PBC_competition.lyx

#LyX 1.6.2 created this file. For more info see http://www.lyx.org/
\lyxformat 345
\begin_document
\begin_header
\textclass article
\use_default_options true
\language english
\inputencoding auto
\font_roman default
\font_sans default
\font_typewriter default
\font_default_family default
\font_sc false
\font_osf false
\font_sf_scale 100
\font_tt_scale 100

\graphics default
\paperfontsize 12
\spacing single
\use_hyperref false
\papersize a4paper
\use_geometry true
\use_amsmath 1
\use_esint 1
\cite_engine basic
\use_bibtopic false
\paperorientation portrait
\leftmargin 2cm
\topmargin 2cm
\rightmargin 2cm
\bottommargin 2cm
\secnumdepth 3
\tocdepth 3
\paragraph_separation indent
\defskip medskip
\quotes_language english
\papercolumns 1
\papersides 2
\paperpagestyle plain
\tracking_changes false
\output_changes false
\author "" 
\author "" 
\end_header

\begin_body

\begin_layout Title
Combining atlas and reference tracks for bundle detection.
\end_layout

\begin_layout Author
E.Garyfallidis, M.Brett, I.Nimmo-Smith
\end_layout

\begin_layout Abstract
We propose a new method which accurately detects preselected bundles from
 the training set in the other brains.
 We generate reference tracks for every bundle in the training set and detect
 the corresponding tracks in the other datasets using the average mean minimum
 distance.
 Then we normalize the LONI atlas onto each of the track dataset brains.
 For a given ROI value in the normalized atlas we extract all the tracks
 going through the corresponding ROI in each dataset and then we remove
 tracks that are not similar enough to the reference tracks.
 Our results are very promising however we learned about the PBC competition
 at a late stage and we didn't manage to complete our work towards the unsupervi
sed learning tasks.
 We have developed some interesting visualization tools, as well as techniques
 for automatic identification of the entire corpus callosum and its removal
 from our datasets.
 This is to overcome the difficulty that the corpus callosum intersects
 many other white matter areas and complicates any classification procedure.
 In addition, we we have developed algorithms for down-sampling the tracks
 in an intelligent fashion so that we do not lose any local or global shape
 characteristics.
\end_layout

\begin_layout Section
Introduction
\end_layout

\begin_layout Standard
Figure 1 shows the whole dataset for subject 1, scan 1 and the bundles identifie
d by the expert.
 The supervised learning challenge is to create an algorithm to label this
 and two other brains to maximise the agreement with the expert.
 We identified that there were critical issues to do with the registrations
 of these brains which we have addressed below.
 In order to achieve consistency between bundles identified in the different
 brains we have concentrated on combining prior information from a published
 atlas together with the selection of a small set of tracks from each labelled
 bundle to use as reference tracks.
 Beyond this we have chosen to use simple but effective geometric measures
 based on the individual tracks.
 
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename pbc_figures/white_brain.png
	scale 20
	rotateOrigin center

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset CommandInset label
LatexCommand label
name "white brain with expert bundles"

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
In non-white color are the 8 bundles identified by the PBC competition.
 The purpose of the supervised learning task was to identify these bundles
 in other brain datasets.
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Section
Methods
\end_layout

\begin_layout Subsection
Registration
\end_layout

\begin_layout Standard
We wanted to use the LONI (ICBM DTI-81) atlas labels to find candidate regions
 in the individual brains.
 To make something like an anatomical image from the tracks, we took a binarized
 track count image - that is an image for which there was a 1 in voxels
 that had one or more tracks passing it, and zeros elsewhere.
 We used SPM8 to calculate warping parameters to match the binarized track
 count image to the ICBM white matter image.
 To reslice the LONI label template, we inverted the SPM normalization parameter
s using the SPM deformations utilities, and resliced with the inverted parameter
s and nearest neighbour resampling.
 Because of the size and orientation differences between the binarized track
 count images for the same subject, we did this separately for each scan
 for every subject.
 This gave us a labeled image from the LONI atlas in the space of each brain
 image.
\end_layout

\begin_layout Subsubsection
Skeleton Track Atlas
\end_layout

\begin_layout Standard
While developing techniques for this competition we have created tools to
 create a skeletonised version of a track dataset in which the skeleton
 tracks are ones which have multiple neighbours which are very similar.
 This is detailed below.
 
