2D Short-Time Fourier Transform for local morphological analysis of meibomian gland images.

Meibography is becoming an integral part of dry eye diagnosis. Being objective and repeatable this imaging technique is used to guide treatment decisions and determine the disease status. Especially desirable is the possibility of automatic (or semi-automatic) analysis of a meibomian image for quantification of a particular gland's feature. Recent reports suggest that in addition to the measure of gland atrophy (quantified by the well-established "drop-out area" parameter), the gland's morphological changes may carry equally clinically useful information. Here we demonstrate the novel image analysis method providing detailed information on local deformation of meibomian gland pattern. The developed approach extracts from every Meibomian image a set of six morphometric color-coded maps, each visualizing spatial behavior of different morphometric parameter. A more detailed analysis of those maps was used to perform automatic classification of Meibomian glands images. The method for isolating individual morphometric components from the original meibomian image can be helpful in the diagnostic process. It may help clinicians to see in which part of the eyelid the disturbance is taking place and also to quantify it with a numerical value providing essential insight into Meibomian gland dysfunction pathophysiology.

Introduction

Assessment of Meibomian glands (MGs) condition has been the focus of many studies in recent years [1, 2]. This interest results from the fact that dysfunction in MG physiology is a leading factor of the dry eye disease with the prevalence that varies widely from 3,5% to 70% based on the age, sex and ethnicity [3, 4]. The most common diagnosis of MGD is based on subjective symptoms and more detailed examination of the anterior eye structures [5-7]. These early subjective methods of the MG state classification (basing on the personal experience of the specialist and characterized by high inconsistent and low repeatability) are slowly being replaced with the sophisticated semiautomatic and automatic image analyzing methods [8-18]. Providing standard quantification of the gland structure, these methods open the possibility for increased measurement repeatability and shortening the diagnostic time [19-29]. Not surprisingly, according to the latest reports [10-16] there is a strong need to develop new image analysis protocols.

A well-known objective measure of MGs condition is the “drop-out area” (DOA) which quantifies the meibomian gland loss [30]. It is defined as the ratio between the area covered by meibomian glands and the total eyelid area. This simple definition makes the value of DOA relatively easy to estimate automatically, directly from the meibomian image [19, 20]. The easy and intuitively understandable definition of DOA makes this parameter the most frequently used objective measure of MGs condition utilized in quantification of MGD progression. The other and less obvious MGD symptoms which relate to more subtle changes in the gland morphology with no visible changes in meibomian gland loss. Recently, it has been shown that apart from the gland atrophy, the distortion in gland’s shape is a valuable complementary clinical feature of MGs [12]. Although the mechanism of the MGD progression is still unclear and the data regarding gland tortuosity in the general population is still needed [9], a clear correlation between MGs deformation and clinical parameters such as meibum expressibility, lid margin score, meiboscore, meibum expressibility score, and TBUT has been demonstrated [9, 12, 31]. It is thus believed that the MGD progresses from an early stage characterized by subtle gland distortion, whereas the loss of MGs is observed only in the advanced stage of the disease [9, 12, 31, 32]. In this perspective the MG’s shape distortion may be considered as an early indicator of various ophthalmic diseases (including MGD and dry eye syndrome) which is a strong motivation for development of methods for objective examination and parametrization of MGs deformation. The ability to parametrize the local morphology of MGs should allow to use these measures (in addition to DOA) for better assistance in the diagnosis process and MGD severity evaluation.

Unfortunately, the objective description of the gland deformity is much more difficult than just determining the degree of its atrophy (measured by DOA). There are several works introducing the meibomian gland classification based on their deformation, but so far the gold standard has not been established [9–12, 24–27]. In searching for other objective descriptors of MG morphological condition, we have recently presented an approach for quantifying and classifying Meibomian images using 2D Fourier Transform (2DFT) [33]. This global analysis, performed on the whole set of the glands, demonstrated that information on mean gland frequency (connected with mean width of glands or inter-gland section) and anisotropy in gland periodicity (related to mean spread in gland directions) can be used for automatic image classification. However, despite currently being global, the method can be blind to some important slight local disturbances in gland patterns. Meanwhile, a recent study has shown the significant differences in meibography grading between regional zones (nasal, central, temporal) and global grades [34]. This shows the need for a method able to extract, present and utilize morphological changes of meibomian gland structure on the local scale. Trying to meet this requirement, in this work an approach based on 2D Short Time Fourier Transform (2D STFT) is proposed [35]. The main advantage of this method is the application of 2DFT on small fragments of the Meibomian image, thus obtaining local values of the six chosen morphometric parameters. The 2D plots of those values (maps) provide an excellent tool for qualitative and quantitative description of the gland pattern. This additional information may help clinicians by highlighting the features of each morphometric parameter separately. A possible way of defining new morphological meibo-scores on the basis of the obtained intrinsic images is shown. As a final step we propose an introduction of new meibo-scores calculated from the morphometric images.

Materials and methods

Subjects

Subjects were healthy volunteers recruited from Faculty of Physics Adam Mickiewicz University in Poznan in Poland. Ethics clearance was issued by the institutional review board of Adam Mickiewicz University of Poznan and adhered to the tenets of the Declaration of Helsinki. Before enrolment into the study all participants were informed about procedures used in the experiment. Written informed consent was obtained from all subjects.

The exclusion criteria were ocular allergies, eyelid and ocular surface disorders, recent ocular infections, any history of ocular surgery or continuous eye drop use. The 55 participants were contact lens wearers. Participants followed the recommendation not to wear contact lenses on a day before the examination procedure.

Meibographic images

The Meibomian gland image analysis developed in this work was tested on the images acquired in our recent research [33]. A total of 146 images (2 images for both upper eyelids of each patient) were collected using home-built meibographic imaging equipment (details in the in the S1 Appendix). The aim was to provide a non-contact and patient-friendly acquisition method, preferably similar to other commercially available imaging techniques. Thus, the meibography system was mounted on the Topcon SL-D701 slit lamp which allowed to record meibographic images during the routine eye examination. An exemplary Meibomian image acquired with this device is presented in Fig 1.

