purpose. The purpose of this study was to apply shape-based analysis techniques of retinal nerve fiber layer (RNFL) thickness to GDx-VCC (variable corneal and lens compensator; Laser Diagnostic Technologies, Inc., San Diego, CA) polarimetry data and to evaluate the techniques’ ability to detect glaucoma in its earliest stages. Wavelet-based (wavelet-Fourier analysis [WFA]), Fourier-based (fast Fourier analysis [FFA]), and several previous variations of shape-based analysis were considered, as well as the standard metric nerve fiber indicator (NFI), and all were compared as a function of disease stage.

methods. GDx-VCC scans of one eye of each of 67 patients with glaucoma and each of 67 healthy age-matched subjects provided RNFL thickness estimates at a fixed distance from the optic disc. Severity of disease was graded according to the Glaucoma Staging System and also by mean deviation (MD) from standard automated perimetry. WFA, FFA, and NFI procedures were performed including the following variations: use of signed or unsigned phase, inclusion of interocular or intraocular asymmetry of analysis parameters, and combination of features by principle components analysis or Wilks λ. Independent samples (*k*-fold variation) were used for training and testing. Sensitivity, specificity, and receiver operating characteristic (ROC) area were obtained.

results. Classification performance of WFA (ROC = 0.978) was significantly better than FFA (ROC = 0.938) and NFI (ROC = 0.900). This difference was largest for the earliest stages of glaucoma. Shape-based analysis methods performed better than NFI overall. Adding between-eye asymmetry measures helped FFA but not WFA.

conclusions. Shape-based analysis, and WFA in particular, makes an important improvement in detecting earliest glaucoma with polarimetry.

^{ 1 }

^{ 2 }

^{ 3 }

^{ 4 }

^{ 5 }

^{ 6 }

^{ 7 }

^{ 8 }

^{ 9 }This conclusion makes it even more important to establish new tests of function and/or neuroanatomic loss that better delineate and characterize early glaucoma. To that end, the present paper reports our efforts to improve the characterization of neuroanatomic disruption in glaucoma. Specifically, we assessed the utility of inferring local thickness of the retinal nerve fiber layer (RNFL) by polarimetry with the GDx-VCC (variable corneal and lens compensator; Laser Diagnostic Technologies, Inc., San Diego, CA).

*shape*of the surface conveyed by the map of these local thickness measurements (Essock EA, et al.

*IOVS*1999;40:ARVO Abstract 3481; Essock EA, et al.

*IOVS*2001;42:ARVO Abstract 93; Sinai MJ, et al.,

*IOVS*2001;42:ARVO Abstract 717; Sinai MJ, et al.

*IOVS*2002;43:ARVO E-Abstract 302; Bryant FD, et al.

*IOVS*2000;41:ARVO Abstract 485; Essock EA, et al.

*IOVS*2003;44:ARVO E-Abstract 3378; Gunvant P, et al.

*IOVS*2004;45:ARVO E-Abstract 5504).

^{ 10 }

^{ 11 }That is, if the shape of the data surface that is characteristic of healthy eyes can be quantified, then deviations from the normative shape could be quantified. In addition, emphasizing shape rather than thickness can obviate the large individual variation among healthy eyes of general thickness.

^{ 12 }

^{ 13 }

^{ 14 }In the typical analysis, RNFL thickness measurements at points at a given distance from the disc as a function of angle are analyzed at one or more distances from the disc (i.e., one or more “rings”). This TSNIT (temporal, superior, nasal, inferior, temporal) graph of thickness for a ring conveys a general double-hump pattern of thickness due to the much greater number of ganglion cell axons entering the disc superiorly and inferiorly. However, the newer imaging techniques indicate that the smooth, “textbook” double-hump pattern of TSNIT RNFL thickness of an individual healthy eye can actually be quite jagged, often with very low local minima at various locations within the superior and inferior humps of the TSNIT pattern. In addition, it has been reported that a significant number of healthy eyes show a bimodal or “split bundle” (Vermeer KA, et al.

