Transcript A Variational Approach for 3D Shape Registration by

Variational Approaches and Image
Segmentation
Lecture #8
Hossam Abdelmunim1 & Aly A. Farag2
1Computer
& Systems Engineering Department, Ain
Shams University, Cairo, Egypt
2Electerical
and Computer Engineering Department,
University of Louisville, Louisville, KY, USA
ECE 643 – Fall 2010
1
Adaptive Multi-modal Segmentation
Outline
• Multiple region representation.
• Energy function formulation for bimodal and
multi modal cases.
• Adaptive region model PDE’s.
• Initialization.
• Experimental results
• Conclusion and criticism.
Related Papers
T. Brox and J. Weickert. ”Level Set Based Image Segmentation with Multiple Regions,” in
Pattern Recognition., Springer LNCS 3175, pp. 415–423, Aug. 2004.
A. A. Farag and Hossam Hassan, “Adaptive Segmentation of Multi-modal 3D Data Using
Robust Level Set Techniques“, in Proc International Conference on Medical Image Computing
and Computer-Assisted Intervention (MICCAI’04), Saint Malo,
France, pp. 143-150, September, 2004.
Regions Representation
Assume that we have image I with K classes (regions).
K (i=1..K) level set functions are defined to represent the
regions:
 D( X ) if inside

i ( X )  0 on the boundary
 D( X ) if outside

D is the minimum Euclidean distance between the current
point and the contour/surface.
The positive part of the level set function is dedicated for
the associated region. It is adaptive because the contour
changes with time.
Segmentation Objectives
K contours are initialized.
They are required to evolve to hit the boundaries of their
associated regions.
Level sets change to minimize a given energy function.
The steady state solution will represent segmented
regions in the positive part of each function.
Image and Feature
Texture tensor
Color intensity
Adaptive Region Parameters
Regions statistics are described by Gaussian models.
The parameters are estimated by M.L.E as follows:
i
H ( ( x))Id


 H ( ( x))d
i

i

i



H (i ( x))(I ( x)   i )(I ( x)   i )T d


H (i ( x))d
The prior probability is estimated as the region area:
i
H ( ( x ))d


  H ( ( x))d
i

K
i 1

i
Automatic Seed Initialization
Results (Natural Image)
Image Size: 200 X 276
Window Size: 15 X 15
Two Classes
Results (MRI-T1 image)
Image Size: 256 X 256
Window Size: 5 X 5
Two Classes
Results (MRI-PD Image)
Image Size: 375 X 373
Window Size: 5 X 5
Three Classes
Results (Synthetic)
Image Size: 300 X 150
Window Size: 25 X 25
Three Classes
Results (Color Image)
Image Size: 342 X 450
Window Size: 35 X 35
Two Classes
Results (Continue)
Discussions
An adaptive multi region segmentation approach is proposed.
This method is very suitable for the homogeneous regions.
The regularization term in the PDE enable segmenting images with
noise. In case of high noise levels, the convergence time increases
and the boundaries are miss-classified by increasing the strength of
the curvature component.
Synthetic, real, and medical examples are given.
Non parametric probability density functions may be investigated
replacing the Gaussian models.
Thank You
&
Questions