Fig 1

Pre-processing and grading of Meibomian images.

a) original meibogram. Red squares show the positions where an angle of deviation exceeds 45°. Blue squares indicate regions with noticeable narrowing of glands. b) Meibomian image with increased contrast. The green dashed line marks the area of eyelid with Meibomian glands. c) binarized Meibomian image.

In the present study only the images of the upper eyelid were collected for further analysis. The upper eyelids of the patients were everted to expose the embedded Meibomian glands and then a series of several images was acquired. The image of the best quality was selected as a representative for a given patient. Recorded photographs of the meibomian gland area were first preprocessed in ImageJ software. A set of filters was applied to firstly enhance the contrast (Fig 1b) and to eventually produce a binary version of the image showing only clear silhouettes of glands (Fig 1c). Then, the region of eyelid with Meibomian glands was manually marked (green dashed line in Fig 1b).

The recorded photographs were also subjectively graded by one experienced optometrist based on their distortions and then grouped into three categories: healthy (24 items), intermediate (75 items), unhealthy (47 items). This subjective analysis was based on several features of the gland pattern: gland direction, gland dilation, cut-off and narrowing [12, 19, 36, 37]. For example, the pattern was considered as distorted when its direction deviates from eyelid axis by more than 45°. Meibographs were graded from 1 to 3 using following rule: no distortion of the Meibomian glands (healthy–grade 1); 1–4 Meibomian glands with distortion (intermediate–grade 2); more than five Meibomian glands with distortion (unhealthy–grade 3). Grading of the images was repeated on the following day. If the grades assigned on the two days were different, the images were reanalysed again to make a proper decision based on the presented criteria. Correlations between the evaluation results were estimated at p<0.05 and r = 0.794. Other ocular symptoms and signs of the dry eye were not collected. The resulting classification served as a ground-truth standard for comparison with the outcome of the proposed automatic classification routine.

Two relevant morphological features of the gland pattern are shown in Fig 1a. The positions on the eyelid where the angle of deviation exceeds 45° are marked with red squares, whereas the regions with noticeable narrowing of glands are indicated with blue squares.

Image analysis with 2D Fourier Transform

The use of the 2D Fourier transform (2D FT) method for Meibomian image analysis is justified by the observation that healthy Meibomian glands forms a periodic stripe pattern, whereas in the image of the glands described as unhealthy this pattern is often distorted [12, 24–25, 27]. The result of the 2D FT operation applied to different gland structures is schematically presented in Fig 2. If the analyzed image shows a unidirectional gland structure with a constant width and a constant distance between the glands (which corresponds to a well-defined spatial frequency), then a pair of characteristic sharp peaks appear in the Fourier-transformed image (Power Spectral Density, PSD, Image) with the center of coordinate system as the center of symmetry (Fig 2). Their distance from the center of the PSD image is a measure of the spatial frequency (corresponding to gland width or separation), while their orientation corresponds to the direction of the gland structure. As illustrated in Fig 2, the change in the gland pattern orientation and in the width of the glands results in corresponding characteristic changes in the PSD image. Real Meibomian gland structures are never perfect and there is always a distribution in gland’s width or separation, as well as in their orientation. As a result, broadening of the spectral features in PSD images occurs. Therefore, the information on gland’s distortion is encoded in the shape of the spectral features of PSD image.

Fig 2

Schematic illustration of 2D Fourier Transformation.

Transformation of an image of undistorted gland pattern results in a PSD image showing two sharp peaks of well-defined position and orientation (black circles in bottom images). Orientation and separation of these peaks correspond to direction and frequency of the gland pattern, respectively. When the gland pattern is not uniform, some distribution in frequency and orientation occur. As a result, the spectral features in PSD images tend to smear out.

Determination of intrinsic images with 2D Short-Time Fourier Transform

To determine the morphological properties locally, the method utilizes the so called Short-Time Fourier Transform (STFT) in a manner similar to that used previously to enhance the analysis of fingerprint images [38]. Application of 2D SFTF applied to the real Meibomian image (Fig 1) is shown in Fig 3. The analyzed image (Fig 3a) is divided into smaller regions and the 2D FT transformation is performed for each region separately. The regions are selected by a window of a given shape and position (Fig 3b and 3e). In order to achieve a uniform map of calculated parameters, the window position was assigned to every 10th pixel of the original Meibomian image (blue dots in Fig 3a). Details of the 2D STFT analysis are provided in the S2 and S3 Appendices.

Fig 3

2D Short-Time Fourier Transform (STFT) used for determination of local probability density for gland frequency, p(q) and orientation, p(θ).

Panel a) shows original (binarized) Meibomian gland image, f(x,y). During the STFT analysis of an image, the Gaussian window is placed in strictly defined positions (xw,yw), which are illustrated a grid of blue dots. Two arbitrary positions of the window, w1 and w2, are presented as a red and a green circle, respectively. Panels b) and e) shows a Meibomian image limited by windows w1 and w2, respectively. The radius of the dashed circles show the width (variance) of the Gaussian window, σr. The image limited by w1 shows broader and more inclined gland structure then that seen in w2. Panels c) and f) shows PSD in Cartesian coordinates calculated for images limited by windows w1 and w2, respectively. The dark spots are the spectral features whose radial distance, q, informs about gland pattern spatial frequency, whereas the angular distance, θ, corresponds to the gland orientation. The thick colored arrow (pointing at θ+90° direction) indicates the mean gland orientation. Notice how it complies with the real structure shown in panels b) and e). Panels d) and g) show PSD in polar coordinates calculated for images limited by windows w1 and w2, respectively. In this representation PSD corresponds to a probability map of finding a gland structure with a given frequency, q, and orientation, θ. Marginal plots show local probability distributions p(q) and p(θ) which were obtained by projection of p(q, θ) on the appropriate axis (S2 Appendix).

