Introduction and background
The proposed adaptive region-based edge smoothing deformable model
The rationale
Pixel-based image representation in multidimensional feature space
Feature name | Equation | Feature name | Equation |
---|---|---|---|
Gaussian filter |
\(\mathcal {N}(\sigma ,i_{x},j_{y}) = \frac {1}{2\pi \sigma ^{2}}e^{-\frac {{i_{x}}^{2} + {j_{y}}^{2}}{2\sigma ^{2}}}\)
| Gamma-normalised derivative |
\(L_{pp,\gamma -norm} = \frac {\sigma ^{\gamma }}{2}(\mathcal {N}_{xx}+\mathcal {N}_{yy}- \sqrt {{(\mathcal {N}_{xx}- \mathcal {N}_{yy})}^{2}+ 4{\mathcal {N}_{xy}}^{2}})\) (\(\frac {\sigma ^{\gamma }}{2}\) is normalisation factor with \(\gamma =\frac {3}{2}\)) |
Dyadic Gaussian |
\(I_{mn} = \frac {(R+G)}{2}\)
Y
r
g
= R + G − 2|R − G| |
\(L_{qq,\gamma -norm} = \frac {\sigma ^{\gamma }}{2}(\mathcal {N}_{yy}+ \mathcal {N}_{yy} + \sqrt {{(\mathcal {N}_{xx}-\mathcal {N}_{yy})}^{2}+ 4{\mathcal {N}_{xy}}^{2}})\)
| |
I
m
n
(c,s) = |I
m
n
(c) − I
n
t
e
r
p
s−c
I
m
n
(s)| | Differential Geometric Edge Definition |
\(L_{uu} = \mathcal {N}_{xx}+\mathcal {N}_{yy}\)
| |
R
G(c,s) = |(R(c) − G(c)) |
\(L_{u,u} = {\mathcal {N}_{x}}^{2}+{\mathcal {N}_{y}}^{2}\)
| ||
− I
n
t
e
r
p
s−c
(R(s) − G(s))| | |||
Y
r
g
(c,s) = |(Y
r
g
(c)) − I
n
t
e
r
p
s−c
(Y
r
g
(s))| |
\(L_{uv} = {\mathcal {N}_{x}}^{2}\mathcal {N}_{xx} + 2\mathcal {N}_{xy}\mathcal {N}_{x} \mathcal {N}_{y}+{\mathcal {N}_{y}}^{2}\mathcal {N}_{yy} \)(u,v) are local coordinate system [39] | ||
Gabor |
\(Gb(x,y,\gamma ,\lambda ,\sigma ,\theta ) = \exp (-\frac {1}{2}(\frac {{\hat {x}^{2}}}{\sigma ^{2}}+\frac {\hat {y}^{2}\gamma ^{2}}{\sigma ^{2}})* \)
| Difference of |
\({\Gamma }_{\sigma _{1},\sigma _{2}}(x,y)\) = \(\frac {1}{\sigma _{1} \sqrt {2\pi }}e^{-\frac {x^{2}+y^{2}}{2{\sigma _{1}^{2}}}}\)-\(\frac {1}{\sigma _{2}\sqrt {2\pi }}e^{-\frac {x^{2}+y^{2}}{2{\sigma _{2}^{2}}}}\)
|
\(\exp (\frac {i2\pi x}{\lambda })\)
| Gaussian (DOG) | ||
\(\hat {x} = x cos\theta + y sin\theta \qquad \hat {y} = y cos\theta - x sin\theta \)
|
Feature extraction and selection
Region classification model for initial optimum contour approximation
Initialisation of shape or contour profile
Contour profile optimisation
Adaptive edge smoothing update
ARESM application to segmentation of optic disc and cup
Optic disc segmentation
Optic cup segmentation
Experimental evaluation
Evaluation metrics
Datasets
RIMONE (1 vs 2) | Drishti-GS | ||||
---|---|---|---|---|---|
Image Type | Optic Disc | Optic Cup | Expert X vs Expert Y | Optic disc | Optic cup |
Normal images | 4.5% ± 2.07% | 6.93% ± 2.22% | 1 vs 2 | 1.00% ± 0.39% | 1.47% ± 0.83% |
Glaucoma images | 5.01% ± 3.15% | 7.31% ± 3.81% | 1 vs 3 | 1.87% ± 0.61% | 3.07% ± 1.57% |
All images | 4.74% ± 2.63% | 7.11% ± 3.06% | 1 vs 4 | 2.99% ± 1.35% | 5.31% ± 2.10% |
2 vs 3 | 0.84% ± 0.27% | 1.57% ± 0.94% | |||
2 vs 4 | 1.96% ± 1.20% | 3.81% ± 1.61% | |||
3 vs 4 | 1.09% ± 1.02% | 2.22% ± 1.25% |
RIMONE | Drishti-GS | |||
---|---|---|---|---|
CDR Type | Normal | Glaucoma | Both | |
Vertical | 0.42 ± 0.10 | 0.60 ± 0.17 | 0.50 ± 0.16 | 0.69 ± 0.13 |
Horizontal | 0.40 ± 0.11 | 0.57 ± 0.16 | 0.48 ± 0.16 | 0.70 ± 0.14 |
Area | 0.18 ± 0.09 | 0.37 ± 0.19 | 0.27 ± 0.17 | 0.51 ± 0.18 |
Model parameterisation
Determination on whether vasculature removal is required
Feature selection
Optic disc | Optic cup |
---|---|
\(\mathcal {N}_{R}(16)\), I
m
n
(4, 8), |
\(\mathcal {N}_{R}(16)\), \( \mathcal {N}_{xxR}(16)\), |
B
Y (4, 8), L
u,u
G
