Page 213 - Computational Retinal Image Analysis

3 Experimental results 209

nels, we have

=
(
I  min p () ( − tp)) + D () (19)
1
p tp().
min
Let Wκ(p) be a κ × κ window centered at pixel p. The simplified dark channels of
the normalized images are given as:

D 
p′
J () = min { D ( )}, (20)
p
d
pW () min
′
p
∈
κ
I 
′
Jp() = min I {  p ( )}. (21)
d
p
′∈
pW () min
κ
We approximate t(p) within W(p) as a constant, therefore
D 
I 
Jp() ( − tp)) + J () (22)
=
p tp().
(
1
d
d
v
h
The guidance vector field V = (V , V ) is calculated as
h
Vm n) = I  min ( mn +1 ) − I  min (, (23)
m n),
,
(,
Vm n) = I  min ( m +1 n ,) − I  min (, (24)
v
(,
m n).
Combining the gradient vector field with Eq. (11), we obtain the output O*.
We further smooth the first item ϕ(p) = 1 − t(p) using the edge-preserving
smoothing filter in Eq. (14) and obtain ϕ*(p).
The transmission map t(p) is then computed as:
*
tp() =−φ * p (). (25)
1
The underlying (dehazed) image is computed as:
Ip() − L
Dp() = c c + L . (26)
c
*
tp() c
Recalled that we ignore α in our model, however, in the cases where the
attenuation α cannot be ignored, we can still solve the problem by estimating α using
1
a precataract image and computing the final output image as Dp(). In this chapter,
c
we simply restore the image based on Eq. (26). α
3 Experimental results
3.1 Dataset
We conduct experiments using the images in the ORIGA dataset [41, 62]. The
ORIGA dataset contains 650 images, including 203 images from eyes with cataracts
and 447 images from eyes without any cataract. We mainly apply SGRIF on the
optic disc area and evaluate how it affects subsequent analysis on the optic disc. To
prevent error propagation from optic disc segmentation to optic cup segmentation,
we use the disc from the original image and the disc boundaries are kept the same.