The PSD image represents the distribution of spatial frequencies along (x,y) coordinates of the original image (Fig 3c and 3f). In this representation, the distance (q) from the center of the Fourier transformed image is a measure of the spatial frequency of the gland pattern (related to gland width), whereas the angle (θ) is connected to the orientation of the gland pattern. The PSD image was transformed from cartesian (qx, qy) to polar coordinates (q, θ) (Fig 3d and 3g). The advantage of this operation is that PSD(q, θ) can be interpreted as distribution of probability p(q, θ) for gland features of a given frequency, q, and orientation, θ, existing in the analyzed region of Meibomian image. Marginal density function p(q) and p(θ) calculated from p(q, θ) (S2 Appendix) were then compared with theoretical models. The result of this procedure is presented on Fig 4.

Fig 4

Derivation of morphometric parameters (q0, σ, θ0, σθ) by the analysis of local probability distributions for a single window position (window w2 from Fig 3).

Panel a) shows the p(q) distribution indicating a probability of finding a gland structure with a given spatial frequency, q. Open circles are experimental data. Solid line is the fitting result with normal distribution providing the values of maximum, q0, and the variance, σ. The maximum of the distributions is a measure of the local gland frequency, q0. Shaded area shows the ideal distribution with a variance, σ, expected for a constant frequency gland pattern limited by a Gaussian window. Broadening of the experimental distribution with respect to the ideal one, Δσq, normalized to the σ, is a measure of true gland frequency variance, σ. The inset in (a) shows the p(q) in the whole range of q values. Panel b) shows the p(θ) distribution indicating a probability of finding a gland pattern with a given orientation, θ. Open circles are experimental data. Solid line is the fitting result with von Mises distribution providing the values of maximum, θ0, and the variance, σθ,. The maximum of the distributions is a measure of the local gland orientation, θ0. The shaded area shows the ideal distribution with a variance, σθ,, expected for a constant frequency gland structure limited by a Gaussian window. Broadening of the experimental distribution with respect to the ideal one, Δσθ, normalized to the σ, is a measure of true gland frequency variance, σθ. The inset in (b) shows the p(θ) in whole range of θ values.

As follows from Fig 4, experimental p(q) and p(θ) distributions (open symbols) show a clear peaks localized at certain positions and characterized by their width. In order to parametrize these features, an assumption was made that gland frequency, q, and orientation, θ, are random variables described by normal distributions and Gaussian and von Mises [39] distributions (S4 Appendix) were used to fit experimental p(q) and p(θ), respectively (solid lines). The obtained values of the peak positions (q0 and θ0) correspond to the mean values of gland frequency and orientation, respectively, whereas peak widths (parametrized by variances σ and σθ,) represent uncertainties in estimation of these parameters. Interpretation of such obtained variances needs some caution. As p(q) and p(θ) distributions were obtained from a Fourier transform of a windowed image, the widths of these distributions are naturally broadened resulting from a finite size of the window (see S3 Appendix). The ideal p(q) and p(θ) distributions, expected for perfect gland structure (characterized by a constant frequency and constant orientation), are shown in Fig 4 as shaded areas. These distributions will be widened if the real gland image differs from the ideal one (as the gland distortion increases). For such a case, Δσ parameter (being the difference between the widths of real and ideal distributions) will take a finite (non-zero) value.

As the real Meibomian gland pattern always shows distortions, the shapes of corresponding probability distributions will change across the eyelid and will depend on the window position (Fig 2). The p(q) and p(θ) distributions were then determined for different window positions so to cover the entire Meibomian gland image (blue dots in Fig 3a). For every window position the values of four parameters (namely: q0, Δσq, θ0, Δσθ) were directly extracted from probability distributions. Plotting the color-coded values of these parameters as a function of window position produces four maps being spatial distributions of individual morphometric parameters’ values. The images of gland frequency, q0, and gland orientation, θ0, were used to generate two additional maps, namely the map of frequency gradient, G, and the map of angular incoherence, Cθ (details are given in S4 Appendix). Therefore, as a result of 2D STFT analysis are six morphometric maps are generated from a single Meibomian image.

Results

Fig 5 shows the result of a 2D Short Time Fourier Transform 2D STFT analysis performed on three exemplary Meibomian images belonging to different categories. A direct comparison of the original images (Fig 5 row a) shows that well-defined unidirectional stripe pattern characteristic for healthy glands gradually disappears with an ailment progression. For the ‘Unhealthy” case it is possible to identify specific regions of the image where the gland width (or separation) clearly changes, as well as areas where glands obviously change their direction. In reality, changes in the width and orientation of the glands may be more subtle, sometimes even difficult to see, and occur over the entire eyelid area where regions of varying width and orientation interpenetrate each other. With a 2D STFT analysis these various contributions were disentangled to create separate images (morphometric maps), each showing spatial distribution of only one of morphological parameter of the gland pattern. These intrinsic images are shown in Fig 5b–5g.

Fig 5

Six sets of morphometric maps calculated from three Meibomian images classified as healthy, intermediate and unhealthy (in columns).

Subsequent rows show: a) original (binarized) Meibomian images; b) maps of gland frequency, q0; c) maps of gland frequency variance, σq; d) maps of frequency gradient, G.; e) maps of gland orientation, θ0; f) maps of gland orientation variance, σθ; g) maps of angular incoherence, Cθ.

As follows from Fig 5, the corresponding maps calculated from images representing various glands condition clearly differ from each other and reflect the gland’s condition. In order to parametrize these changes, for each parameter, the distribution of its values was determined (Fig 6) and the shapes of the distributions were quantified with five measures of distribution, namely: Entropy, Mean, Variance, Skewness and Kurtosis (S5 Appendix). This gives in total 30 descriptive features for each Meibomian image.

Fig 6

Distributions of pixel values for 6 morphometric maps plotted for Meibomian images classified as healthy, intermediate and unhealthy.

Notice that the shape of each distribution depends on the image category (gland ailment). To quantify these changes five measures of distribution were calculated (Entropy, Mean, Variance, Skewness and Kurtosis) giving in total 30 descriptive features for each Meibomian image.

Using principal component analysis (PCA) and linear discriminant analysis (LDA) [40] the dimensionality of the dataset was reduced from 30 features to only 2 new variables which best describe the data: PCA1,2 (or LDA1,2). The correlation plots of both PCA1,2 (and LDA1,2) components extracted for all meibomian images are shown on Fig 7. Marginal plots on Fig 7 were interpreted as probability distributions of corresponding components (PCA1,2 or LDA1,2).

