Retrospective data from a study of the tear film using high-speed videokeratoscopy, captured at 25 frames per second, were used.13 The study cohort involved 22 subjects with normal tear film and 12 subjects diagnosed with dry eye syndrome. Only the right eyes of the subjects were measured. Dry eye was diagnosed if the subject exhibited all three of the following characteristics of dry eye; significant subjective dry eye symptoms (McMonnies test score, >14), objective signs of tear film instability (FTBUT, <10s), and surface staining (corneal and/or conjunctiva stain score, >3 (National Eye Institute grading scale14)). Further details on the study can be found in Ref. 13.

For the initial phase of this study, a number of representative images and videos were manually selected from the whole data set (Fig. 1), and analyzed to obtain the best parameter selection for the proposed method. Thus, these data derived from the images in Fig. 1 are used to test the proposed method, while in the second phase of the study, the whole data set which contained measurements from 22 normal and 12 dry eye subjects was used to evaluate the performance of the proposed technique in assessing tear film surface quality.

The videokeratoscopic grey scale intensity digital image forms a 2D matrix I[n,m], with n=1, 2,…,N and m=1, 2,…,M. In the videokeratoscope used for this study, Medmont E300 (Melbourne, Australia), the matrix is N=648 by M=572 pixels. Before the calculation of the Grey Level Co-occurrence Matrix (GLCM), an area of analysis is manually selected. This area contains the maximum rectangular area of the image that is not affected by the shadows from eyelashes. To extract this region, which avoids the undesirable effect from eyelashes, a methodology that has previously been presented in detail6 was used. The key focus of this paper is the separation between tear film related interferences and the signal. The selected area is further divided into non-overlapping blocks of equal size. The block size is optimized so it contains a significant amount of information without reducing the spatial resolution when locating the potential interference. In our case, the image was divided into square blocks of 25×25 pixels. Given that the maximum width of a ring is approximately 8.78 pixels,15 a 25×25 pixel block is sufficient to encompass a significant amount of information (at least two rings) and to keep sufficiently high spatial resolution.

A videokeratoscopy image is composed of two elements: the background (the anterior eye – iris and pupil) and the foreground (the reflected pattern of the Placido disc rings). The background does not provide any essential information for the analysis of the pattern. For that reason it is important to remove it from the image to avoid misleading information in further processing. This can be achieved with statistical block normalization, in which the intensity information is normalized to zero mean and unit variance.15

The Grey Level Co-occurrence Matrix (GLCM), proposed by Haralick et al.,12pθ(d), for an image is the joint conditional probability density function (a two dimensional histogram), p(i,j|φ(d,θ)); where φ(d,θ) is a vector of length d and angle θ measured from an element in the image. The joint conditional probability density function represents the probability of finding grey levels, i and j, at the base and termination points of the vector φ(d,θ) for any pixel within the image.

Fig. 2 shows an example of the GLCM (for d=1 and θ=0). Therefore, in this example the GLCM calculates how often a pixel with grey-level (grey-scale intensity) value i occurs horizontally adjacent to a pixel with the value j. In Fig. 2, two different sections from a videokeratoscope image are presented: an optimal (top) and sub-optimal (bottom) reflected pattern. As an example, the occurrence values at grey level (3,4) (i.e., grey level 3 at the start of the vector and 4 at the end) are shown in the images (with red lines) and its corresponding occurrence/cumulative GLCM value. The high occurrence level around the (5,5) grey level corresponds to the background. In general, for the optimally reflected pattern, extra information can be seen in the GLCM. From these GLCMs a set of texture statistical descriptors can be extracted which represent global measures of the data. Two representative features are presented here as an example. The Entropy (measures the randomness of the distribution) and the Energy (measurement of the texture uniformity, the opposite of entropy) are provided in Fig. 2 (right side), and as expected based upon the definitions of these metrics, both values behave in opposing ways in these two examples. The rest of the set of texture features used in this study are described in detail in Table 1.

Figure 2.