\end_layout

\begin_layout Subsection
Track Metrics
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename pbc_figures/arcuate_zhang.png
	scale 20
	rotateOrigin center

\end_inset


\begin_inset Caption

\begin_layout Plain Layout
Arcuate fasciculus using the average mean minimum distances.
 
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Subsubsection
Average Mean Minimum Distance Metric
\end_layout

\begin_layout Standard
We explored a number of metrics for the similarity or closeness of two tracks.
 This is based on the work of 
\begin_inset CommandInset citation
LatexCommand cite
key "corouge2004towards"

\end_inset

 as developed by 
\begin_inset CommandInset citation
LatexCommand cite
key "zhang2008identifying"

\end_inset

; the method was also used by 
\begin_inset CommandInset citation
LatexCommand cite
key "ODonnell_MICCAI06"

\end_inset

.
 If 
\begin_inset Formula $P=[p_{0},p_{1},\ldots,p_{N}]$
\end_inset

 and 
\family roman
\series medium
\shape up
\size normal
\emph off
\bar no
\noun off
\color none

\begin_inset Formula $Q=[q_{0},q_{1},\ldots,q_{M}]$
\end_inset


\family default
\series default
\shape default
\size default
\emph default
\bar default
\noun default
\color inherit
 are two tracks then the mean minimum distance of 
\begin_inset ERT
status open

\begin_layout Plain Layout

P
\end_layout

\end_inset

 from 
\begin_inset ERT
status open

\begin_layout Plain Layout

Q
\end_layout

\end_inset

 is defined as 
\begin_inset Formula \[
\mathrm{m.m.d.(P,Q})=\frac{1}{N}{\displaystyle \sum_{i=0}^{N-1}\,\min_{0\le j\le M-1}|p_{i}-q_{j}|}.\]

\end_inset


\end_layout

\begin_layout Standard
In general 
\begin_inset Formula \[
\mathrm{{m.m.d.}(P,Q)}\ne\mathrm{{m.m.d.}(Q,P)}\]

\end_inset

To provide a symmetric distance measure we define the average mean minimum
 distance between P and Q as 
\begin_inset ERT
status open

\begin_layout Plain Layout

$$
\backslash
frac{
\backslash
mathrm{m.m.d.}(P,Q)+
\backslash
mathrm{m.m.d.}(Q,P)}{2}$$
\end_layout

\end_inset

.
 
\begin_inset CommandInset citation
LatexCommand cite
key "corouge2004towards"

\end_inset

 introduced two other symmetrisations of the two m.m.d.
 measures, either selecting the greater or the lesser of the two.
 This appears to be a very effective metric for filtering a collection of
 candidate tracks to identify ones which are reasonably similar to a specified
 reference track (see Figure 2).
\end_layout

\begin_layout Subsection
Down-sampling
\end_layout

\begin_layout Standard
Doing calculations with all the miles of identified tracks is computationally
 very demanding.
 Therefore, we developed three different types of down-sampling to speed
 up our calculations.
 We used the two first types of down-sampling (see Figure 3) to reduce the
 number of points needed to describe a track and the third type we used
 to select tracks that had many other tracks that were very similar.
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename pbc_figures/Left_raw_center_mdl_right_down.png
	scale 20

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
Left: Raw bundle, centre: MDL approximation, Right: Simple down-sampling
 along the length.
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Subsubsection
Minimum description length approximation
\end_layout

\begin_layout Standard
This is based on the work of 
\begin_inset CommandInset citation
LatexCommand citet
key "lee2007trajectory"

\end_inset

 who devised an information theoretic approach based on minimum description
 length (MDL) to generate adaptive sub-samplings of tracks as a precursor
 to breaking them up into their constituent component line-segments.
 The criteria for the sub-sampling are based on the degree to which sections
 of the track can be approximated by the chord joining its end points, with
 an MDL penalty function that compares the loss of local position and direction
 information in the approximation with the information required to represent
 the full data.
 However, instead of then partitioning the tracks into segments, we used
 this MDL version as an approximation for the entire track.
 The sub-sampling ratio was approximately 1:8 and automatically produced
 tracks with long segments on the straighter elements and a higher density
 of shorter segments where there was significant curvature.
 This appears to preserve essential shape characteristics of the tracks
 with good fidelity (see Figure 3).
\end_layout

