27-06-2014, 11:50 AM
Novel Fractal Feature-Based Multiclass Glaucoma Detection and Progression Prediction
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Abstract
We investigate the use of fractal analysis (FA) as the
basis of a system for multiclass prediction of the progression of
glaucoma. FA is applied to pseudo 2-D images converted from 1-D
retinal nerve fiber layer data obtained from the eyes of normal
subjects, and from subjects with progressive and nonprogressive
glaucoma. FA features are obtained using a box-counting method
and a multifractional Brownian motion method that incorporates
texture and multiresolution analyses. Both features are used for
Gaussian kernel-based multiclass classification. Sensitivity, specificity,
and area under receiver operating characteristic curve
(AUROC) are computed for the FA features and for metrics obtained
usingwavelet-Fourier analysis(WFA) and fast-Fourier analysis
(FFA). The AUROCs that predict progressors from nonprogressors
based on classifiers trained using a dataset comprised
of nonprogressors and ocular normal subjects are 0.70, 0.71, and
0.82 for WFA, FFA, and FA, respectively. The correct multiclass
classification rates among progressors, nonprogressors, and ocular
normal subjects are 0.82, 0.86, and 0.88 for WFA, FFA, and
FA, respectively. Simultaneous multiclass classification among progressors,
nonprogressors, and ocular normal subjects has not been
previously described. The novel FA-based features achieve better
performance with fewer features and less computational complexity
thanWFA and FFA.
INTRODUCTION
GLAUCOMA is a progressive optic neuropathy that results
in structural damage to the retina and loss of vision [1].
The retina has about a million retinal ganglion cells, the axons
of which constitute the retinal nerve fiber layer (RNFL) [2]. At
a cellular level, glaucoma is characterized by a progressive and
rapid death of the ganglion cells and their axons in the RNFL
due to the process of apoptosis [2].
Progressive glaucomatous damage to the RNFL is irreversible
and worsens vision loss. Consequently, detecting glaucomatous
progression is critical in the management of the disease. Visual
field (VF) tests using standard automated perimetry are widely
used in diagnosing progression; however, structural changes in
the RNFL often precede functional changes in VF data [3]. In
addition, inherent variability in VF test results often interferes
with clinical determinations of progression. Improved methods
for detecting and/or predicting progressive changes in the RNFL
structural data are needed.
Evaluation of structural damage to the RNFL is difficult due
to the heterogeneous nature of glaucoma [4], [5]. The mean
RNFL values, obtained with imaging technologies such as the
scanning laser polarimetry (SLP) and optical coherence tomography,
do not provide a reliable basis for predicting progression
because of interpatient variations [6], [7]. Feature-based
techniques including fast-Fourier analysis (FFA) and wavelet-
Fourier analysis (WFA) have been proposed [8], [9].Alimitation
of these techniques is that they do not fully capture the inherent
randomness and irregularity of RNFL damage [10]–[16].
METHODS AND DATASETS
flowchart of the implementation of our methods is shown
in Fig. 1. For preprocessing, the RNFL data are normalized to
zero mean and transformed to the pseudo 2-D image [10]. Normalization
is performed at different stages because our methods
involve multiple analyses in which the data need to be brought
on similar scale for further processing. WFA and FA featurebased
techniques are applied on the pseudoimages to obtain
representative features for subsequent classification.
Principal component analysis (PCA) and the Gaussian kernel
method are utilized for feature selection. PCA is used because
our data are correlated and PCA is more effective in handling
correlated data over other equivalent methods. Note we do not
use multiple discriminant analysis (MDA) because MDA maximizes
the difference between values of the dependent variables,
whereas PCA maximizes the variance in all the variables.
Evaluation of Ocular Normal Subjects
Along with predicting change in glaucoma, it is also crucial to
avoid a high rate of false positives (specificities) that would limit
the usability of our classifiers for further analysis. Consequently,
for measuring specificities, the same training data (90% of 14
progressors and 45 nonprogressors) are used as discussed in the
previous analysis, in Section III-E. However, the testing data
are different and consist of 37 ocular normal subjects (100%).
Here, only specificities are obtained, since the progressors are
not included in testing. The reason for this testing is to assess the
effectiveness of previous classifiers for avoiding false positives
in ocular normal subjects
Datasets and Training Options
Atotal of 96 subjectswere followed starting from the baseline
up to 40 months. The RNFL data were obtained on each subject
approximately every six months, using SLP. Fig. 5(a) shows a
typical 2-D retinal fundus image, centered and focused on its
retinal nerve head. Fig. 5(b) shows the resulting 1-D RNFL data
consisting of thickness measurement obtained along a circular
path in the retina, as shown in Fig. 5(a). SLP provides 256
RNFL depth estimates within an 8-pixel-wide ring with inner
and outer radii of 27 and 35 pixels, respectively. These estimates
are grouped into 64 sectors to yield a RNFL data vector of 64
points in the 360◦ around the optic disk, as shown in Fig. 5(b).