Two representative blocks (centre) from a videokeratoscopic image (left) with their corresponding co-occurrence matrices (right). The top subplots represent an example with optimal reflection conditions (good tear film) while the bottom subplots represent suboptimal reflection conditions (poor tear film). The red lines in the central block image illustrate the pixels in each of the block images with occurrence values of grey level equal to (3,4) (see text for details).

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A range of different GLCMs can be generated from each image depending on the choice of vector length (d) and orientation (θ), which should be selected in a way to maximize the likelihood of separating the interference pattern from the signal. Using visually representative images from each pattern type, various choices for vector length and orientation were examined. Although the examples provided here are for a reduced number of images, they represent a typical set of images that can be encountered in videokeratoscopy. The effect of the level of quantization (Ng), which is the specific number of grey-levels to scale the image, is not considered in this paper. In general, the lower is the values of Ng, the lower the classification accuracy. The images from the videokeratoscope have a 256 grey-scale level, however choosing Ng=64 keeps the computational load low, while ensures that the classification accuracy will not be affected.16

Once the GLCM is generated, a set of texture statistical descriptors can be extracted. In Haralick's initial study 14 features were described.12 This set has been extended in other works.17,18 Through a preliminary trial, those features that appeared to be the most sensitive for the classification of the different videokeratoscopy textures were identified. Following the notation provided in Haralick et al.12 definitions of these features along with a brief explanation of the aspect of the image that they quantify are presented in Table 1.

The receiver operating characteristic (ROC) curves are commonly used to measure the performance of a two-class classification. The ROC curve provides the sensitivity and specificity of the measurement in separating the interference from the signal. Eight different ROC curves were calculated to show the capability of each of the texture features listed in Table 1 to discriminate between interference and signal pattern in the videokeratoscopic images.

Once the image is divided into blocks, the GLCM and the features are extracted for each of the blocks. In order to calculate the ROC, the data of the features from each of the two groups of pattern (i.e., signal and interference) were used to estimate the probability density function. This was achieved by using kernel density estimator with an Epanechnikov window.19 The ROC curves were then numerically evaluated from each such pair of non-parametric kernel density estimators. From the ROC curve, the area under the curve (AUC) was calculated using numerical integration. The AUC is normally used as a measure of the performance of how well detection is carried out, value of AUC=1 indicates an ideal detection, while a value of AUC=0.5 corresponds to random classification. Additionally, this approach utilizing ROC curve analysis was also applied to examine the effectiveness of each of the texture features in discriminating between normal patients and those with dry eye. Additionally to the AUC, the sensitivity and specificity of each texture-feature to detect dry eye was also calculated.

This section examines the optimum selection of the vector length and its orientation for the texture feature analysis, in such a way as to maximize the likelihood of separating the interference pattern from the signal, using a set of representative images (images I–IV in Fig. 1).

Orientation

It is important to differentiate between the pattern's directionality and the GLCM orientation. In the example shown in Fig. 2 (top), the pattern's (Placido disc) directionality is vertical while for this example the GLCM orientation to create the co-occurrence matrix was chosen horizontally (red lines in the image). The reflected videokeratoscopy pattern has directionality associated with it; hence it is important to ensure that the GLCM is not biased by this pattern's direction. Thus the vector's orientation used to create GLCM should be chosen to ensure that the statistics generated from the GLCM are rotationally invariant. To reduce the angular variance of the statistics, the GLCM can be generated using multiple vectors at the same time, so that each pixel contributes multiple times to the final GLCM. Fig. 3 shows the orientation dependency of four different features for four different vector orientations. As the number of orientations used to created GLCM increases, the separation of statistics (mean) between signal and interference increases, hence the separation between these two classes strengthens. This means that to properly characterize the GLCM matrix different orientations need to be considered. This effect is particularly clear when three or four orientations are used simultaneously (see Fig. 3). For our application, discrete angles theta=[0°, 45°, 90°, 135°] were selected, these values correspond to the adjacent pixels as shown in the inset of Fig. 3. As shown in the example, the advantage of using this approach is that it avoids the angular-dependency of GLCM.

