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F. Shi et al.
10.2.2 Method
The automated method consists of pre-processing, layer segmentation and region
segmentation. The pre-processing, includes fast bilateral filtering for denoising and
B-scan alignment for motion distortion correction. During layer segmentation, Surfaces 1–6, 11, and 12 are detected by multi-resolution graph-search method [2, 28]
with various smoothness constraints. Region segmentation is carried out based on
the positions of surfaces 11 and 12. Their difference in height (z-coordinate) is used
to form a PED footprint map. Finally, the other surfaces are detected in a flattened
OCT volume and then corrected using the PED footprints.
In this section, we define the 3-D coordinates as follows. The x-axis is along the
width of a B-scan, the y-axis represents the different B-scans, and the z-axis is in the
vertical direction. Therefore a B-scan is in the x-z plane.
10.2.2.1 Multi-resolution Graph Search
The 3-D graph search algorithm was proposed by Li et al. [29] for optimal surface
segmentation in volumetric images. In the method, the volumetric image is defined
as a 3-D matrix I (x, y, z) with size X × Y × Z , and a feasible surface is defined by a
function S(x, y) as the surface height, where x ∈ {0, . . . , X − 1}, y ∈ {0, . . . , Y − 1}
and S(x, y) ∈ {0, . . . , Z − 1}. Two parameters, x and y , control the smoothness
of feasible surfaces, defined as the maximum height difference between neighboring
surface points in x- and y- direction, respectively. A cost function c(x, y, z) is assigned
to each voxel, and the optimal surface is found to be the one with minimum overall
cost.
To find the optimal surface, the volumetric image is first transformed into a nodeweighted directed graph where each node corresponds to one and only one voxel.
Arcs are constructed according to the spatial relationship between voxels as well as
the smoothness constraints, and node weights are computed from the cost function.
Searching for the optimal surface is transformed to seeking a minimum weight closed
set in this graph. This graph is then further transformed to an arc-weighted digraph
where the optimal solution can be found in polynomial time by computing a minimum
s-t cut [30, 31].
In the following we focus on the cost functions, smoothness parameters, and
constraints used in our method. From prior knowledge, in each B-scan, surfaces 1, 3,
5, 7, 9 and 10 are edges with dark-to-bright transition, while surfaces 2, 4, 6, 8 and 11
are with bright-to-dark transition. For most surfaces, the edge-based cost functions
are used, calculated by 2-D Sobel operator in the z-direction. For different type of
transitions, values of the cost function are inversed. An additional region-based cost
is used for detection of surface 1, calculated as the summation of intensities of the
voxels above but within certain distance to the current voxel. Both surface 1 and 7
are high-contrast dark-to-bright edges, but the region above surface 1 is darker than
that above surface 7. Therefore, by adding the region-based cost to the edge-based
F. Shi et al.
10.2.2 Method
The automated method consists of pre-processing, layer segmentation and region
segmentation. The pre-processing, includes fast bilateral filtering for denoising and
B-scan alignment for motion distortion correction. During layer segmentation, Surfaces 1–6, 11, and 12 are detected by multi-resolution graph-search method [2, 28]
with various smoothness constraints. Region segmentation is carried out based on
the positions of surfaces 11 and 12. Their difference in height (z-coordinate) is used
to form a PED footprint map. Finally, the other surfaces are detected in a flattened
OCT volume and then corrected using the PED footprints.
In this section, we define the 3-D coordinates as follows. The x-axis is along the
width of a B-scan, the y-axis represents the different B-scans, and the z-axis is in the
vertical direction. Therefore a B-scan is in the x-z plane.
10.2.2.1 Multi-resolution Graph Search
The 3-D graph search algorithm was proposed by Li et al. [29] for optimal surface
segmentation in volumetric images. In the method, the volumetric image is defined
as a 3-D matrix I (x, y, z) with size X × Y × Z , and a feasible surface is defined by a
function S(x, y) as the surface height, where x ∈ {0, . . . , X − 1}, y ∈ {0, . . . , Y − 1}
and S(x, y) ∈ {0, . . . , Z − 1}. Two parameters, x and y , control the smoothness
of feasible surfaces, defined as the maximum height difference between neighboring
surface points in x- and y- direction, respectively. A cost function c(x, y, z) is assigned
to each voxel, and the optimal surface is found to be the one with minimum overall
cost.
To find the optimal surface, the volumetric image is first transformed into a nodeweighted directed graph where each node corresponds to one and only one voxel.
Arcs are constructed according to the spatial relationship between voxels as well as
the smoothness constraints, and node weights are computed from the cost function.
Searching for the optimal surface is transformed to seeking a minimum weight closed
set in this graph. This graph is then further transformed to an arc-weighted digraph
where the optimal solution can be found in polynomial time by computing a minimum
s-t cut [30, 31].
In the following we focus on the cost functions, smoothness parameters, and
constraints used in our method. From prior knowledge, in each B-scan, surfaces 1, 3,
5, 7, 9 and 10 are edges with dark-to-bright transition, while surfaces 2, 4, 6, 8 and 11
are with bright-to-dark transition. For most surfaces, the edge-based cost functions
are used, calculated by 2-D Sobel operator in the z-direction. For different type of
transitions, values of the cost function are inversed. An additional region-based cost
is used for detection of surface 1, calculated as the summation of intensities of the
voxels above but within certain distance to the current voxel. Both surface 1 and 7
are high-contrast dark-to-bright edges, but the region above surface 1 is darker than
that above surface 7. Therefore, by adding the region-based cost to the edge-based