ENGN 2500Medical Image Analysis

ProjectProgress 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.

1st Presentation Plan

April 12 – April 19

Find or implement an appropriate 3D Distance Transform algorithm.

Try to revive the existing code (doesn't compile and run)

April 20 – April 27

Finish revival of the code or implement ENO interpolation as described in the paper.

Obtain some interpolation results.

April 28

MID-PROJECT PRESENTATION

April 29 – May 06

Implement the wave propagation algorithm explained in the paper if the existing code doesn't work

May 07 – May 15

Experiments.

May 16 – May 17

FINAL PROJECT PRESENTATION

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. Luckily, simple thresholding + mathematical

morphology are sufficient!

Thresholding

Fill holes

Median filtering

Erosion

Subtraction

3D Signed Distance Transform

Apply these 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.

Isovalue = -3

Isovalue = 4

Isovalue = 0

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.

– Export the ENO anchor points computed by the program in a format that can be read by matlab.

– Visualize the points in matlab.

Plan

April 29 – May 06

Revive the wave propagation code Get more data

May 07 – May 15

Experiments. May 16 – May 17

FINAL PROJECT PRESENTATION