Team Name: Fit happens
Team Members: Daniel Gehrig
Adrian Ruckli
Maximilian Göttgens
Summary of Approach:
1. - Convert the given raw data to a matrix of size 176x208x176 using a publically
available 3D-Data Reader ((c) 2010, Dirk-Jan Kroon).
- Reduce dimensionality of the 3D matrix to 2D by cutting it into slices and
attach the slices to one another in a 2D plane. (This step is important for
the next step.)
- Generate an intensity histogram of every brain with 5000 bins using MATLABs
histcounts function.
Every bin has a width of 1 intensity unit and thus counts the number of
voxels with intensity i. Voxels with intensity 0 are excluded as they
correspond to background.
- Normalize the histogram to compensate for noise generated by varying
brain volume and the use of different MRI scanners or settings.
2. - The intensity histogram generally exhibits 3 peaks which are used for
feature extraction. Three features are extracted from the intensity:
- voxels in the range 170-270 around the first peak (including limits).
- voxels in the range 715-785 around the second peak (including limits).
- voxels in the range 1340-1560 around the third peak (including limits).
These are called [x1, x2, x3]
3. - Fit a quartic polynomial with interaction terms for the three features.
The final feature vector has the form:
X = [x1, x2, x3, x2^3, x1*x3, x2*x3, x2^4, x2^3*x3] and the age prediction
has the following formula:
y = b0 + x*b where b = [b1; b2; b3; b4; b5; b6; b7; b8]
- The parameters where chosen to minimize the Bayesian Information Criterion (BIC).
- b is chosen through MLE with weighted LS. The weight matrix is of a bisquare
type so as to reduce the impact of outliers on the fit. A second weight matrix
is multiplied to take into account the high density of old and young test subject.
The final formula for b is:
b = (X^T*W*X)^-1*X^T*W*y
where W is the weight matrix, X is the data matrix and y are the targets.
4. - No post processing steps.