Figure 3.

Class statistics, mean±one standard deviation, of four different texture features as a function of the number of orientations considered. 1=[0°], 2=[0°, 45°], 3=[0°, 45°, 90°], 4=[0°, 45°, 90°,135°]. The central inset shows a diagram with the relation between the angle and the adjacent pixels.

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Vector length

Similar to the orientation parameter, the choice of the vector's length has a substantial impact on the feature's statistics. Fig. 4 shows the influence of the length on the class statistics. A vector length of 1 pixel is the optimal option in this case and shows good separation between the classes as well as being the shortest possible length. The shorter the length, the more entries go into the GLCM.

Figure 4.

Class statistics, mean±one standard deviation, of four different texture features as a function of the vector's length.

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In order to evaluate the performance of the proposed technique the algorithm was tested on a number of representative videokeratoscopy images, shown in Fig. 1, as well as on a video sequence. The video, composed of 330 frames, corresponds to a full interblink interval of a dry eye patient. The detailed results from the ROC curve analysis for the performance of each of the features are given in Table 2. The area under the curve (AUC) is provided for the eight different considered features. It is worth noting that the entropy feature results in the largest AUC for all the cases, hence separating more effectively the interference from the signal. Overall, none of the considered features performs below AUC=0.77. Of special interest is the high AUC values obtained on the video sequence.

Table 2.

Area under the curve for the eight considered texture features for the four videokeratoscopic images from Fig. 1 and the video sequence. The bold numbers indicate the best feature within each case (highest AUC).

Area under the curve
Feature	Energy	Cluster Shade	Cluster Prominence	Entropy	Diff. Entropy	Sum. Entropy	Homogeneity	Max. probability
Case I	0.80	0.77	0.79	0.88	0.84	0.85	0.80	0.79
Case II	0.96	0.93	0.92	0.97	0.92	0.97	0.87	0.95
Case III	0.83	0.77	0.86	0.86	0.83	0.83	0.81	0.82
Case IV	0.99	0.95	0.98	0.99	0.98	0.99	0.94	0.98
Video	0.94	0.94	0.93	0.95	0.88	0.92	0.93	0.93
Average	0.90	0.87	0.90	0.93	0.89	0.91	0.87	0.89

In order to evaluate the performance of the proposed technique to discriminate normal subjects from those with dry eye, data collected in a previous clinical study13 from 34 subjects (22 normal and 12 dry eyes) were used. The data were acquired under suppressed blinking conditions (SBC). In the SBCs, three measurements were taken. Subjects were asked to blink several times before the beginning of the measurement and then focus on the instrument's fixation target and keep their eyes open as long as they could. The maximum time of the recording sequence was 30s and a 3-min break was given between measurements. More details on the measurement protocol are given in Ref. 13.

The subject's data corresponding to each blink was cropped to a specific length. The first 5s of each recording was used, excluding the first second after the blink to avoid the effect of tear film formation/spreading on the estimates of TFSQ. The 5s interval ensures that 100% of the subjects were included in each group in the analysis (i.e., all subjects had a minimum of 5s or more of data prior to a blink in the recording). The three recordings per subject were averaged into one single measurement. Receiver operating characteristic (ROC) curves were calculated to show the capability of the considered texture features to discriminate dry eye from normal tear film subjects. To arrive at the best possible detection performance for the non-invasive test, a group of ROC curves were evaluated at different sampling intervals between the time interval from the 1st second to the 6th second. This may provide an optimal time threshold in terms of discrimination performance. A detailed result of each of the features performance in terms of area under the curve (AUC), specificity and sensitivity as well as its optimal time threshold is given in Table 3. The entropy and homogeneity features resulted in the largest AUC, in other words the best dry eye detection. For all the considered texture features, the AUC value range from 0.77 to 0.82, while the sensitivity shows values above 0.9 and the specificity shows values around 0.6.