*IOVS*2004;45:ARVO E-Abstract 3309; Varma R, et al.

*IOVS*2002;43:ARVO E-Abstract 262).

^{ 15 }

*set*of sinusoids in which each sinusoid is a different scale, or frequency) and thus has a different number of humps across the TSNIT data set.

^{ 10 }Fourier analysis breaks an individual’s TSNIT pattern into the sum of a set of sine-wave patterns of particular amplitude and phase (position). We have applied this analysis method to the TSNIT pattern previously in three ways: simultaneously at multiple distances from the disc in a two-dimensional polar Fourier analysis (Essock EA, et al.

*IOVS*1999;40:ARVO Abstract 3481) at a single ring with the Fourier analysis performed separately on the superior and inferior halves of the data (Essock EA, et al.

*IOVS*1999;40:ARVO Abstract 3481; Essock EA, et al.

*IOVS*2001;42:ARVO Abstract 93; Bryant FD, et al.

*IOVS*2000;41:ARVO Abstract 485; see also Ref.

^{ 16 }); and most typically, at a single ring for the full TSNIT pattern (Essock EA, et al.

*IOVS*2001;42:ARVO Abstract 93; Sinai MJ, et al.

*IOVS*2001;42:ARVO Abstract 717; Sinai MJ, et al.

*IOVS*2002;43:ARVO E-Abstract 302; see also Ref.

^{ 11 }).

^{ 17 }We have also considered combinations of amplitudes of specific frequencies (i.e., specific shapes) (Essock EA, et al.

*IOVS*1999;40:ARVO Abstract 3481; Essock EA, et al.

*IOVS*2001;42:ARVO Abstract 93; Bryant FD, et al.

*IOVS*2000;41:ARVO Abstract 485)

^{ 10 }both unsigned phase (i.e., indicating magnitude) (Sinai MJ, et al.

*IOVS*2001;42:ARVO Abstract 717; Sinai MJ, et al.

*IOVS*2002;43:ARVO E-Abstract 302)

^{ 17 }and signed phase (indicating magnitude and direction) (Essock EA, et al.

*IOVS*2001;42:ARVO Abstract 93) and measures of asymmetry of these amplitude and phase parameters, both between the fellow eyes and also between superior and inferior hemiretinas within an eye (Essock EA, et al.

*IOVS*1999;40:ARVO Abstract 3481; Essock EA, et al.

*IOVS*2001;42:ARVO Abstract 93; Sinai MJ, et al.

*IOVS*2002;43:ARVO E-Abstract 302; Bryant FD, et al.

*IOVS*2000;41:ARVO Abstract 485). The use of asymmetry values has appeared to be a particularly promising addition to FFA and are directly examined herein. However, despite the success of these various approaches, a Fourier analysis may not be the best choice to capture the shape of the normal TSNIT pattern in relatively few parameters. In the present paper, we report use of a different shape analysis method (Essock EA, et al.

*IOVS*2003;44:ARVO E-Abstract 3378; Gunvant P, et al.

*IOVS*2004;45:ARVO E-Abstract 5504)

^{ 18 }

^{ 19 }

^{ 20 }that was developed to address this weakness of using FFA for RNFL analysis. Instead of a Fourier analysis that emphasizes the frequency domain (i.e., a set of the infinite regular repeating patterns of sine waves), we adopted a wavelet analysis for the primary analysis of the TSNIT pattern. A wavelet analysis offers the advantage that it emphasizes local shape (i.e., the space domain) and is better suited to capture the irregular or abrupt changes in the TSNIT shape that are particularly evident in GDx-VCC data (see Fig. 6B ) (Vermeer KA, et al.

*IOVS*2004;45:ARVO E-Abstract 3309).

^{ 21 }

*P*> 0.05). None of the study participants had significant ocular media opacity that could affect their visual field results or imaging with GDx-VCC.

^{ 22 }

^{ 23 }and were also staged with respect to their mean deviation (MD). All healthy subjects had normal intraocular pressure and had normal appearance of optic discs. Visual fields were measured in most, but not all, cases and were normal.

