ENGN 2500 Medical Image Analysis Project Progress 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 of A 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.

1 st 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 2 nd 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