Segmentation of retinal layers in OCT-images
using optimal graph search
Søren Trads Steen
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Many diseases threatening eyesight have root in the
retina. Many of these diseases can be prevented if 120
diagnosed early. This can be done using OCT images. However, a doctor has to shift through all the 100
images to find symptoms manifesting in the differ80
ent layers of the retina - if an algorithm can supply
clues of where to look, it would be a great help.
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Parallel scans are taken as seen by the horizontal
lines to the left and could be flattened to look like 40
the one to the right.
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Introduction
s9
RNFL
s8
s7
s6
s5
s4
s3
s2
s1
GCL+IPL
INL
OPL
ONL+IS
OS
s4 = external limiting
membrane.
s2 = interdigitation-zone
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Cost 50
functions
Graph search
The algorithm takes two types of cost functions:
- Surface cost functions describing the reverse probability of a pixel being on that surface. Examples of surface cost functions are
seen on the right. A convolution is used to construct cost functions favouring gradient shifts as well as favouring a number of dark
or bright pixels above/below the surface.
- Regional cost functions describe the probability of a pixel beloning to a specific region, where a region is the area between two
surfaces. If there are K surfaces, there are K+1 regions. To construct the regional costs, fuzzy membership functions has been
used. We discern between three different regions - dark, medium and bright regions.
The algorithm uses a transformation from the multiple surface segmentation problem to a problem of
finding a mimum-cost closed set in a closed graph
by constructing a graph with each voxel becoming
a vertice. The node weights will then correspond to
cost functions while the structure of the edges will
reflect the feasibility constraints(such as a known interval of distances of the surfaces or how quickly a
surface is allowed to rise and fall.). The minumum
cost closed set is found by finding a minimum st-cut
in a closely related graph.
The algorithm works in 3D, so instead of segmenting surfaces in individual 2D images, we can perform the segmentation with volumetric data, and
not lose 3D information.
Dark region
Cost function for s1
Medium region
Cost function for s9
Bright region
Splitting up the problem
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The problem is split up - first we find surface 1, 3, and 9 using only on surface cost functions in an image
downsampled by a factor 2.
Next we transform the area between surface 3 and 9 into a rectangular area using linear interpolation of the
downsampled image(see an example on the left). Now surface 5,6,7, and 8 are found using both surface costs
and regional costs.
At last a smaller part can be made of the area between surface 1 and 3, in which surface 2 is found using
a surface cost function, however now the fullsize image is used, as not enough information is present in the
downsampled image to discern the small detail required to find this surface. A smaller area between surface 3
and 5 is made in a similar fashion to find surface 4.
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Results
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The algorithm works. A slice from the final segmentation is shown below. The
thickness of the different layers are shown beside it.
slice y=1/1
RNFL thickness
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GCL+IPL thickness
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0
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INL thickness
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OPL thickness
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ONL + IS thickness
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OS thickness
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