^{ 22 }Briefly, it is a nomogram that uses the MD and pattern standard deviation (PSD) on a Cartesian coordinate diagram with MD on the

*x*-axis and corrected PSD on the

*y*-axis. The GSS can be used to stage visual field damage in any field report that gives the visual field indices (MD and the corrected PSD). If the corrected PSD was not available or was unreliable, the corrected PSD was calculated by adding 0.7 to the PSD.

^{ 22 }The GSS classifies subjects into six categories: normal, and stages 1 to 5 of severity.

^{ 22 }All patients in the glaucoma group had a visual field defect of GSS stage 1 or greater. The stages 1 to 3 are considered to be mild to moderate severity with stage 1 considered to have very subtle defects; stage 2 is usually field plots with nasal steps or mild scotoma; and stage 3 is usually an overt defect such as dense arcuate scotoma. The visual field at stage 4 is considered to be at an advanced stage of disease and a stage 5 visual field has a very low threshold with only small remnants of sensitivity. The GSS can also classify the visual field defects into three other categories: generalized defects, localized defects, and mixed defects. Generally, the mixed defect is observed to be the most common type of defect, whereas patients with early glaucoma are typically observed to have localized defects.

^{ 22 }The present sample was consistent with this finding.

^{ 24 }Macular images are obtained, and the combined polarization of the radially oriented axons of Henle’s fiber layer of the macula and the anterior segment (a bow-tie pattern on the retardation image) is analyzed. A software program within the GDx-VCC then determines an estimate of polarization magnitude and axis that is due to the anterior segment birefringence. These estimates are applied to compensate a polarization retardation map at the disc for the individual eye’s anterior segment contribution to such maps. Retardation is converted to an estimate of depth

^{ 25 }and the software provides 256 RNFL depth estimates within an eight-pixel-wide ring with inner and outer radii of 27 and 35 pixels, respectively. These estimates are grouped into 64 sectors to yield a TSNIT curve of 64 points in the 360° around the disc.

^{ 26 }and is highly suitable for analyzing discontinuities and abrupt changes contained in signals.

^{ 27 }The wavelet transform applies the scaling function (Fig. 2A)and the wavelet function (Fig. 2B)yielding a down-sampled signal represented by two sets of coefficients, termed the

*approximation*part and the

*detail*part. The approximation coefficients contain down-sampled spatial information, and the detail coefficients contain detailed information characterizing the difference between the signal and the approximation (Fig. 3) . DWT is a

*multiscale analysis*method, meaning that the analysis can be based on various scales.

^{ 27 }At each transformation scale (or “level” of this multiscale pyramid), there is a different resolution ability encoded in that level’s approximation and detail coefficients (i.e., at each level, the DWT analysis is applied to the prior level’s approximation coefficients). We found that a second-level DWT analysis works well for 64-point VCC data. The second-level decomposition preserves high enough spatial resolution ability (in the approximation part), but results in a relatively low-frequency resolution of the detail part. For this reason, a further step, drawing from our previous work,

^{ 10 }applies a Fourier transform to the second-level DWT detail part (constituting a

*second-step*transformation), and provides frequency amplitudes to achieve high frequency resolution for WFA. The final part of this step is to normalize DWT approximation coefficients and FFT amplitudes separately, and to join them together as the final set of features used in the analysis (i.e., the “feature vector”). Second, the dimensions of the feature vectors are reduced by using principal components analysis (PCA)

^{ 27 }to combine (and weight) various features to maximize the spread of the data points in the resultant multidimensional (reduced) feature space. The resultant lower dimensionality of the feature vectors can make the classifier more efficient and more stable. Third, a classification procedure is applied to the data. The Fisher linear discriminant function (LDF) was used as a classifier, as it performs slightly better than other similar methods.

