Transcript Final Project Presentation - Computer Vision @ LEMS

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
Problem
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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 of
A Dog
humerus
ulna
radius
CT Images
Approach
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“Subvoxel Polygonization of Discrete Implicit Surfaces Using ENO
Interpolation” by Rodehorst and Kimia
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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.
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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
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Requires a 3D binary volume where 1's
correspond to boundaries and 0's correspond to
elsewhere.
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But, we have a gray level volume!
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We can obtain boundaries using segmentation.
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The output of simple thresholding +
mathematical morphology is good enough.
3D Signed Distance Transform
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Matlab implementation (bwdist) → very fast
Ricardo Fabbri's implementation of 3D distance transform
explained in the paper:
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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 look
merged!
This is the problem
of standard
iso-surface
techniques.
This paper claims
that it is capable of
separating these
bones.
3D Signed Distance Transform
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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
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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
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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.7176, July, 2008.
Takes a gray level volume and produces a distance
transform.
Zero level set
of the Level Set Segmentation
Algorithm after 40 iterations
ENO Anchor Points
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“Subvoxel Polygonization of Discrete Implicit Surfaces Using ENO
Interpolation” by Rodehorst and Kimia
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An old C/C++ implementation exists → not compatible with recent compilers
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Managed to revive the ENO anchor point extraction algorithm.
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Procedure:
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Export the distance transform in a format that can be read by the
ENO interpolation program.
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Run ENO anchor point extraction code
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Input: 3D signed distance transform
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For each grid line in each direction (x,y,z)
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Associate a 2nd order polynomial with each interval
between consecutive grid points using ENO
interpolation.
Output: Roots of the polynomials are the anchor points.
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Wave Propagation
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Managed to revive the wave propagation
component.
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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.
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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
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Managed to revive the whole program
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Couldn't fix all the problems.
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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!