Fig 7

Correlation plots between first two components of a) Principal Component Analysis (PCA) and b) Linear Discriminant Analysis (LDA) for images classified as healthy, intermediate and unhealthy.

Marginal plots show probability distributions of corresponding components. Notice that although both analyses provide noticeable separation of categories, the LDA analysis (being a supervised method) provides much better clustering of classes.

Knowing the probability distributions of a given component (PCA1,2 or LDA1,2) for each category, a simple threshold classifiers were created: an image being parametrized with a pair of component values (PCA1/PCA2 or LDA1/LDA2) is assigned to a category specified by the highest value of the product of corresponding probability functions (p(PCA1)p(PCA2) or p(LDA1)p(LDA2)). The classification performance of this approach is presented in Table 1. For more information see S6 Appendix.

Table 1

Classification efficiency (in percentage of correctly classified) for different classifiers (column headers) used to distinguish images of Meibomian glands.

95% Confidence Interval (see S7 Appendix for details).

Classifier	Healthy	Intermediate	Unhealthy
PCA	83±12	48±4	83±9
LDA	88±14	79±9	91±12
PCA [33]	88±11	46±3	83±10

Discussion

Fig 1 shows how the morphological condition of the glands are “traditionally” assessed. Although more descriptive features have been defined in the literature [19–20, 24–28], the following discussion focuses on only two examples: the angle of deflection and the narrowing of the glands. From Fig 1 it is clear that both these features occur in different and separate locations on the eyelid surface. Moreover, there are regions were glands shows clear angular deviation but the angle value is smaller than the arbitrary threshold value (45° in this case). Similarly, there are many locations where glands obviously narrow (or broadens), however as the “narrowing” of glands is not well defined, it is hard to pinpoint those regions. It is clear that any valuation protocol being based on comparing the value of a certain morphological feature with an accepted threshold value will focus only on very specific regions of an eyelid. Regions other than those will be omitted in assessment procedure and treated as clinically irrelevant. Lastly, the clinical description of a single Meibomian image with only two morphological features requires many annotations and calculations and, because of arbitrariness in the feature definition, is very subjective.

The method proposed in this work allows for overcoming the difficulties mentioned above by automatic mapping of objectively determined values of different morphometric properties across entire eyelid surface. The results of such analysis are presented in the form of 6 morphometric maps, as in Fig 5.

One of the most obvious morphological feature of Meibomian gland pattern is their width or their separation. The presented image analysis method estimates this property using the gland pattern frequency, q0 (being an inverse of gland width and/or gland-gland separation) and visualizes this property on the entire surface of the eyelid. Comparing original gland structures (row a in Fig 5) with corresponding maps of gland frequency q0 (row b on Fig 5), it is clear that the regions with higher values of q0 correspond to regions where narrower glands are observed. Hence, the map of gland frequency q0 allows for easy identification of glands narrowing regions.

If the gland separation changes within the window of STFT analysis, then the value of q0 is estimated with some uncertainty. This property is shown on the map of gland pattern frequency variance, σq (row c of Fig 5). Areas with low σq values correspond to a gland pattern with well-defined value of frequency (well-defined gland width or well-defined separation).

For better localization of areas in which narrowing or broadening of Meibomian glands occurs, it is helpful to determine how quickly the glands are changing their width (or separation). The map of frequency gradient, G (Fig 5d), shows the rate of change in the gland pattern frequency. Looking at this map one notices that areas where gland narrowing or broadening occurs are clearly highlighted, whereas regions where the frequency of gland structure does not change much are mapped with low value of G.

As mentioned earlier (Fig 1), a common method of assessing the glands morphology is based on the absolute values of the gland’s angle of deflection and involves counting the events of exceeding a certain threshold angle value (45°). This task can be facilitated by determining an exact value of glands angle for every position of an eyelid. This is exactly what is presented on the map of gland orientation, θ0 (Fig 5e).

The values of deviation angle, θ0, are estimated with some uncertainty. The measure of this uncertainty is shown on the map of gland orientation variance, σθ (Fig 5f). Similarly to σq map, regions with low values of σθ correspond to gland pattern with well-defined orientation. We recall that this parameter but measured on the global scale (for the whole Meibomian image), was used previously as a measure of anisotropy in gland periodicity [33].

Aside from a knowledge of the glands angle at certain location, it may be just as important to visualize where this angle is changing. This property is shown on the map of angular incoherence, Cθ (Fig 5f), which shows the spatial variation in the mean direction of gland pattern. Comparing original Meibomian images (row a in Fig 5) with corresponding maps of Cθ, one can easily notice that regions where the orientation of glands suddenly changes are highlighted. Regions with low value of Cθ correspond to locations where glands are orientated in roughly similar direction.

It is worth recalling that the morphometric maps are calculated directly from a raw Meibomian image. Therefore, if the described approach was implemented in the meibograph control software, the clinician would have access to them immediately after taking a picture of the glands. Thanks to the large amount of objective information collected in the form of morphometric maps, qualitative analysis of meibomian gland morphological condition is made easier. Even simple visual inspection of the maps presented in Fig 5 may be useful in clinical practice and may improve the accuracy of the diagnosis.

It is also possible to attempt a more advanced analysis of the obtained results. Because the presented method produces new images, a further image analysis can be performed on each of them. For example, similarly to the popular drop-out area parameter (the ratio between the area occupied by Meibomian glands to the total area of the eyelid), it is possible to define simple measures of gland deformity by comparing the areas occupied by glands considered to be deformed to the total area of the eyelid. This measure can easily be obtained by firstly comparing the pixel numbers present in the appropriate morphometric map from Fig 5, with a certain value considered as the threshold between undisturbed and distorted state. Then the value of a new morphometric parameter is calculated as the ratio between the number of pixels that exceed the threshold value to the total number of pixels in the map. The effect of such a procedure performed on the image of frequency gradient, G (Fig 5d) and on the image of angular incoherence, Cθ (Fig 5f) is presented in Fig 8. Using these particular images, the values of two morphometric measures were estimated: 1) Aq quantifies the percentage of an eyelid area where significant changes in the glands width occur (that is narrowing and broadening); 2) Aθ measures the percentage of an eyelid area where the change in glands orientation is noticed.