^{ 28 }The role of an LDF is to provide a criterion that optimally classifies a set of values into two categories (in the present study: glaucoma and healthy). To assure external validity of the obtained LDF, the LDF must be tested on data (a “test” set) that are independent of the “training” set from which they were derived. To achieve this, the dataset was first randomly split into two independent subsets, one for training the classifier and obtaining the LDF, and one for testing it. To provide a robust validation procedure, a variation of

*k*-fold cross validation

^{ 29 }

^{ 30 }was used, as it is superior to methods such as split-half or holdout and is especially advantageous when a very large sample is not possible. The procedure is similar to the split-half procedure, but the estimates are based on the mean of estimates from

*k*random splits, where

*k*is usually several hundred. This method reduces bias and increases reliability.

^{ 29 }

^{ 30 }Also, this repetition allows the use of a larger proportion of the cases for the training set, resulting in greater stability of the final estimate. The method has been used effectively previously in similar studies,

^{ 20 }

^{ 31 }and, in effect, is a resampling procedure comparable to the bootstrap method.

^{ 32 }For this procedure, the majority of cases (in our study, 90%) are selected for the training set, and the classification is applied to the small test set consisting of the remaining cases (10%). Then a new random selection is obtained and classification performed, and this procedure is repeated

*k*times (in our study, 400 times) and the results averaged.

*Symlets*(Fig. 2) , although numerous wavelets are likely to work. Symlets is a modification of

*Daubechies wavelets*, the symmetry of which is increased while retaining great simplicity. First, we applied the two-scale DWT to the 64-sector GDx-VCC data, then retained the second-level approximation coefficients but applied an FFT to the second-level DWT detail coefficients (Fig. 3) . Note that we used only the coefficients of the

*second scale*and discarded those of the first scale. We found that the coefficients of the two scales were so similar that they would be suppressed by the PCA even if both were used as features. Coefficients of only the amplitudes, and no phases, from the FFT were used. Next, the DWT coefficients and FFT coefficients were each normalized to the range (0–1) and were joined as preliminary feature vectors. It is difficult to decide the number of the reduced features to use (

*n*) in PCA. We varied

*n*and empirically evaluated the classification performance (using area under the ROC curve to compare performance) which is shown in Figure 4 . The best value of

*n*was found to be 4 (where a global maximum of the area under the curve was achieved; Fig. 4 ) and this value was selected for all subsequent PCA and classification. These optimized features with lower dimensionality were then supplied to the Fisher linear discriminant analysis (LDA) program, which produced an LDF based on the training set. Finally, this LDF was applied to classify the independent test set, and the parameters used to evaluate performance (sensitivity/specificity and area under the curve [AUC]) were obtained on 400 runs and averaged. All results for FFA and WFA reported herein, except as noted, are based on these averages of 400 runs.

*IOVS*1999;40:ARVO Abstract 3481; Essock EA, et al.

*IOVS*2001;42:ARVO Abstract 93; Sinai MJ, et al.

*IOVS*2001;42:ARVO Abstract 717; Sinai MJ, et al.

*IOVS*2002;43:ARVO E-Abstract 302; Bryant FD, et al.

*IOVS*2000;41:ARVO Abstract 485; Essock EA, et al.

*IOVS*2003;44:ARVO Abstract 3378).

^{ 10 }

^{ 11 }

^{ 17 }The basic FFA method is to perform an FFT on the TSNIT data set (in this study, 64 points). All amplitude and phase coefficients (and the DC, or offset value) are entered into a procedure to obtain a classification function. In the present work, we compared the utility of several variations of this method, most of which have appeared previously in the literature. The following comparisons were made: The FFA features were optimized either by Wilks λ, which has been the main method used previously for FFA (Essock EA, et al.

*IOVS*2001;42:ARVO Abstract 93; Sinai MJ, et al.

*IOVS*2001;42:ARVO Abstract 717; Sinai MJ, et al.

*IOVS*2002;43:ARVO E-Abstract 302),

^{ 11 }

^{ 17 }or by PCA, as used in the WFA procedure. The phase coefficients from the FFT were coded as either signed or unsigned (i.e., absolute values taken). Signed coefficients indicating the direction (clockwise or counterclockwise) as well as magnitude that a given sine-wave component was located on the TSNIT pattern compared with another component. Unsigned coefficients indicated only the magnitude of a shift of the given component relative to a reference. Asymmetry of the FFT values was added as another set of features, in addition to the amplitude and phase values produced by FFA.

