Computers in Biology and Medicine 47 (2014) 27–35
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Application of vascular bundle displacement in the optic disc for glaucoma detection using fundus images José Abel de la Fuente-Arriaga a, Edgardo M. Felipe-Riverón b,n, Eduardo Garduño-Calderón c a
Tecnológico de Estudios Superiores de Jocotitlán, Jocotitlán, Mexico Centro de Investigación en Computación, Instituto Politécnico Nacional, México City (D.F.), Mexico c Centro Oftalmológico de Atlacomulco, Atlacomulco, Mexico b
art ic l e i nf o
a b s t r a c t
Article history: Received 4 July 2013 Accepted 14 January 2014
This paper presents a methodology for glaucoma detection based on measuring displacements of blood vessels within the optic disc (vascular bundle) in human retinal images. The method consists of segmenting the region of the vascular bundle in an optic disc to set a reference point in the temporal side of the cup, determining the position of the centroids of the superior, inferior, and nasal vascular bundle segmented zones located within the segmented region, and calculating the displacement from normal position using the chessboard distance metric. The method was successful in 62 images out of 67, achieving 93.02% sensitivity, 91.66% specificity, and 91.34% global accuracy in pre-diagnosis. & 2014 Elsevier Ltd. All rights reserved.
Keywords: Glaucoma detection Vascular bundle displacement Excavation detection Optic papilla segmentation Chessboard distance metric
1. Introduction Application of noninvasive techniques in automatic retina analysis is an important area in medicine [1]. The information extracted from the analysis of digital images can be used to determine the existence of ocular diseases, such as glaucoma [2]. The optic disc (or optic papilla) yields the clearest area in images of the rear pole of the retina. Anatomically in a normal papilla, the vascular network emerges from the choroids through the center of the nervous fibers that constitute the optic nerve. In turn, the optic nerve passes through a tube-like structure toward the brain. Glaucoma, an ocular asymptomatic neuropathy, creates excessive intraocular pressure and an increase in size of the excavation (or cup) in the papilla. This excavation produces a thickening of the wall of the papilla, which then pushes the blood vessels (arterial and venous) located within the optic disc boundary (called also the vascular bundle) toward the nasal side of the affected eye(s). In time, the increased size of the cup and the displacement of the vascular bundle, damages the optic nerve. If left untreated, glaucoma causes first a progressive irreversible loss of peripheral vision and finally leads to blindness. Glaucoma occurs only in the optic disc of the retina.
n
Corresponding author. Tel.: þ 52 55 5729 6000x56515. E-mail addresses: [email protected] (J.A.d.l. Fuente-Arriaga), [email protected] (E.M. Felipe-Riverón), [email protected] (E. Garduño-Calderón). 0010-4825/$ - see front matter & 2014 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compbiomed.2014.01.005
Between 12% and 15% of the total world population suffering from various stages of blindness is affected by glaucoma in its different stages [2,3]. In Mexico, glaucoma represents the second cause of blindness [4]. Consequently, it is important to develop new methods for the effective early detection of glaucoma. The clinical procedures that contribute to the pre-diagnosis of glaucoma by the ophthalmologists are (a) analysis of the clinical history of the patient; (b) measurement of the intraocular pressure; (c) analysis of alterations in the optic disc; and (d) functional study of the visual field (called a Campimetry test). Some important changes of the optic disc resulting from glaucoma are [2] excavation growth; localized and generalized thinning of the optic nerve; presence of notches in the excavation perimeter; loss of nerve fibers; asymmetry of the excavation in both eyes; blood vessels bayonet; deep excavation with visible scleral holes; and neuroretinal rim thickness. In arriving at a diagnosis, ophthalmologists make significant use of the so-called cup/disc ratio and the ISNT Rule (in normal retinas the neuroretinal rim generally is thicker in the inferior zone, followed by the superior, nasal, and temporal zones) [5]. If the diameter of the cup (or its equivalent in area) exceeds 0.4 of the diameter of the optic papilla, then the eye has a high probability of becoming glaucomatous. It is easier for specialists to estimate at a glance qualitatively the cup/disc ratio than to measure the displacement of the vascular bundle towards the nasal zone. This work presents a new method for the detection and classification of retinal images that depicts various stages of glaucoma. The method analyzes morphological alterations detected
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within the optic disc. The approach is based on the close relationship found between the vascular bundle displacement and the excavation growth within the optic disc in the superior, inferior, and nasal zones. It is possible using the proposed method to classify physiologically normal versus suspect excavations, even when they are in their initial stages of development.
