# Introduction

Magnetic resonance imaging (MRI) is one of the most commonly used tests in neurology. MRI provides detail of brain, spinal cord and vascular anatomy, and has the advantage of being able to visualize anatomy in all three planes: axial, sagittal and coronal (see the example image below) (from (Preston, 2006)). Machine Learning is being used heavily on brain images in various forms as classification, brain segmentation, identification of tumors or damage and much more. Still there are some challenges that would have a great impact in how doctor deals with images.

Figure 1: A generic image of an MRI scan of a brain. What you are looking at is a T2 weighted scan. For more information about MRI image types you can check the nice overview by Preston (Preston, 2006)

Understanding and analysing MRI brain images requires a huge experience and it takes many years for young doctors to learn. We at TOELT work on applying machine learning (and in particular deep learning) to mri imaging. One of our goal is to build mathematical frameworks that allow us to better understand the brain and its development (especially in children). We use several techniques from density analysis to fractal gemotry. To be able to do this, we have built an infrastructure that allows us to do segmentation, skull stripping, skull extraction, symmetry determination and much more.

Figure 2: A slice extracted from a 3D MRI scan of an adult. The different panels shows how it is possible, with our infrastructure, to separate different parts of the head anatomy (in this example skull and brain).
Figure 3: A slice extracted from a 3D MRI scan of a child. The different panels shows how it is possible, with our infrastructure, to separate different parts of the head anatomy (in this example skull and brain).

# Symmetry Axis of a T2-weighted MRI Scan

To be able to compare images in a meaningful way, first all scans should be “vertical”. This is an intuitive concept that must be quantified properly. If you check Figure 1 above, you will realize that the brain image is slightly tilted. Can we find the symmetry axis automatically and rotate the image appropriately? Turns out this can be done in several ways.

The first problem one has to solve is how to identify the relevant pixels in the image. In Figure 2 you can see, for example, highlighted in yellow all pixels that have an intensitry larger than a given treshold (you find the values in each of the three panels). Unless you filter out a portion of the pixels, it is impossible to really get the right symmetry axis.

Figure 2: Pixels with a gray value higher than the tresholds listed in the titles of each panel are highlighted in yellow. One can clearly see how the background is not completely black and must be removed effectively to be able to determine the correct symmetry axis.

## Symmetry Axis

By using information about $$x$$ and $$y$$ points in the appropriate way, one can find the symmetry axis of the image. The results obtained with the algorihm we developed at TOELT can be seen in Figure 3 below.

Figure 3: The two lines in the image are the directions of the two symmetry axis.

At this point the image can be rotated to make the scan “vertical” as it can be seen in Figure 4.

Figure 4: After finding the two symmetry axis it is possible to rotate the image to make it "vertical".

Note that this is possible because the image is already symmetric, since it is an image of a healhty brain. If the brain has some kind of damage, i.e. a tumor, this approach will not work and the axis that will be found will be highly out of place. To address this issue one has to use only the skull to determine the symmetry axis. But to do that a more complex algorithm must be used.

# Skull Shape Determination

## Axial Skull Shape Determination (ASSD) Algorithm

It is not an easy task to determine the skull in an MRI image. One of the algorithm that we developed is called Axial Skull Shape Determination (ASSD). You can see the result applied to two generic images in in Figure 5 (healthy brain) and Figure 6 (brain with tumor).

Figure 5: the result of the ASSD algorithm to determine the shape of the skull to a healthy brain.
Figure 5: the result of the ASSD algorithm to determine the shape of the skull to a case with a large tumor.

With the information of the skull shape we can now determin the symmetry axis of the skull without being influenced by possible brain damage appearing in the image.

You can see in Figure 6, how better the symmetry axis evaluated with the results of the ASSD algorithm are (yellow lines), with respect with those obtained by using the entire brain image (clearly asymmetric and with a wrong intersection) (red line). Note that the image has not been rotated.

Figure 6: comparison of symmetry axis obtained with the results of the ASSD Algorithm (yellow lines) and the ones obtained with the entire brain image (red lines). Note that the image has not been rotated.

# References

1. Preston, D. C. (2006). MRI Basics. In MRI  BASICS. https://case.edu/med/neurology/NR/MRI%20Basics.htm.
@misc{preston,
title = {MRI Basics},