ENGN 2500Medical Image Analysis

ProjectFinal Presentation

Extraction and Visualization of Humerus, Radius and Ulna of Dogs

“Subvoxel Polygonization of Discrete Implicit Surfaces Using ENO Interpolation”

Firat Kalaycilar

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.

Elbow ofA Dog

ulna

humerus

radius

CT Images

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.

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.

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.

Thresholding

Fill holes

Median filtering

Erosion

Subtraction

How does the polygon look

like when boundary

images are stacked and

meshed?

Two bones lookmerged!

This is the problemof standard iso-surface techniques.

This paper claims that it is capable of separating these bones.

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.

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.71-76, July, 2008.

Takes a gray level volume and produces a distance transform.

Zero level setof the Level Set SegmentationAlgorithm after 40 iterations

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.

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.

Wave Propagation Example

Merging still occurs,but smaller

More examples

ENO Anchor Point Cloud Resulting Polygon

ENO Anchor Point Cloud Resulting Polygon

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!