*between-eye asymmetry*, an FFA was also completed on the fellow eye and the absolute arithmetic difference between a given FFA feature was obtained in the two eyes. Thus, for this analysis, the DC level of the test eye, the 32 amplitudes, the 32 phase values, and 65 asymmetry values (all amplitude, phase, and DC values) were used as the feature set (i.e., a total of 130 features). For WFA, the 32 features of the test eye and the 32 values obtained from the absolute arithmetic difference of these values for the fellow eyes were used as features. Hence, 64 features were used before application of PCA. For NFI, to add a measure of between-eye asymmetry, the absolute arithmetic difference between the NFI of the fellow eyes and the NFI of the test eye were combined in a Fisher LDA procedure to obtain the optimal classifier.

*within-eye asymmetry measures*, data from separate analyses of the superior 32 points and the inferior 32 points was compared by taking the absolute difference in transformed feature space. For FFA, the eye’s full 64-point transformed coefficients (65 features) were combined with 33 within-eye asymmetry features, creating a total of 98 features to be used as preliminary features fed to the PCA. Similarly, for WFA, 32 transformed features plus the 20 within-eye asymmetry features were used. For NFI, within-eye asymmetry was not possible to calculate without changing the nature of the NFI measure, so this measure was omitted.

*t*-tests were used as appropriate with a significance level of 0.05 adopted. To evaluate the classification performance of the three metrics, WFA, FFA, and the NFI, the sensitivity, specificity, and the receiver operating characteristic (ROC) curves were calculated. ROC curves were generated in the standard fashion by systematically varying the cutoff value and noting performance. In the instances of numerous (400) runs (i.e., for the WFA and FFA methods) test cases from all runs were plotted to provide the most accurate estimate of the mean ROC curve. To compare the ROC curves, the following procedure was used. For each particular pair-wise comparison (e.g., WFA versus FFA), the difference in the areas of the ROC curves (based on the 400

*k*-fold samples) were then easily computed (ROC area for WFA minus ROC area for FFA). These could then be used to compute approximate confidence intervals, by using the percentile method.

^{ 32 }Bonferroni-corrected confidence intervals, each with a confidence level of 98.3% were computed as 0.83% and 99.17% to achieve an overall coverage of 95%.

^{ 33 }

*P*< 0.0001), in addition to outperforming the NFI method (ROC area of 0.900;

*P*< 0.003). (However, the obtained difference in FFA and NFI performance (0.938 vs. 0.900) was not statistically significant (

*P*> 0.05), with FFA producing larger ROC areas in 92% of the samples.) A similar trend showing the best performance with WFA, worst with NFI, and intermediate with FFA, is also seen in the sensitivity at a fixed specificity (90% or 95%) as shown in Table 1 . For example, when specificity is fixed at 90% or 95%, sensitivity with WFA is 92.5%, and 87.8%, respectively, considerably higher than that with the other methods.

*P*> 0.05, correlated

*t*-test). There was no evidence of a systematic advantage of either PCA or Wilks λ (Table 2 3) .

*P*< 0.05, correlated

*t*-test). Including asymmetry information in the NFI helped only slightly, but not significantly (ROC AUC of 0.900 increased to 0.911;

*P*> 0.05). WFA performance, however, was not affected by inclusion of between-eye asymmetry of its features (ROC AUC, 0.978 and 0.977). Use of within-eye asymmetry did not help any measure and appeared to hurt performance at times.

*mean*curves for either the third or fourth features showed very little difference in the glaucomatous and healthy eyes. Examples of the fit to individual eyes are shown in Figure 6 , for an eye with a smooth TSNIT pattern (Fig. 6A)and for an eye with a fairly jagged VCC TSNIT curve (Fig. 6B) .