Fig 8

Definition of exemplary new morphometric parameters using the maps presented in Fig 5.

Row a) original Meibomian images; Row b) locations where frequency gradient (blue regions) or angular incoherence (red regions) exceed an arbitrary threshold values of 0.007 and 0.1, respectively; Row c) percentages of the areas covered by glands with significant changes in the glands width (Aq, are of blue region) and with noticeable change in glands orientation (A, area of red region).

Fig 8 clearly shows that the area covered by deformed Meibomian glands correlate with the ailment progression. In an Meibomian image classified as unhealthy, morphological changes concern a significant area of the eyelid and meiboscores Aq and A take correspondingly high values. The surface of healthy glands is much less affected which results in lower values of Aq and A. Interestingly, the regions indicated by the human specialist and considered to be disturbed coincide roughly with the areas highlighted automatically with the presented method (compare Fig 1a with the Fig 8b/Intermediate). Looking at the values of Aq and A it is also clear that some of them are similar even if estimated for images belonging to different categories. This shows that a correct morphological condition assessment should not be based on a single parameter only.

The above-estimated morphometric scores (Aq and A) are only an example of the possibility offered by the presented method. On the basis of morphometric maps (Fig 5), other measures of the morphological state can be defined just as easily. This makes the proposed approach very promising as there is a strong evidence that the Meibomian gland morphological changes correlate with the ocular symptoms and signs of the dry eye [10-12]. The further work should focus on the associations between the obtained local morphometric features and the ocular symptoms and signs of the dry eye disease, which may confirm the clinical usefulness of the proposed approach.

In addition to the above detailed analysis of individual morphometric maps, it is interesting to check whether the mapped values of morphometric parameters can be used for the automatic classification of images. This will serve as an additional indirectly confirmation that the morphometric maps contain clinically useful information. As follows from Fig 5, for healthy Meibomian glands, the morphological properties sensitive to homogeneity in the frequency and in the orientation of Meibomian glands (σq, G, σθ and Cθ) take very low values and their maps are rather uniform. However, when gland ailment progresses, the shape of the glands begins to distort in some place. As a result, the values of homogeneity-sensitive properties increase in the corresponding position of the image. This observation suggests that distribution of pixel values presented on intrinsic images should be different for different categories. For healthy images most pixel values are expected to be low. Distribution should move to higher pixel values when the ailment progresses. This situation is well illustrated on Fig 6 where pixel value distributions for each intrinsic image are presented. The shapes of these distributions were quantified by determining their Entropy, Mean, Variance, Skewness and Kurtosis. As a result, for each Meibomian image 30 descriptive features were determined (6 intrinsic images x 5 measures of distribution).

Differences in the values of the 30 descriptive features found for each Meibomian image can be used to automatically categorize the images into subjective categories. There are a number of machine learning algorithms that can be used for this purpose. Finding the best solution based on its classification efficiency is beyond the scope of the present work. Therefore, the performance of only one simple classifier was tested, which separates Meibomian images based on their probability of belonging to a certain category. The classification performance of this approach is presented in Table 1.

As follows from Table 1, both classification approaches give satisfactory results, although the PCA classifier performs worse than the LDA. This is especially true for the category “intermediate”. This observation can be explained by broad and strongly overlapped probability distributions (marginal plots in Fig 7a) making the distinction between the classes inherently uncertain. Comparing current results from PCA classifier with the previous outcomes [33] one sees that increasing the number of descriptive features (current 30 features vs. previous 2) is not the way for improving categorization efficiency. The data reduction method based on maximizing variability in the data set (utilized by PCA approach) has probably hit the limit of efficiency. Further increase in categorization performance can be obtained using different algorithms. This is demonstrated by the output of the same type of classifier but using LDA data reduction method. As follows from Fig 7b, for LDA approach much better clustering of data points belonging to different categories was obtained. As a result, appropriate probability distributions are narrower and better separated which translates into observed classification improvement.

Conclusions

The presented method for Meibomian image analysis allows for a truly objective estimation of few strictly defined morphometric parameters. The newly developed automated procedure calculates numerical values of these parameters and generates their maps across entire eyelid area thereby allows for tracking the local morphometric changes. Moreover, each map presenting particular morphological property can be subjected to further detailed analysis to extract even more quantitative information and define new morphometric scores. Isolating individual morphometric components from the original Meibomian image may help clinicians to see in which part of the eyelid disturbance is taking place and also to quantify it with a numerical value providing a better insight into disease pathophysiology. Since many ophthalmic disorders start with a slight deformation of the meibomian glands (before their atrophy begins) the results based on the presented method may be particularly important in detection of the initial stages of Meibomian gland disease.

Automatic categorization of Meibomian images was successfully performed confirming that the maps of morphological parameters contain clinically useful information and that taking into account more morphological features can improve classification efficiency.

The presented method is fast, user-friendly and can be integrated with Meibograph software. To confirm its clinical utility, further work should focus on the associations between the introduced morphometric parameters with the ocular symptoms and signs of the dry eye disease.

Meibomian gland images acquisition.

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2D Short-Time Fourier Transform.

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The consequence of finite width of Gaussian window.

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Calculation of intrinsic images.

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Quantification of intrinsic images.

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Dimensionality reduction and image categorization.

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Estimation of confidence interval for classification efficiency.

