8 Segmentation of Optic Disc and Cup-to-Disc Ratio Quantification …
199
where p 0 denotes the NCO candidate in the RPE boundary and C(x, y) represents
the curvature of the given point. We used the location constraint to ensure p 0 in an
appropriate region. w denotes the width of the image so that the lateral position x
is limited at the center part of the image. We also restricted the height of the NCO
between h 1 and h 2 , which are two adaptive parameters. Taking the left NCO point
as an example, we fitted a straight line to the left-side flat part of the RPE boundary,
indicated as g(x) (shown in red in Fig. 8.3d), and assigned h 1 min(g(x 1 ), g(x 2 ))
and h 2 max(g(x 1 ), g(x 2 )), where x 1 and x 2 are assumed as the start and the end
x-coordinate of the fitting line, fixed to 0–300 in this paper. The equivalent operation
was also conducted for the right NCO point and the right-side part of the RPE
boundary. An example of the initial NCO detection is shown in Fig. 8.3d.
In the projection fundus image, we firstly defined a scope of disc margin in x-axis
direction as [x l − 10, x r + 10], where x l and x r are the average x-coordinate of the
left and right NCO candidates in B-scans 95#–105#, respectively, considering the
distance between the left and right NCO is largest in central B-scans, and filtered
the individual outliers beyond this scope. Then, we defined a disc margin smoothing
procedure by the spatial correlation smoothness constraint as:
p i
⎧
⎪ ⎪ ⎪ ⎪ ⎨
⎪ ⎪ ⎪ ⎪ ⎩
(x, y i )
if
p j ∈N ( p i )
||x − x j ||/n ≤ k
p j ∈N ( p i )
x j /n, y i
else
(8.2)
where p i indicates the point of the disc margin in projection image corresponding
to the column of p 0 , and y i is the serial number of the B-scan. The N ( p) denotes
the disc margin points in former 2 and latter 2 consecutive B-scans of the current
B-scan defined as a neighborhood and n 4 represents the neighborhood size, while
the constant k is set to 5. The x-coordinate locations of the initially selected points
are smoothed by considering the selected locations in neighboring B-scans, in order
to restrict the NCO locations in the consecutive B-scans to not change more than a
threshold amount.
Figure 8.3e shows the NCO detection result in the projection fundus image. The
green curve indicates the coarse disc margin by mapping NCO points from each Bscan to the projection image. For preserving the shape of the optic head, we refined
the disc margin using a convex hull fitting operation, as shown in Fig. 8.3f. A manual
expert-defined reference standard is shown in Fig. 8.3g for comparison.
Although the result indicates that the coarse disc margin is close to the reference
standard, its determination still depends on the precision of the RPE segmentation.
The points with maximum curvature may not be the optimal location for the NCO
when the segmentation result is poor. Therefore, we developed a SVM-based patch
searching method to refine the NCO detection in a following step.
199
where p 0 denotes the NCO candidate in the RPE boundary and C(x, y) represents
the curvature of the given point. We used the location constraint to ensure p 0 in an
appropriate region. w denotes the width of the image so that the lateral position x
is limited at the center part of the image. We also restricted the height of the NCO
between h 1 and h 2 , which are two adaptive parameters. Taking the left NCO point
as an example, we fitted a straight line to the left-side flat part of the RPE boundary,
indicated as g(x) (shown in red in Fig. 8.3d), and assigned h 1 min(g(x 1 ), g(x 2 ))
and h 2 max(g(x 1 ), g(x 2 )), where x 1 and x 2 are assumed as the start and the end
x-coordinate of the fitting line, fixed to 0–300 in this paper. The equivalent operation
was also conducted for the right NCO point and the right-side part of the RPE
boundary. An example of the initial NCO detection is shown in Fig. 8.3d.
In the projection fundus image, we firstly defined a scope of disc margin in x-axis
direction as [x l − 10, x r + 10], where x l and x r are the average x-coordinate of the
left and right NCO candidates in B-scans 95#–105#, respectively, considering the
distance between the left and right NCO is largest in central B-scans, and filtered
the individual outliers beyond this scope. Then, we defined a disc margin smoothing
procedure by the spatial correlation smoothness constraint as:
p i
⎧
⎪ ⎪ ⎪ ⎪ ⎨
⎪ ⎪ ⎪ ⎪ ⎩
(x, y i )
if
p j ∈N ( p i )
||x − x j ||/n ≤ k
p j ∈N ( p i )
x j /n, y i
else
(8.2)
where p i indicates the point of the disc margin in projection image corresponding
to the column of p 0 , and y i is the serial number of the B-scan. The N ( p) denotes
the disc margin points in former 2 and latter 2 consecutive B-scans of the current
B-scan defined as a neighborhood and n 4 represents the neighborhood size, while
the constant k is set to 5. The x-coordinate locations of the initially selected points
are smoothed by considering the selected locations in neighboring B-scans, in order
to restrict the NCO locations in the consecutive B-scans to not change more than a
threshold amount.
Figure 8.3e shows the NCO detection result in the projection fundus image. The
green curve indicates the coarse disc margin by mapping NCO points from each Bscan to the projection image. For preserving the shape of the optic head, we refined
the disc margin using a convex hull fitting operation, as shown in Fig. 8.3f. A manual
expert-defined reference standard is shown in Fig. 8.3g for comparison.
Although the result indicates that the coarse disc margin is close to the reference
standard, its determination still depends on the precision of the RPE segmentation.
The points with maximum curvature may not be the optimal location for the NCO
when the segmentation result is poor. Therefore, we developed a SVM-based patch
searching method to refine the NCO detection in a following step.