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In the previous video we
identified clusters, or tissue

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substances, in a
healthy brain image.

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It would be really
helpful if we can

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use these clusters to
automatically detect

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tumors in MRI images
of sick patients.

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The tumor.csv file corresponds
to an MRI brain image

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of a patient with
oligodendroglioma,

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a tumor that commonly occurs
in the front lobe of the brain.

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Since brain biopsy is the
only definite diagnosis

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of this tumor, MRI guidance is
key in determining its location

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and geometry.

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Now, make sure that
the tumor.csv file

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is in your current directory.

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Let's go to the console,
and clear it, and then

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read the data, and
save it to a data frame

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that we're going to call tumor,
and use the read.csv function,

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which takes as an input
the tumor dataset,

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and make sure to turn off
the header using header

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equals FALSE.

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And let's quickly
create our tumorMatrix,

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using the as.matrix
function over the tumor data

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frame, and the tumorVector,
using the as.vector

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function over the tumorMatrix.

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Now, we will not run the
k-means algorithm again

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on the tumor vector.

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Instead, we will apply the
k-means clustering results

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that we found using
the healthy brain

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image on the tumor vector.

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In other words, we
treat the healthy vector

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as training set and the tumor
vector as a testing set.

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To do this, we first
need to install

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a new package that
is called flexclust.

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So let us type
install.packages("flexclus").

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And then the first
thing R will ask

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us is to set the
region that is closest

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to our geographical location.

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And after that, press
OK, and the installation

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shouldn't take more than
two seconds to complete.

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OK.

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Now that the package
is installed,

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let us load it by typing
library(flexclust).

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The flexclust package contains
the object class KCCA,

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which stands for K-Centroids
Cluster Analysis.

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We need to convert the
information from the clustering

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algorithm to an object
of the class KCCA.

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And this conversion
is needed before we

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can use the predict function
on the test set tumorVector.

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So calling our new
variable KMC.kcca

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and then using the
as.kcca function, which

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takes as a first input the
original KMC variable that

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stored all the information
from the k-means clustering

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function, and the second input
is the data that we clustered.

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And in this case,
it's the training set,

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which is the healthyVector.

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And now, be aware that
this data conversion

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will take some time to run.

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Now that R finally finished
creating the object KMC.kcca,

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we can cluster the
pixels in the tumorVector

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using the predict function.

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Let us call the cluster
vector tumorClusters =

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predict(KMC.kcca,
newdata=tumorVector).

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And now, the
tumorClusters is a vector

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that assigns a value 1 through
5 to each of the intensity

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values in the
tumorVector, as predicted

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by the k-means algorithm.

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To output the segmented
image, we first

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need to convert the tumor
clusters to a matrix.

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So let's use the
dimension function,

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and then the input is
simply tumorClusters,

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and then using the c
function with the first input

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as the number of rows
in the tumorMatrix

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and the second
input as the number

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of columns in the tumorMatrix.

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And now, we can
visualize the clusters

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by using the image function with
the input tumorClusters matrix,

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and make sure to set
the axes to FALSE,

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and let's use again these
fancy rainbow colors, here.

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So col=rainbow(k).

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Again, k is equal to 5.

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Alright.

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Let's navigate to
the graphics window,

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now, to see if we
can detect the tumor.

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Oh, and yes, we do!

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It is this abnormal
substance here

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that is highlighted
in blue that was not

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present in the
healthy MRI image.

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So we were successfully able
to identify, more or less,

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the geometry of the
malignant structure.

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We see that we did a good job
capturing the major tissue

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substances of the brain.

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The grey matter is highlighted
in purple and the white matter

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in yellow.

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For the sick patient, the
substance highlighted in blue

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is the oligodendroglioma tumor.

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Notice that we do not see
substantial blue regions

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in the healthy
brain image, apart

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from the region around the eyes.

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Actually, looking
at the eyes regions,

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we notice that the two images
were not taken precisely

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at the same section
of the brain.

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This might explain
some differences

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in shapes between
the two images.

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Let's see how the images
look like originally.

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We see that the tumor region
has a lighter color intensity,

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which is very similar to
the region around the eyes

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in the healthy brain image.

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This might explain highlighting
this region in blue.

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Of course, we cannot claim
that we did a wonderful job

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obtaining the exact geometries
of all the tissue substances,

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but we are definitely
on the right track.

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In fact, to do so, we need to
use more advanced algorithms

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and fine-tune our
clustering technique.

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MRI image segmentation is an
ongoing field of research.

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While k-means clustering
is a good starting point,

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more advanced
techniques have been

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proposed in the literature, such
as the modified fuzzy k-means

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clustering method.

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Also, if you are
interested, R has

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packages that are specialized
for analyzing medical images.

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Now, if we had MRI
axial images taken

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at different sections
of the brain,

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we could segment each image
and capture the geometries

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of the substances
at different levels.

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Then, by interpolating
between the segmented images,

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we can estimate
the missing slices,

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and we can then obtain
a 3D reconstruction

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of the anatomy of the brain
from 2D MRI cross-sections.

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In fact, 3D reconstruction
is particularly

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important in the medical
field for diagnosis,

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surgical planning, and
biological research purposes.

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I hope that this
recitation gave you

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a flavor of this fascinating
field of image segmentation.

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In our next video, we will
review all the analytics tools

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we have covered so
far in this class

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and discuss their
uses, pros, and cons.