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28 Mar 2022

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Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #1: Partly

Reviewer #2: Partly

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2. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: No

Reviewer #2: Yes

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3. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: Yes

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4. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: No

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5. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: This manuscript describes a novel image analysis method to provide detailed information on the local morphology of meibomian glands. This was then tested on meibomian gland images which were classified as healthy, intermediate and unhealthy. The bulk of the manuscript seems to contain a very detailed and technical explanation of the development of the image analysis technique, which to be honest, as a clinical researcher, I found challenging to follow. My general comments include:

• Please include details of the original ethics approval, from which the images were obtained. It would also be helpful to understand the general inclusion/exclusion criteria of the original study population

• Materials and Methods – the meibomian gland images were graded 1-3 on two consecutive days and the results were well correlated. However, it would be helpful if the authors could clarify how many researchers were involved in the grading, and how the images were classified if the grades assigned were different on the two days

• Table 1 – please add confidence intervals or other statistical analyses to this table. Otherwise, it is difficult to determine whether these proportions are significantly different from one another

• Line 211 belongs in the Materials and Methods section, but further detail needs to be added regarding the “home-built meibographic imaging equipment” used. How does this compare to commercially available imaging tools?

• Line 121 – the sentence beginning “In next section” is unnecessary

• The manuscript should remove all personal pronouns e.g. line 121 “we”, line 132 “our”

• Line 316 – please soften the conclusion “invaluable aid” – this is too strong and not necessarily supported by the data

• Do the findings correlate with any ocular symptoms or other signs of dry eye?

• What is the clinical utility of this analysis system? Is it something that can be easily incorporated into clinical practice? What do the findings actually mean, since no associations are discussed relating the health of the glands and other signs and symptoms of dry eye?

Reviewer #2: How was MG function scored?

How user-friendly this method is?

Adding 1 or 2 sample images to the manuscript will help readers better understand and visualize to what extent authors are referring to deformity of glands.

Also, I would like to know about the complete tarsal area what was exposed to calculate MGs height. Height of MGs may differ with eversion specially for lower lids as we have less surface area.

Good but do comment on use fullness of this method. What is the clinical utility of this technique?

Tortuosity is related more to the twisting or curved MGs. In literature, there are several methods to measure tortuosity and deformity. I would like to know more about the method authors have used and its reliability as well. Better to describe with sample images.

There are various ways to quantify Meibomian gland images particularly three-dimensional Fourier domain OCT. How this 2D Fourier transform is better?

Better to revise keeping in mind above mentioned points.

**********

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Reviewer #1: No

Reviewer #2: No

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10 May 2022

Response to the points raised by an Academic Editor:

"1. Please include ethics approval details for the current study. This used images from the study in The Ocular Surface 2020 (also not very details regarding ethics). Details on inclusion/exclusion criteria should also be included, and how many patients were examined should be stated. The number of images is noted in the manuscript, and that there were 2 images per person, but 'n' not provided."

New subsection named “Subjects” in “Materials and methods” was introduced where details on ethics approval, inclusion/exclusion criteria and number of examined patients were included.

"2. Please give full details on the imaging techniques used for meibography. The authors used a custom built meibographer (based on the 2020 study). How does this compare to the clinically used (commercial) instruments, in terms of image resolution for of upper eyelid meibomian glands. Have the authors used their 2D Fourier transform analysis on routine clinical meibography images?"

Standard IR retro-reflection meibograph is very simple device. Actually it is ordinary camera adapted to work with infrared light. The quality of the acquired images is determined just by the quality of the lens, resolution and dynamical range of the camera. The parameters of our system (resolution 20pix/mm and 8-bit dynamics) were sufficient to record a clear image of the basic structure of the Meibomian glands, that is, the feature we were interested during our study. We added new figure (Fig.1) which shows an exemplary raw meibographic image acquired by our system. As one can see it does not look much different from what is obtained with commercial instruments. We did not test our method on images acquired with such devices. It is certain that the quality of the images provided by these instruments will not be worse than ours. Therefore, we are confident that the described method will work also for that case.

More information on imaging technique used for meibography was introduced into “Meibographic images” section of “Materials and methods” as well as in dedicated “S1 Appendix. Meibomian gland images acquisition” supplementary document.

"3. Can the individual meibomian gland analysis described here be practically applied in a clinical context - the analysis is complex, and it is not clear how this would be incorporated into a routine clinical examination."

A routine clinical examination can easily be extended to include proposed objective analysis of the morphological status. We remind that only the raw image of meibomian glands is sufficient to perform the described analysis. In the case of such an extended examination, the clinician would have access to both: a real picture of the glands, and to the corresponding morphometric maps. Of course, we do not expect the clinician to perform this analysis himself. Our method should be included into the imaging software. Most conveniently to imaging software of commercial meibograph (sort of module/plug-in). We hope we provide all the necessary technical details of the technique to make it easier to replicate it by software engineers.

We agree that the analysis is not trivial, but from the clinician's point of view, what is important is the way of interpreting the morphometric maps produced by our method. We have significantly expanded the "Discussion" section with additional information on how to read those maps so that the reader has a better understanding of their interpretation.

Another clinically useful feature of presented method is that morphometric maps can also be used to define and automatically estimate the values of new meibo-scores. We added new Fig.8 to show the potential definition of such score. Of course, the usefulness of any specific parameter determined this way in the clinical practice must be demonstrated by the future dedicated and systematic tests.

"4. This is important to justify, noting the conclusion (line 316): "To conclude, our method for isolating individual morphometric components from the original Meibomian image can be of invaluable aid in the diagnostic process. It may help clinicians to see in which part of the eyelid disturbance is taking place and also to quantify it with a numerical value providing essentially insight into disease pathophysiology." The results presented do not really support the 'invaluable aid' comment and should be modified as such."

The new section “Conclusion” was introduced where we summarize our results in a broader way. The statement on 'invaluable aid' was softened.

"5. Can the authors comment on associations between the eyelid meibography 'heatmaps' generated using the local analysis, and symptoms reported by the patients. Thank you."

The connection between the observed gland distortion and the patient’s symptoms was already recognized and described in the literature. We have cited appropriate papers in our manuscript [9-11, 14-15, 24-25, 32-34]. This observation was based on manual measurements of different morphological features. The aim of our work was not to search for a new correlation between gland’s morphological change and particular symptom, but to provide a tool for automatic and objective characterization of local gland distortion. This tool allows for quick and automatic mapping of defined morphological parameters in an objective manner, not requiring manual measurements. We hope that in the near future the systematic research using this tool may speed up and objectify the measurement of morphological features providing deeper understanding of the connection between gland distortion and various clinical measures.