The subjects were regarded as progressors, nonprogressors, or
ocular normal subjects on the basis of clinical evaluations of the
VFs. The complete dataset consists of the baseline RNFL data
for 14 progressors and 45 nonprogressors.
Classification of Progressors Versus Nonprogressors:
Training With 67% of Nonprogressors and Ocular Normal
Subjects
As previously explained (see Section III-G), it is important to
differentiate the nonprogressors from ocular normal subjects for
predicting the changes in the progressors. In this case, our LDA
classifiers are trained with 67% of nonprogressors (31 out of
45 subjects) and 100% of ocular normal subjects (37 subjects).
Based on the LDA classifiers obtained from this training set, the
ocular normal subjects are classified from those who convert to
nonprogressors. By assessing the relationship between ocular
normal subjects and nonprogressors, future progressors may
be predicted. The test data are composed of 14 progressors at
one scan prior, two scans prior
Multiclass Classification of Progressors, Nonprogressors,
and Ocular Normal Subjects
Fig. 6 shows the scatter plot using our kernel-based multiclass
SVM classification technique. The kernel-based method
typically enhances the separability of features (see Fig. 6). In
Fig. 6(a) and ©, the three classes require a nonlinear classifier.
However, in Fig. 6(b) and (d), the three sets of data are relatively
better separated than those in Fig. 6(a) and ©. In Fig. 6©, the
features are aligned in straight lines. A possible explanation for
this feature alignment is that it is a characteristic of the FAof 1-D
RNFL shapes, which accounts for the closeness of irregularity.
After preprocessing the data, training is done using the complete
1-D baseline RNFL data comprised of 14 progressors,
45 nonprogressors, and 37 ocular normal subjects. By using a
multiclass SVM, we are able to train three classes concurrently,
which was not possible using the methods shown in Sections
III-E–III-H. We then obtain the multiclass SVM classifiers that
best characterize each class’s decision function. Finally, the testing
is done in a repeated manner and the rate of correct class
prediction is measured
RESULTS AND DISCUSSIONS
Two-Class Classification
Table II shows the sensitivity, specificity, and AUROC at different
visits after the first scan prior to progression as explained
in Section III-E. These values indicate that the prediction rate
using all feature-based analyses is highest at the first scan prior
to the progression. Although AUROC remains the same in one
and two scans prior for WFA, the sensitivity and specificity
values can change because they depend on the distribution of
the dataset. Note that with a different split ratio (70%:30%), the
performance is decreased. Note also that with leave-one-out, the
performance is slightly increased
Multiclass Classification
Table VI summarizes and compares the results of a multiclass
SVM classification with those of a feed-forward NN method for
predicting glaucomatous progression. This table again shows
FFA performance results for complete comparison. Since this
result is for multiclass classification, separate sensitivity and
specificity measures cannot be obtained. Alternatively, we measure
correct rates, which measure the rates of correct prediction
CONCLUSION AND FUTURE WORK
The efficacy of novel FA feature-based techniques for detecting
and predicting glaucomatous progression is demonstrated.
The performance of our method is compared with those of conventional
feature-based methods (WFA and FFA). Our method
yields an AUROC of 0.82, compared with those of 0.70 and
0.71 forWFA and FFA, respectively. The effectiveness of multiclassification
of progressors, nonprogressors, and ocular normal
subjects is also shown using Gaussian kernel-based multiclass
SVM (see Table VI). Our FA feature-based multiclass SVM
method achieves a correct rate of 0.88 using FA, compared with
those of 0.82 and 0.86 usingWFA and FFA, respectively. In addition,
it is also shown that multiclass SVM can simultaneously
discriminate the different stages of progression, which is the first
attempt in the literature. Our FA feature-based techniques also
perform with fewer features and less computational complexity
than those works reported in the literature [8], [9].
Glaucomatous progression is highly patient-dependent. To
achieve a clinically important progression predictor, further algorithmic
improvements are needed. A potential area for developing
these improvements involves fusing structural and functional
data. Fusion of both data may better reflect glaucomatous
damages since clinically discernible changes are shown both in
structure and function. For such an application, it is expected
that investigation of correlation among different features and
appropriate multiclass classification will be necessary.