\begin_layout Subsubsection
Three Point Tracks
\end_layout

\begin_layout Standard
We needed a very fast way to remove tracks that are very far away from a
 reference track.
 In order to do this we have used a three-point distance as a coarse filter
 to remove tracks which are distant from a reference track or bundle.
 This metric is the arithmetic average of the euclidean distances between
 the end points and the mid-points of the two tracks.
\end_layout

\begin_layout Subsubsection
Skeletal Tracks
\end_layout

\begin_layout Standard
Here we tried to identify some core tracks that could possibly be good represent
atives of many of their neighbouring tracks.
 In order to do this we randomly selected 5000 tracks from the 250000 given
 tracks (2%) and for these tracks we kept only those who had at least 50
 other tracks in the full dataset which had every single point closer than
 5mm from the closest point in the reference track.
 For all three brains the number of skeletal tracks was reduced from 5000
 to approximately 1800 by this technique.
\end_layout

\begin_layout Subsection
Object Detection
\end_layout

\begin_layout Subsubsection
Corpus Callosum
\end_layout

\begin_layout Standard
The corpus callosum (CC) is the major white matter fibre structure connecting
 the two hemispheres.
 We found that it accounted for more than 40% of the tracks in the competition
 datasets.
 Because the CC is such a massive structure with ramifications throughout
 the brain we saw that if we could remove it, we would be better able to
 identify other structures near the CC.
 To do that we tried the following very simple technique.
 We know that in a normal brain there will be plenty of fibres passing through
 the mid plane separating the two hemispheres.
 Finding this mid-plane is very easy with normalized brains in MNI space
 because this is the sagittal plane passing though the centre of the volume.
 Then we find all the points of intersection of tracks with this plane and
 mapped them from the track space to a 2d binary image space so that every
 pixel in the image plane has 1 if one or more tracks passes through it
 and 0 if none.
 In this 2d image the biggest visible object is the corpus callosum (CC)
 which is very easy to identify and label, thus separating it from the other
 smaller objects in the plane using standard morphological operations i.e.
 erosion followed by dilation.
 After the CC has been detected in the 2d image it is straightforward to
 find the tracks that pass through the corresponding voxel in MNI space.
 The corpus callosums detected in this way are shown in Figure 4 for two
 different brains.
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename pbc_figures/corpus_callosum.png
	scale 80
	rotateOrigin center

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
Detecting and separating corpus callosum.
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Subsubsection
Bottleneck Finding - Cut Plane
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename pbc_figures/blue_green_dragon.png
	scale 30
	rotateOrigin center

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
Cut plane - hidden dragon
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Standard
One of the techniques that we have partially developed as a tool for the
 unsupervised learning task is based on the use of cutting-planes generated
 from a reference track.
 Given a bundle of tracks 
\begin_inset ERT
status open

\begin_layout Plain Layout

B
\end_layout

\end_inset

, and a reference track 
\begin_inset ERT
status open

\begin_layout Plain Layout

$R = [r_0, r_1, 
\backslash
ldots, r_N]$
\end_layout

\end_inset

 , we construct the family of planes 
\begin_inset ERT
status open

\begin_layout Plain Layout

$
\backslash
pi_j$
\end_layout

\end_inset

 normal to 
\begin_inset ERT
status open

\begin_layout Plain Layout

R
\end_layout

\end_inset

 at each point 
\begin_inset ERT
status open

\begin_layout Plain Layout

$r_j, j=1,
\backslash
ldots,N-1$
\end_layout

\end_inset

, and consider the local geometry of the hit sets, i.e.
 the intersections 
\begin_inset ERT
status open

\begin_layout Plain Layout

$
\backslash
pi_j 
\backslash
cap B$
\end_layout

\end_inset

.
 The metric we have introduced is the radial divergence metric (RDM), which
 is given by the radial component towards or away from 
\begin_inset ERT
status open