We addressed this issue in several places in the significantly expanded "Discussion" section and in the "Conclusions" section.

"6. A careful edit for English grammar and expression in the entire manuscript would improve the communication; there are sections that are not well expressed."

We have reviewed the manuscript to improve language usage. In addition to minor corrections, many new sentences appeared and old sentences have been rewritten to improve their readability without changing their meaning.

Response to the points raised by Reviewer #1:

"1. Please include details of the original ethics approval, from which the images were obtained.

It would also be helpful to understand the general inclusion/exclusion criteria of the original study population"

New subsection named “Subjects” in “Materials and methods” was introduced where details on ethics approval, inclusion/exclusion criteria and number of examined patients were included.

"2. Materials and Methods – the meibomian gland images were graded 1-3 on two consecutive

days and the results were well correlated. However, it would be helpful if the authors could clarify how many researchers were involved in the grading, and how the images were classified if the grades assigned were different on the two days"

Only one experienced optometrist was involved in the grading of meibomian images and the rating was done on two consecutive days. If the grades assigned were different on the two days, the images were reanalysed again to make a proper decision based on the presented criteria.

We have added the appropriate sentences in the section “Meibographic images” to better clarify this point.

"3. Table 1 – please add confidence intervals or other statistical analyses to this table. Otherwise,

it is difficult to determine whether these proportions are significantly different from one another"

95% Confidence intervals were added to the table. Details on their evaluation was also introduced into the Supplementary Materials document (S7 Appendix).

"4. Line 211 belongs in the Materials and Methods section, but further detail needs to be added

regarding the “home-built meibographic imaging equipment” used. How does this compare to commercially available imaging tools"

Standard IR retro-reflection meibograph is very simple device. Actually it is ordinary camera adapted to work with infrared light. The quality of the acquired images is determined just by the quality of the lens, resolution and dynamical range of the camera. The parameters of our system (resolution 20pix/mm and 8-bit dynamics) were sufficient to record a clear image of the basic structure of the Meibomian glands, that is, the feature we were interested during our study. We added new figure (Fig.1) which shows an exemplary raw meibographic image acquired by our system. As one can see it does not look much different from what is usually presented as obtained with commercial instruments. We did not test our method on images acquired with such devices. It is certain that the quality of the images provided by these instruments will not be worse than ours. Therefore, we are confident that the described method will work also for that case. Surely, with better equipment better results can be expected.

More information on imaging technique used for meibography was introduced into “Meibographic images” section of “Materials and methods” as well as in dedicated “S1 Appendix. Meibomian gland images acquisition” supplementary document.

"5. Line 121 – the sentence beginning “In next section” is unnecessary"

The sentence was removed

"6. The manuscript should remove all personal pronouns e.g. line 121 “we”, line 132 “our”"

Personal pronouns were removed

"7. Line 316 – please soften the conclusion “invaluable aid” – this is too strong and not necessarily supported by the data"

The new section “Conclusion” was introduced where we summarize our results in a broader way. The statement on 'invaluable aid' was softened.

"8. Do the findings correlate with any ocular symptoms or other signs of dry eye?"

The aim of our work was not to search for a correlation between gland’s morphological change and particular symptom, but to provide a tool for automatic and objective characterization of local gland distortion. Of course, the motivation for creating such a tool is a strong evidence that the meibomian gland morphological changes correlate with the ocular symptoms and signs of the dry eye. We have cited appropriate papers in our manuscript [9-11, 14-15, 24-25, 32-34]. The presented method allows for quick and automatic quantification of defined morphological parameters in an objective manner, not requiring manual measurements. While we do not provide any evidence for this, this logical sequence implies that the reported results should correlate with ocular symptoms.

We hope that in the near future the systematic research using this tool will provide such a proof and will confirm the clinical usefulness of the proposed approach.

"

9. What is the clinical utility of this analysis system? Is it something that can be easily

incorporated into clinical practice? What do the findings actually mean, since no associations are discussed relating the health of the glands and other signs and symptoms of dry eye?"

Distortion of the glands is a well-known indicator of the health of the glands and it is considered to be a symptom of early stage dry eye disease. Our finding concerns the quantitative and automatic assessment of the degree of deformation of the glands. Additionally, morphological parameters are presented in the form of spatial color-coded maps.

A routine clinical examination can easily be extended to include the proposed objective analysis of the morphological status. We remind that in principle only the raw image of meibomian glands is sufficient to perform the described analysis. Of course, we do not expect the clinician to perform this analysis himself. Our method should be included into the imaging software. Most conveniently to imaging software of commercial meibograph (sort of module/plug-in). In the case of such an extended examination, the clinician would have access to both: a real picture of the glands, and to the corresponding morphometric maps. We have significantly expanded the "Discussion" section with additional information on how to read those maps so that the reader has a better understanding of their interpretation.

Another clinically useful feature of presented method is that morphometric maps can also be used to define and automatically estimate the values of new meibo-scores. We added new Fig.8 to show the potential definition of such score. Of course, the usefulness of any specific parameter determined this way in the clinical practice must be demonstrated by the future dedicated and systematic tests.

We have expanded the "Discussion" section with many additional descriptive sentences, hoping that the potential clinical utility will be better understood.

Response to the points raised by Reviewer #2:

"1. How was MG function scored?"

The aim of our research was to develop a method for automatic and objective determination of local changes in the morphology of Meibomian glands. For such a task, scoring of the MG functions was not necessary. Therefore, the function of the MG and other ocular symptoms and signs of the dry eye disease were not scored. To make it clear, we've added a sentence to the "Meibographic images" section.

Of course, it would be very useful to determine the correlation between morphological changes and other features that determine the condition of the glands. This task is beyond the scope of our work. However, there is a strong evidence that the meibomian gland morphological changes correlate with the ocular symptoms and signs of the dry eye. We have cited appropriate papers in our manuscript [9-11, 14-15, 24-25, 32-34]. Therefore, we can hope that the parameters estimated by us may also be useful in diagnosis of the ocular symptoms and the image analysis method will make the procedure faster and more objective.

"2. How user-friendly this method is?"

