distribution of neighborhood region at x.
Distribution of global region with parameters
theta.
12
Gradient Descent Flow
When distributions of all regions follow
Gaussian, the evolution equation can be
simplified as follows
Mean
Variance
Original Image
This is why Gaussian Distribution and
J-Divergence are explored
13
Some Special Cases
1. When KL-divergence with sigma0, it reduces to
the geodesic active region model ( Paragios
Deriche)
2. When sigmasigma1sigma2, it reduces to
piecewise constant Mumford-Shah model (Chan
Vese)
14
Numerical Discretization
Velocity Normalization

• Semi-implicit finite differences scheme and
  iterative algorithm (Aubert Rudin)

2. Regularization of Dirac measure (Chan)
15
Experimental Results
Similar means but variance of significant
difference
Similar variance but means of significant
difference
Means and variance of significant difference
16
Experimental Results
17
Experimental Results
18
Experimental Results
19
Experimental Results
20
Experimental Results
21
Experimental Results
22
Experimental Results
3D Real MRI Images
23
Experimental Results
24
3-Phase Brain Tissue Segmentation
Based on the proposed variational segmentation
model. We present a 3-phase brain tissue
segmentation method. Three regions are
represented by two level set functions. The
characteristic functions are
25
3-Phase Gradient Descent Flow
26
GM_CSF Surface Evolution
27
Experimental Results
28
Conclusions

• We proposed a variational segmentation model
  combined dissimilarity between neighborhood and
  global regions using J-divergence.
• Based on the proposed model, a 3-phase
  segmentation model was proposed to perform brain
  MR image tissue segmentation

29
Books or Journals

• Springer Series Books on Computational Imaging
  and Vision
• IEEE Transactions on Medical Imaging

30
Acknowledgements
31
Thanks For more information, please search with
Google by Tianzi Jiang