1. Medical Image Analysis
ENGN 2500
Medical Image Analysis
Project
Final Presentation
Extraction and Visualization of Humerus, Radius and Ulna of Dogs
“Subvoxel Polygonization of Discrete Implicit Surfaces Using ENO Interpolation”
Firat Kalaycilar

2. Problem
Elbow dysplasia is a condition involving multiple developmental abnormalities of the elbow-joint in the dog, specifically the growth of cartilage or the structures surrounding it (from Wikipedia).
The disease can be diagnosed using 3D reconstruction of bones from CT data.
Goal: Extract and visualize bones of interest in 3D.

4. Elbow of
A Dog

5. humerus
ulna
radius
CT Images

6. Approach
“Subvoxel Polygonization of Discrete Implicit Surfaces Using ENO Interpolation” by Rodehorst and Kimia
Take 3D distance transform of input CT images → DT
Find surface zero-crossings of DT at grid lines using ENO interpolation → ENO anchor points (APs)
Connect APs to obtain a 3D polygon mesh.
Start from an unambiguous voxel and connect APs → initial mesh
Grow the current mesh by considering adjacent voxels.
If the voxel being considered is ambiguous, choose the connections which result in smoothest surface.
This algorithm works like wave propagation.
Visualize the resulting mesh.

7. 3D Signed Distance Transform
Requires a 3D binary volume where 1's correspond to boundaries and 0's correspond to elsewhere.
But, we have a gray level volume!
We can obtain boundaries using segmentation.
The output of simple thresholding + mathematical morphology is good enough.

8. 3D Signed Distance Transform
Matlab implementation (bwdist) → very fast
Ricardo Fabbri's implementation of 3D distance transform explained in the paper:
J. C. Torelli, R. Fabbri, G. Travieso, O. M. Bruno "A high performance 3D exact Euclidean distance transform algorithm for distributed computing", International Journal of Pattern Recognition and Artificial Intelligence, 2010.
It also requires boundary images (filled region images are not OK, because it treats every foreground pixel as boundary.)
So, I decided to continue with the matlab implementation.

9. Thresholding

10. Fill holes

11. Median filtering

12. Erosion

13. Subtraction

14. How does the polygon look like when boundary images are stacked and meshed?
Two bones look
merged!
This is the problem
of standard
iso-surface
techniques.
This paper claims
that it is capable of
separating these
bones.

15. 3D Signed Distance Transform
Apply the operations to every slice → stack of binary boundary images
Use matlab's bwdist function to obtain an unsigned distance transform.
Multiply the interior regions by -1 to obtain a signed distance transform.

16. 3D Level Set Segmentation
I might have used 3D Level Set segmentation instead of binary segmentation + 3D distance transform.
VXL Implementations: Not clear which one to use? How to use?
Found a matlab implementation
Y. Zhang, B. J. Matuszewski, L.-K. Shark, and C. J. Moore. Medical Image Segmentation Using New Hybrid Level-Set Method. IEEE International Conference on Biomedical Visualisation, MEDi08VIS, London, pp , July, 2008.
Takes a gray level volume and produces a distance transform.

17. Zero level set
of the Level Set Segmentation
Algorithm after 40 iterations

18. ENO Anchor Points
“Subvoxel Polygonization of Discrete Implicit Surfaces Using ENO Interpolation” by Rodehorst and Kimia
An old C/C++ implementation exists → not compatible with recent compilers
Managed to revive the ENO anchor point extraction algorithm.
Procedure:
Export the distance transform in a format that can be read by the ENO interpolation program.
Run ENO anchor point extraction code
Input: 3D signed distance transform
For each grid line in each direction (x,y,z)
Associate a 2nd order polynomial with each interval between consecutive grid points using ENO interpolation.
Output: Roots of the polynomials are the anchor points.

19. Wave Propagation Managed to revive the wave propagation component.
Spent most of my time on this.
Unfortunately, due to some bugs I couldn't resolve, it doesn't work on every input I provide.
Doesn't work on 3D level set output (finds odd number of ENO points and terminates).
Works on binary segmentation + distance transform output.

21. Wave Propagation Example

26. Merging still occurs,
but smaller

27. More examples

28. ENO Anchor Point Cloud
Resulting Polygon

29. ENO Anchor Point Cloud
Resulting Polygon

30. Conclusion Managed to revive the whole program
Couldn't fix all the problems.
The program still complains when level set segmentation results are used.
Managed to reconstruct bones from 3D CT volumes although the results still looked merged.
Promising!