_{s}) between the fitted and actual data:

*t*′ and

*t*

_{ i }are RNFL thickness for reconstructed and original curves, respectively, yielding a shape deviation of 3.5 and 5.3 for the WFA and FFA fits, respectively, in glaucomatous eyes and 4.8 and 5.0 in the healthy eyes.

^{ 22 }is shown in the top part of the table and severity of MD loss is shown in the middle part. From Table 4 , it can be seen that it is the earlier/milder visual field losses in which WFA and NFI performances differ most. At the mildest levels of disease (i.e., stage 1 GSS and MD < −5.0), the performance of both shape-based methods is considerably superior to that of NFI performance. For example, WFA performance is superior to NFI performance for GSS stage 1 patients (Fig. 8)by about 0.20 in ROC AUC (and superior to FFA performance by ∼ 0.06), whereas it is superior to NFI performance across the other stages by ∼0.03). Of note, NFI performed slightly better across the higher GSS stages than FFA, falling intermediate to WFA and FFA at the more advanced stages (Fig. 8) . Thus, it is at the

*mildest*levels of field loss that performance of the methods differs most.

^{ 11 }applied the Fourier analysis LDF method to data from a VCC prototype device and found sensitivity of 84% at 92% specificity and an ROC area of 0.949 (they also cite an unpublished analysis on a different sample yielding comparable results of 80% sensitivity at 90% specificity and 0.941 ROC area). The study had a similar number of patients and an average MD (−5.91) similar to that in the present study. Those investigators used Fourier analysis amplitude and unsigned phase (and no asymmetry measures). The present results with FFA with the VCC device are quite similar, 0.938 ROC area and 79% sensitivity at 90% specificity using PCA and unsigned phase FFA, and 0.932, 87%/90% with Wilks λ and unsigned phase, which were improved to 0.968 ROC area (90%/90%) and 0.962 (87%/90%), for PCA and Wilks λ, respectively, by adding between-eye asymmetry measures. Use of the WFA method was better than all versions of the FFA method. As reported by Medeiros et al.,

^{ 11 }the performance of Fourier TSNIT shape analysis is generally not as good with GDx data (Essock EA, et al.

*IOVS*1999;40:ARVO Abstract 3481; Essock EA, et al.

*IOVS*2001;42:ARVO Abstract 93; Sinai MJ, et al.

*IOVS*2001;42:ARVO Abstract 717; Sinai MJ, et al.

*IOVS*2002;43:ARVO E-Abstract 302; Bryant FD, et al.

*IOVS*2000;41:ARVO Abstract 485; Essock EA, et al.

*IOVS*2003;44:ARVO E-Abstract 3378)

^{ 17 }as with GDx-VCC data, although it is significantly better than standard GDx analysis with the number (i.e., the VCC standard metric, NFI, improves the GDx standard metric, the number, just as TSNIT shape analysis with VCC data improves TSNIT analysis with GDx data). A thorough shape-based analysis with OCT data is yet to be reported, although preliminary analysis is available for an FFA metric.

^{ 17 }

*IOVS*2001;42:ARVO Abstract 93; Bryant et al.

*IOVS*2000;41:ARVO Abstract 485). Second, certain coefficients (features) tend to appear fairly consistently when trained on different samples from different clinics. For full-curve analysis (i.e., not analyzed by hemifield), amplitudes for the second and fifth harmonics are often the more important features (Essock EA, et al.

*IOVS*2001;43:ARVO Abstract 93).

^{ 11 }

^{ 17 }In the present study, with a sample of VCC data, the phases for the second, third, and fourth harmonics were most important, after the DC component. The Fourier features that were important for a limited set of OCT data,

^{ 17 }DC level, amplitude of the second harmonic, and phase of the third harmonic, fit well with these trends. Clearly what is needed next is to apply FFA, and preferably WFA, to a very large sample of patients with early-stage glaucoma to establish a standardized equation. Another apparent regularity of FFA studies is that performance can be improved significantly by adding interocular asymmetry of RNFL thickness shape (Essock EA, et al.

*IOVS*1999;40:ARVO Abstract 3481; Bryant FD, et al.

