13 Modeling and Prediction of Choroidal Neovascularization …
375
where
E(θ )
N −2
i1
w · (1 − T PV F(I
i+1 (θ ), I i+1 ))
+ (1 − w) · F PV F(I
i+1 (θ ), I i+1 ).
(13.6)
and
T PV F
|I
i+1 ∩ I i+1 |
|I i+1 |
(13.7)
F PV F
|I i+1 | − |I
i+1 ∩ I i+1 |
|I |
(13.8)
In (13.6)–(13.8), |*| represents the volume of *, I
i+1 is the model-simulated CNV
region achieved from the true ith image and I i+1 is the ground truth CNV region in
the i +1th image. The true positive volume fraction (TPVF) represents the proportion
of correctly identified CNV volume to the ground truth CNV volume, and the false
positive volume fraction (FPVF) represents the proportion of falsely predicted CNV
volume to the total background volume. In the experiment the weight w is set to 0.5
to enforce equal importance of true positive and false positive.
The optimization is achieved by genetic algorithm [25]. Using random initialization, the algorithm is run several times. With outliers excluded, the average value of
the output is taken as the optimal parameter.
The growth parameter ρ N −1 for the last time point, is then estimated by curve
fitting based on the optimal value of ρ 1 , ρ 2 . . . ρ N −2 .
13.3 Experimental Results
In the experiment, there are 7 subjects, each scanned at 12 time points, i.e., N 12.
This means the reaction-diffusion model is applied to the first 11 images to compute
the prediction result for the 12th image. Then the result is validated by comparing it
with the real 12th image. The ground truth of CNV volumes are obtained by manual
segmentation in each B-scan by two experts independently. Figure 13.8a shows the
high correlation (r 0.978) of CNV volumes between ground truth I and II.
Figure 13.8b, c show the correlation of CNV volumes between the prediction
results and ground truth I, or ground truth II. From the figure, we can see that the
predicted results are highly positively correlated with both of the ground truth. The
correlation coefficient are 0.988 and 0.993 respectively. Therefore in the following
we choose ground truth I for comparison.
Figure 13.9 shows the curve fitting results of the CNV growth parameters for the
7 patients, in the treatment group and reference group, respectively. The last point in
375
where
E(θ )
N −2
i1
w · (1 − T PV F(I
i+1 (θ ), I i+1 ))
+ (1 − w) · F PV F(I
i+1 (θ ), I i+1 ).
(13.6)
and
T PV F
|I
i+1 ∩ I i+1 |
|I i+1 |
(13.7)
F PV F
|I i+1 | − |I
i+1 ∩ I i+1 |
|I |
(13.8)
In (13.6)–(13.8), |*| represents the volume of *, I
i+1 is the model-simulated CNV
region achieved from the true ith image and I i+1 is the ground truth CNV region in
the i +1th image. The true positive volume fraction (TPVF) represents the proportion
of correctly identified CNV volume to the ground truth CNV volume, and the false
positive volume fraction (FPVF) represents the proportion of falsely predicted CNV
volume to the total background volume. In the experiment the weight w is set to 0.5
to enforce equal importance of true positive and false positive.
The optimization is achieved by genetic algorithm [25]. Using random initialization, the algorithm is run several times. With outliers excluded, the average value of
the output is taken as the optimal parameter.
The growth parameter ρ N −1 for the last time point, is then estimated by curve
fitting based on the optimal value of ρ 1 , ρ 2 . . . ρ N −2 .
13.3 Experimental Results
In the experiment, there are 7 subjects, each scanned at 12 time points, i.e., N 12.
This means the reaction-diffusion model is applied to the first 11 images to compute
the prediction result for the 12th image. Then the result is validated by comparing it
with the real 12th image. The ground truth of CNV volumes are obtained by manual
segmentation in each B-scan by two experts independently. Figure 13.8a shows the
high correlation (r 0.978) of CNV volumes between ground truth I and II.
Figure 13.8b, c show the correlation of CNV volumes between the prediction
results and ground truth I, or ground truth II. From the figure, we can see that the
predicted results are highly positively correlated with both of the ground truth. The
correlation coefficient are 0.988 and 0.993 respectively. Therefore in the following
we choose ground truth I for comparison.
Figure 13.9 shows the curve fitting results of the CNV growth parameters for the
7 patients, in the treatment group and reference group, respectively. The last point in