Our meibography system is based on the usual retroreflective approach. It has been mounted on a Topcon SL-D701 slit lamp allowing the recording of meibographic images of the upper and lower eyelids during a routine eye examination. Image analysis method described in the article can be easily integrated into an image acquisition software. What is important for the clinical practice this method is fast and is not only user-friendly but also patient-friendly causing no discomfort during the procedure and providing the images which can be easily demonstrated to the patients. Information on this point was added to the conclusion section.

"3. Adding 1 or 2 sample images to the manuscript will help readers better understand and visualize to what extent authors are referring to deformity of glands."

In the "Materials and methods" section, a new image has been added (Fig. 1), which shows the effect of image preprocessing and marks the areas considered by the optometrist as distorted.

"4. Also, I would like to know about the complete tarsal area what was exposed to calculate MGs height. Height of MGs may differ with eversion specially for lower lids as we have less surface area."

In our work, the measure of distortion was strictly defined by derivatives of the orientation and the width of the glands and did not require knowledge of their length. Therefore, the height of the glands was not calculated. However, even if our approach focuses on the shape of the glands (rather than their dimensions) it was very important to expose the eyelid properly, especially in order to correctly image the distal areas of the eyelid. We used only the images of the best quality and presenting the largest area of the tarsal plate containing the Meibomian glands.

Although we have always collected a set of meibographic images of the upper and lower eyelids for each patient, we only used images of the upper eyelid to test our method. This decision was made only because of the larger surface of the upper eyelid on which the shape changes can be easier to visualized. In the further study the lower eyelids should be examined as well.

"5. Good but do comment on usefullness of this method. What is the clinical utility of this technique?"

As mentioned before, distortion of the glands is a well-known indicator of the health of the glands and it is considered to be a symptom of early stage dry eye disease. Therefore the detailed morphometric analysis is needed to establish what kind of changes are crucial in the proper diagnostic procedure. Our finding concerns the quantitative and automatic assessment of the degree of deformation of the glands. Additionally, morphological parameters are presented in the form of spatial color-coded maps. Compared to the other methods our algorithm allows to indicate subtle changes in the MG morphology, which is important for the proper follow up examinations.

A routine clinical examination can easily be extended to include proposed objective analysis of the morphological status. Our method should be included into the imaging software. Most conveniently to imaging software of commercial meibograph (sort of module/plug-in). Then, the clinician would have access to both: a real picture of the glands, and to the corresponding morphometric maps indicating where in the eyelid there is a specific morphological change (change in angle or change in width). We have added new sentences into the "Discussion" section on how to read those maps so that the reader has a better understanding of their interpretation.

Another clinically useful feature of presented method is that morphometric maps can also be used to define and automatically estimate the values of new meibo-scores. We added new Fig.8 to show the potential definition of such score. Of course, the usefulness of any specific parameter determined this way in the clinical practice must be demonstrated by the future dedicated and systematic tests.

We have significantly expanded the "Discussion" section and introduced additional information into “Conclusion” section, hoping that the potential clinical utility will be better understood.

"6. Tortuosity is related more to the twisting or curved MGs. In literature, there are several methods to measure tortuosity and deformity. I would like to know more about the method authors have used and its reliability as well. Better to describe with sample images."

So far, all the recognized in the literature methods to measure tortuosity and deformity of the meibomian gland consider only individual the most affected glands as a representation of the entire eyelid area. The simplest approach is to simply count the number of distortion events. In the new Fig.1 we have marked, for example, the regions considered by the optometrist to be distorted. Here we have limited ourselves to only two features: change of gland direction and glands narrowing. With our method, the values of these features (or their derivatives) can be estimated automatically for each position on the eyelid. This not only makes the analysis procedure more objective and faster, but also makes it possible to define new meibo-scores. An example of two such scores that quantify the percentage of the eyelid area covered by deformed regions of the glands is shown in the new Fig. 8.

"7. There are various ways to quantify Meibomian gland images particularly three-dimensional Fourier domain OCT. How this 2D Fourier transform is better?"

The method of 3D Fourier domain OCT is just another tool for collecting images of the gland structure. It is imaging technique, not an analytical technique. Here, the Fourier transformation is used to speed-up acquisition process. This imaging technique is much more sophisticated than simple retroflection of usual meibographs (after all it is OCT method). The data are better quality (although the field of view is rather small) and provide information also on the depth of the gland (instead of just its surface studied by usual retroreflection meibographs). So surely, 3D OCT tool provide a lot of high-quality data. But again, it does not provide ways for quantitative analysis. In order to extract information about any gland feature (e.g. drop-out volume or gland orientation), the data from 3D OCT should also be subjected to appropriate analysis. This is the area of application of our method. Our work does not involve new method for acquiring images (we used usual retroreflection method), but rather a new way of their analysis focused on automatic and objective quantification of glands distortion. This is where Fourier transform came in handy. We are confident that our method can be successfully used also to analyze data from 3D OCT instruments.

Submitted filename: Response to Reviewers.docx

Click here for additional data file.

13 Jun 2022

2D Short-Time Fourier Transform for local morphological analysis of meibomian gland images

PONE-D-22-01430R1

Dear Dr. Pochylski,

We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements.

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Kind regards,

Michele Madigan

Academic Editor

PLOS ONE

Additional Editor Comments (optional):

Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.

Reviewer #2: All comments have been addressed

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2. Is the manuscript technically sound, and do the data support the conclusions?

The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented.

Reviewer #2: Yes

**********

3. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #2: Yes

**********

4. Have the authors made all data underlying the findings in their manuscript fully available?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #2: Yes

**********

5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #2: Yes

**********

6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #2: Authors have addressed all comments. This is a good research area and authors have efficiently managed to highlight important elements.

**********

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If you choose “no”, your identity will remain anonymous but your review may still be made public.

Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #2: No

**********

15 Jun 2022

PONE-D-22-01430R1

2D Short-Time Fourier Transform for local morphological analysis of meibomian gland images

Dear Dr. Pochylski:

I'm pleased to inform you that your manuscript has been deemed suitable for publication in PLOS ONE. Congratulations! Your manuscript is now with our production department.

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