2. Background A medical procedure used in the detection of glaucoma consists of evaluating the morphological alterations in the optic disc, visible with the help of instruments such as a slit lamp; highpower convex lenses [7]; optical photographs of the retina [6]; retinal confocal tomography [8,9]; laser polarimetry tomography [8,9]; and optical coherence tomography [8,10]. The performance and reproducibility of papillary measurements in glaucomatous retinas have been successfully evaluated and compared in numerous investigations [11]. The analysis of glaucoma begins with the detection and evaluation of some parts of the retina, mainly the optic disc (or optic papilla), the excavation, and the blood vessels located within it (vascular bundle). The characteristics most frequently analyzed are the measurement of the cup/disc ratio and the neuroretinal rim thickness. The latter shows in normal eyes a characteristic configuration that generally is thicker in the inferior zone, followed by another feature, known as the ISNT rule, which is related to the distribution of blood vessels in the superior, nasal, and temporal zones. Current methods for the automatic detection of glaucoma have difficulties in segmenting the disc and cup. Segmentation is a crucial step in automatic analysis that ultimately determines the accuracy of the results. In the present application, segmentation is affected mainly by the presence of blood vessels in images of the optic disc [12–15,22] This difficulty affects detection of the exact contour of the optic disc, as well as the detection of possible excavations. Despite this, many reported results on glaucoma detection methods are based on the cup/disc ratio [12], such as [16,18,19]; they show results between 60% to 94% sensitivity and 82% to 94.7% specificity in pre-diagnosis. Other works measure this same characteristic using pairs of stereo retinal images to find the disparity of the corresponding points of both images [17] achieving results of 87% sensitivity and 82% specificity. However, the accuracy and actual effectiveness of reported results remain a subject of much controversy. Other authors have employed combined approaches, using the cup/disc ratio and the analysis of vessel bends or kinks (small
vessels emanating from the excavation) that provide physiological validation for the boundary cup [21,23]. These methods have been reported to yield results between 18.6% to 81.3% sensitivity and 45.5% to 81.8% specificity. When combined with the ISNT rule [26– 28], where, instead of measuring the neuroretinal rim thickness, they measure the proportion of the blood vessels in the inferior, superior, nasal, and temporal disc zones, have been reported between 97.6% to 100% sensitivity and 80% to 99.2% specificity. When adding the detection of defects of retinal nerve fiber layer [31], results of 80% to 90% sensitivity and 54% to 75% specificity in the pre-diagnosis have been reported.
3. Methodology This work presents a new method for the automatic classification of retinal images suspect of depicting glaucoma conditions. The method relies only on the analysis of morphological alterations that can be detected within the optic disc, even when the size of the excavation is in the initial stage of glaucoma. The method proposes a different way of glaucoma detection based on the analysis of the vascular bundle displacement within the optic disc caused by the excavation. This approach is motivated by a high degree of correlation between excavation growth and the blood vessel displacement in the inferior, superior, and nasal zones of the optic disc. The proposed method consists of the following steps: (1) RGB image acquisition; (2) segmentation of the optic disc region; (3) detection of a reference point in the excavation or cup; (4) detection of centroids of three zones of the vascular bundle; and (5) measurement of the distance between the reference point of the cup to the three centroids. 3.1. Data used The data used for evaluating the method were 67 retina JPEG and BMP color images of 720 576 pixels. Of these, 24 are retinal images from 20 normal patients, and the remaining 43 images consists of 21 isolated images and 11 pairs of images from 23 patients (22 images had advanced stage of glaucoma development). These images were acquired with a conventional eye fundus camera [6] and were previously selected from a greater collection of images acquired from 51 patients evaluated by an ophthalmologist that specializes in glaucoma. The images used in the research were chosen based on their clarity and the quality of the parts of the retina to be analyzed. Other images from the collection are related to other diseases, not to glaucoma. This
Fig. 1. Optical color eye fundus image from a left eye classified in an advanced stage of development of glaucoma showing the following anatomic parts: a. optic disc; b. excavation or cup; c. vascular bundle; d. neuroretinal rim, and the zones of the optic disc: I, inferior zone; S, superior zone; N, nasal zone; and T, temporal zone.