*IOVS*2000;41:ARVO Abstract 485)

^{ 34 }(present study; see also Ref.

^{ 35 }). All variations of FFA (Wilks λ or PCA, and signed or unsigned phase) had performance improved by adding between-eye asymmetry values. It remains to be seen, however, whether the specific asymmetry values used will remain consistent enough across different samples to be of general use. This study also shows that contrary to prior suggestion (Bryant FD, et al.

*IOVS*2000;41:ARVO Abstract 485),

^{ 34 }using within-eye asymmetry of Fourier coefficients does not necessarily improve performance. Finally, whether the signed or unsigned phase is used does not affect performance. This latter observation may suggest that deviations from a TSNIT template matter more than the exact shape of that deviation. WFA, in contrast, is not helped by adding either within-eye or between-eye asymmetry. This suggests that WFA may be more stable across different samples than FFA with between-eye asymmetry measures, in addition to performing the best of all measures tested.

*IOVS*2004;45:ARVO E-Abstract 5504).

^{ 20 }This type of work should be extended to VCC data and other RNFL measurement methods with large sample sizes.

**Figure 1.**

**Figure 1.**

**Figure 2.**

**Figure 2.**

**Figure 3.**

**Figure 3.**

**Figure 4.**

**Figure 4.**

WFA | FFA (PCA) | FFA (Wilks) | NFI | |
---|---|---|---|---|

ROC Area | 0.978 | 0.938 | 0.932 | 0.900 |

Sensitivity at 90 | 0.925 | 0.794 | 0.873 | 0.716 |

Sensitivity at 95 | 0.878 | 0.729 | 0.838 | 0.716 |

WFA | FFA (PCA) | FFA (Wilks) | NFI | |
---|---|---|---|---|

No asymmetry measures | 0.978 | 0.938 | 0.932 | 0.900 |

Between-eye asymmetry used | 0.977 | 0.968 | 0.962 | 0.911 |

Within-eye asymmetry used | 0.954 | 0.933 | 0.894 | N/A |

Dataset | WFA | FFA Wilks λ (Unsigned) | FFA Wilks λ (Signed) | FFA PCA (Unsigned) | FFA PCA (Signed) | NFI |
---|---|---|---|---|---|---|

No asymmetry measures | 0.892/0.930/0.978 (0.925; 0.878) | 0.857/0.908/0.932 (0.873; 0.838) | 0.775/0.857/0.909 (0.750; 0.658) | 0.835/0.848/0.938 (0.794; 0.729) | 0.823/0.842/0.930 (0.779; 0.712) | 0.761/0.821/0.900 (0.722; 0.716) |

Between-eye asymmetry | 0.884/0.946/0.977 (0.927; 0.885) | 0.839/0.942/0.962 (0.873; 0.833) | 0.895/0.949/0.975 (0.922; 0.894) | 0.867/0.969/0.968 (0.903; 0.886) | 0.868/0.970/0.969 (0.904; 0.886) | 0.717/0.949/0.911^{†} (0.762; 0.709) |

Within-eye asymmetry | 0.863/0.878/0.954 (0.840; 0.771) | 0.761/0.859/0.894 (0.730; 0.630) | 0.794/0.861/0.904 (0.761; 0.667) | 0.828/0.874/0.933 (0.803; 0.714) | 0.828/0.877/0.934 (0.805; 0.715) | N/A |