(8), | Γ16,4,G
, L
u,u
G
(8), |
\(\mathcal {N}_{G}(16)\), L
u
u
G
(16), |
B
Y (4, 7),I
m
n
(4, 8), |
L
q
q,γ−n
o
r
m
R
(16), |
L
u
v,v
u
G
(16), \(\mathcal {N}_{G}(16)\), |
I
m
n
(4, 7), B
Y (4, 7), |
I
m
n
(4, 7), I
m
n
(3, 7), \(\mathcal {N}_{R}(8)\), |
L
u
v
R
(4), L
u
v,v
u
G
(2), |
\(\mathcal {N}_{G}(16)\), \(\mathcal {N}_{yG}(8)\), |
L
u
u
G
(2), L
u
v
G
(4), |
\(\mathcal {N}_{yyG}(16)\), \(\mathcal {N}_{xxR}(8)\), |
L
u
u
R
(16), L
u
v,v
u
R
(16), |
L
q
q,γ−n
o
r
m
G
(8), |
L
u
v,v
u
G
(16), Γ8,4,R
, |
R
G(4, 8), \(\mathcal {N}_{xxG}(16)\), |
L
q
q,γ−n
o
r
m
G
(16), Γ4,2,G
, | Γ16,4,G
|
L
u
v,v
u
R
(8) |
Training protocol
Accuracy comparison with state-of-the-art approaches
-
Accuracy performance comparison with the previous approaches.
-
Accuracy performance comparison based on CDR values (Cup-Disc-Ratio).
Optic Disc Segmentation Accuracy Comparison
RIMONE | Drishti-GS | |||
---|---|---|---|---|
Normal | Glaucoma | All | ||
ARESM | 0.92 ± 0.06 | 0.90 ± 0.07 | 0.91 ± 0.07 | 0.95 ± 0.02 |
ASM model | 0.85 ± 0.10 | 0.77 ± 0.16 | 0.76 ± 0.13 | 0.87 ± 0.06 |
ACM model | 0.86 ± 0.07 | 0.85 ± 0.09 | 0.86 ± 0.08 | 0.91 ± 0.03 |
C-V model | 0.88 ± 0.13 | 0.86 ± 0.14 | 0.87 ± 0.14 | 0.85 ± 0.11 |
Optic cup segmentation accuracy comparison
RIMONE | Drishti-GS | |||
---|---|---|---|---|
Normal | Glaucoma | All | ||
ARESM | 0.91 ± 0.06 | 0.89 ± 0.06 | 0.89 ± 0.06 | 0.81 ± 0.10 |
ASM | 0.78 ± 0.09 | 0.73 ± 0.13 | 0.76 ± 0.12 | 0.72 ± 0.14 |
ACM | 0.76 ± 0.10 | 0.81 ± 0.09 | 0.79 ± 0.10 | 0.71 ± 0.12 |
C-V | 0.71 ± 0.18 | 0.73 ± 0.17 | 0.72 ± 0.18 | 0.80 ± 0.08 |
Accuracy Comparison based on CDR
Vertical CDR | Horizontal CDR | Area CDR | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
N | G | G+S | All |
p-value (N vs. G) | N | G | G+S | All |
p-value (N vs. G) | N | G | G+S | All |
p-value (N vs. G) | |
ARESM | 0.08 | 0.11 | 0.08 | 0.07 | 0.05 | 0.08 | 0.10 | 0.08 | 0.07 | 0.16 | 0.05 | 0.11 | 0.08 | 0.06 | 0.02 |
ASM | 0.22 | 0.21 | 0.21 | 0.22 | < 0.0001 | 0.31 | 0.29 | 0.27 | 0.29 | 0.05 | 0.26 | 0.33 | 0.29 | 0.27 | < 0.0001 |
ACM | 0.20 | 0.13 | 0.13 | 0.17 | < 0.0001 | 0.20 | 0.12 | 0.12 | 0.16 | < 0.0001 | 0.19 | 0.14 | 0.13 | 0.16 | < 0.0001 |
C-V | 0.13 | 0.14 | 0.14 | 0.13 | < 0.0001 | 0.12 | 0.13 | 0.12 | 0.12 | < 0.0001 | 0.09 | 0.14 | 0.12 | 0.11 | < 0.0001 |
Conclusion
-
We have developed the Region Classification Model (RCM) which identifies the initial optimum contour approximation representing optic disc or cup boundary between inside and outside region of interest based on pixel-wise classification in a multidimensional feature space, and performs region search for optimum contour profile. This is different from the existing models such as the conventional ASM model where the contour is static once it has been trained from the training set. Our model can dynamically search the region and obtain the most optimum contour.
-
To overcome misclassification and irregularity of contour points, we have proposed the Adaptive Edge Smoothing Update model (AESU) which can dynamically smooth and update the irregularities and misclassified points by minimising the energy function according to the force field direction in an iterative manner. Our model does not require a predefined template such as a circle or an ellipse. It could be any contour generated from the RCM model. This is different from the existing approaches which used a circular or ellipse fitting for smoothing update.