Our paper was accepted in ISBI 2013! 🙂

## Globally Optimal Spinal Cord Segmentation Using a Minimal Path in High Dimensions

I think the title really summarizes the work pretty nicely so I’ll break down each part of the title to give you a brief overview of the paper.

**“Spinal Cord Segmentation”** = this is the goal of the work. Given a 3D MRI, we want a method that can mark those voxels that belong to the spinal cord. Segmentation means to label the voxels as spinal cord or background.

**“High Dimensions”** = we represented the segmented spinal cord by a list of 6 numbers. I’ll explain this a bit more since this a bit tricky to understand. We used principle component analysis (PCA) to represent the “shape” of a 2D slice of the spinal cord. PCA allows us to represent each shape by its center point (x,y,z) and three principle components (giving us a total of 6 numbers per 2D slice). We can represent our spinal cord as a stack of these 2D shapes, or equivalently, a list of 6 numbers.

Now the question is, how to find this list of 6 numbers? Well we can search for them. This is similar to finding the shortest path in between 2 points, but instead of searching over 2 or 3 (spatial) dimensions, we search over the 6 dimensions (3 spatial and 3 shape).

**“Minimal Path”** = a minimal path finds the shortest path in between two points. In our methods, a user enters the start and end point of the spinal cord, and we find the minimal path in 6D between these two points. We use a slightly modified version of the A* search to find this minimal path. A path is defined to be “short” if the shapes “fits” well (e.g. the borders match) with what is in the MRI.

**“Globally Optimal”** = means that we can find the best segmentation that exists based on how we defined how well the shape “fits”. Our method will always find the global minimum and will not get stuck in any local minima.

You can take a look at the paper here.

Here’s the poster we did for the ISBI conference.

The nice PDF can be viewed here.

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