\begin_layout Plain Layout

$r_j$
\end_layout

\end_inset

 of the tangent vector of each track 
\begin_inset ERT
status open

\begin_layout Plain Layout

$b 
\backslash
in B$
\end_layout

\end_inset

 where it meets 
\begin_inset ERT
status open

\begin_layout Plain Layout

$
\backslash
pi_j$
\end_layout

\end_inset

.
 Preliminary evidence is that RDM is a useful metric in identifying tracks
 which maintain a course parallel to a reference track though displaced
 some distance.
 This is particularly relevant in trying to identify tracks which may belong
 to a broad, thin, strap-like bundle.
 Figure 5 shows features of this implementation where the blue points indicate
 cutting points with low divergence.
\end_layout

\begin_layout Subsection
Algorithmic Description
\end_layout

\begin_layout Standard
We have developed many more tools than those we actually incorporated in
 our submission - for example the corpus callosum finding algorithm and
 cut plane.
 Here we give a short algorithmic description restricted to those used to
 make the results we submitted for the supervised learning challenge.
\end_layout

\begin_layout Enumerate
Normalize ICBM atlas with all brains, as described in the registration section.
\end_layout

\begin_layout Enumerate
Generate most similar tracks (
\noun on
reference tracks
\noun default
) using minimum average distances and manually pick some extra fibres so
 you can have a better shape description of the bundle.
\end_layout

\begin_layout Enumerate
For an ROI value in the atlas corresponding to each dataset, generate the
 tracks (
\noun on
value tracks
\noun default
) which pass through the region having that value.
\end_layout

\begin_layout Enumerate
Remove very far tracks from the 
\noun on
reference tracks
\noun default
 using the 3-point method.
\end_layout

\begin_layout Enumerate
Compare the 
\noun on
reference tracks
\noun default
 with the 
\noun on
value tracks
\noun default
.
 If they do not have any tracks in common then 
\noun on
the value tracks
\noun default
 are used in place of the 
\noun on
reference tracks
\noun default
.
\end_layout

\begin_layout Enumerate
Finally, use the minimum average minimum distances to reduce the number
 of 
\noun on
value tracks
\noun default
 which are far from every corresponding 
\noun on
reference track
\noun default
.
\end_layout

\begin_layout Enumerate
Compare with the training set.
\end_layout

\begin_layout Enumerate
If the intersection of the training set with the current bundle set is not
 maximised go to 6 else 
\noun on
stop
\noun default
.
\end_layout

\begin_layout Standard
The results we obtained after running this algorithm were very accurate
 as can be seen in Figure 6 below.
\end_layout

\begin_layout Standard
\begin_inset Float figure
wide false
sideways false
status open

\begin_layout Plain Layout
\align center
\begin_inset Graphics
	filename pbc_figures/OhYeah.png
	scale 30
	rotateOrigin center

\end_inset


\end_layout

\begin_layout Plain Layout
\begin_inset Caption

\begin_layout Plain Layout
Detecting all 8 bundles
\end_layout

\end_inset


\end_layout

\end_inset


\end_layout

\begin_layout Section
Software
\end_layout

\begin_layout Standard
We developed all our software in Python for fast code development, and Cython
 for fast execution whenever it was necessary.
 Our core-detection functions and IO readers were build in the 
\noun on
DiPy
\noun default
 module which we plan to embed in the Neuroimaging in Python (
\noun on
NiPy
\noun default
) suite.
 We developed our visualization methods in a package we called 
\noun on
Fos
\noun default
 which is our python-vtk implementation for visualizing tractographic and
 brain imaging datasets.
 All pictures shown in this paper were obtained from 
\noun on
Fos
\noun default
.
 
\noun on
Fos
\noun default
 has also the property that it is able to visualize many track datasets
 simultaneously.
 For example you could visualize in the 3d space simultaneously all 5 brains
 of the datasets or even more.
 It also allows you to pick and select specific fibres with the mouse.
\end_layout

\begin_layout Section
Conclusion
\end_layout

\begin_layout Standard
With a simple geometric approach to this problem, incorporating prior informatio
n, we have managed to get very promising results for all 5 datasets.
 Unfortunately, we didn't have time to test these for the unsupervised learning
 Challenges 2a/b/c, however this competition has inspired us to continue
 working on this problem full hearted and batteries included!
\end_layout

\begin_layout Standard

\lang british
\begin_inset CommandInset bibtex
LatexCommand bibtex
bibfiles "diffusion"
options "plain"

\end_inset


\end_layout

\end_body
\end_document