**Figure 5.**

**Figure 5.**

**Figure 6.**

**Figure 6.**

**Figure 7.**

**Figure 7.**

Grouping Based on Visual Fields | ROC Area | ||||
---|---|---|---|---|---|

WFA | FFA | NFI | |||

Glaucoma staging system | |||||

Stage 1 | 0.947 | 0.888 | 0.749 | ||

Stage 2 | 0.974 | 0.921 | 0.951 | ||

Stage 3 | 0.996 | 0.960 | 0.959 | ||

Stage 4 | 0.997 | 0.952 | 0.978 | ||

Stage 5 | 0.983 | 0.983 | 0.949 | ||

Grouped by MD | |||||

Group 0 to −5 | 0.961 | 0.903 | 0.816 | ||

Group −5 to −10 | 0.990 | 0.958 | 0.964 | ||

Group −10 to −15 | 0.997 | 0.956 | 0.976 | ||

Group −15 to −20 | 0.979 | 0.982 | 0.934 | ||

Group −20 to −25 | 1.000 | 0.946 | 1.000 | ||

Type of defect | |||||

Localized | 0.977 | 0.941 | 0.892 | ||

Mixed | 0.980 | 0.946 | 0.909 | ||

Generalized | 0.983 | 0.536 | 1.000 |

**Figure 8.**

**Figure 8.**

**Figure 9.**

**Figure 9.**

*Invest Ophthalmol Vis Sci*. 2000;41:1774–1782. [PubMed]

*Invest Ophthalmol Vis Sci*. 2002;43:2213–2220. [PubMed]

*Arch Ophthalmol*. 1982;100:807–814. [CrossRef] [PubMed]

*Am J Ophthalmol*. 1989;107:453–464. [CrossRef] [PubMed]

*Ophthalmology*. 1992;99:19–28. [CrossRef] [PubMed]

*Arch Ophthalmol*. 1977;95:2149–2156. [CrossRef] [PubMed]

*Arch Ophthalmol*. 1991;109:77–83. [CrossRef] [PubMed]

*Ophthalmology*. 1993;100:587–597.discussion 597–598 [CrossRef] [PubMed]

*Ophthalmology*. 1998;105:224–231. [CrossRef] [PubMed]

*J Glaucoma*. 2000;9:444–452. [CrossRef] [PubMed]

*Invest Ophthalmol Vis Sci*. 2003;44:2606–2612. [CrossRef] [PubMed]

*J Comp Neurol*. 1990;300:5–25. [CrossRef] [PubMed]

*Graefes Arch Clin Exp Ophthalmol*. 1999;237:474–479. [CrossRef] [PubMed]

*Ophthalmology*. 1996;103:2114–2119. [CrossRef] [PubMed]

*Ophthalmology*. 2001;108:151–156. [CrossRef] [PubMed]

*Br J Ophthalmol*. 2003;87:413–419. [CrossRef] [PubMed]

*Arch Ophthalmol*. 2003;121:1238–1245. [CrossRef] [PubMed]

*IEEE Trans Med Imag*. .In press.

*Proceedings of the Seventh Joint Conference on Information Sciences*. 2003;672–675.JCIS/Association for Intelligent Machinery, Inc. Research Triangle Park, NC.

*J Glaucoma*. 2005;14:20–25. [CrossRef] [PubMed]

*Curr Opin Ophthalmol*. 2002;13:68–76. [CrossRef] [PubMed]

*Eur J Ophthalmol*. 1996;6:402–407. [PubMed]

*J Glaucoma*. 2003;12:417–426. [CrossRef] [PubMed]

*Invest Ophthalmol Vis Sci*. 2002;43:2221–2228. [PubMed]

*Arch Ophthalmol*. 1990;108:557–560. [CrossRef] [PubMed]

*Pattern Recognition with Neural Networks in C++*. 1996;CRC Press Boca Raton, FL.

*Digital Image Processing*. 2002; 2nd ed.Prentice Hall Englewood Cliffs, NJ.

*Pattern Classification and Scene Analysis*. 1973;Wiley New York.

*Statistical and Neural Classifiers: an Integrated Approach to Design*. 2001;Springer London.

*Machine Learning*. 1997;149–150.WCB/McGraw-Hill New York.

*Proteins*. 2005;58:855–865. [CrossRef] [PubMed]

*An Introduction to the Bootstrap*. 1993;Chapman & Hall/CRC New York.

*Biometrics*. 1988;44:837–845. [CrossRef] [PubMed]

*J Glaucoma*. 2000;9:154–162. [CrossRef] [PubMed]

*Jpn J Ophthalmol*. 2004;48:281–286. [CrossRef] [PubMed]