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group of images is a part of the private collection of retinal images that belongs to the Center for Computing Research of the National Polytechnic Institute, Mexico. 3.2. RGB image acquisition The proposed method was evaluated in retina images with all visible anatomic parts of the eye fundus. Fig. 1 shows an eye fundus image from our collection with the anatomic parts indicated: a. optic disc; b. excavation or cup; c. blood vessels within the optic disc (vascular bundle); d. neuroretinal rim, and the different zones of the optic disc (image is from a left eye): I, inferior zone; S, superior zone; N, nasal zone; finally, T, temporal zone. The image shown was classified as glaucomatous in an advanced stage of development, due to the excessive size of the excavation with respect to the size of the optic disc. 3.3. Segmentation of the optic disc region The objective of the optic disc area segmentation is to limit the region of interest for detecting and segmenting the anatomic elements that are described in the next steps, as well as to obtain approximately the diameter of the disc to be used in the process of normalization. In this paper we use the technique developed in Ref. [22] for optic disc segmentation. This technique consists of six steps from which we use only the first five (the sixth step deals with contour segmentation, which is not required in our procedure). The segmentation steps we used are as follows: (1) Technique uses human retinal images acquired in the color model RGB. (2) Normalization of images in size in case the images are provided from different sources. (3) Localization of the region of interest (ROI) of the optic disc using individual points (named seeds) through the Fourier transformation and P-Tile for thresholding. (4) Elimination of the arterioles and venous for segmenting the optic disc more accurately using the red plane and the morphological Closing and Opening operations with a flat disc structuring element (SE) whose diameter was set to the thickness of the largest blood vessel in the normalized image (six pixels of diameter). (5) Segmentation of optic disc area is carried out in the red plane with the combination of the circular Hough transform and active contours. The segmentation technique was tested in 80 color retina images with low contrast, high levels of noise, and discontinuities in the edges, achieving the exact segmentation in 74 images corresponding to 92.5% accuracy on the basis of the prediagnosis carried out previously by the specialist. Finally, the segmented optic disc area is superposed on the ROI image, while at the same time zeroing the pixels of the background (AND logic operation). The segmentation of the image shown in Fig. 1 appears
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in Fig. 2, where Fig. 2(a) shows the ROI of the optic disc of the normalized-size image; (b) the optic disc zone without arterioles and venous (morphological Closing and Opening operations); (c) segmented optic disc area (the circular Hough transform and active contours); (d) the segmented area shown in (c) superimposed onto the image shown in (a). 3.4. Detection of a reference point in the excavation or cup This step begins with the approximate detection of the excavation by the technique developed in Ref. [12] on images similar to in Fig. 2(a), which uses the green plane of the image and a strategy that combines: (a) thresholding based on method of Otsu [32]; (b) the sequential application of binary Opening and Closing using a flat disc structure element of 5 and 43 pixels of diameter, respectively, to eliminate the isolated small spurious components; and (c) so-called external border morphological operation to extract the external border of the excavation. This procedure is named OOCE (Otsu, Opening, Closing, External border) rule in [12]. There, an accuracy of 92.52% was reported. Then, so that the vascular bundle displacement manifests itself as large as possible, a reference point toward the temporal region farthest to the optic disc center is located in the segmented cup by means of the automatic selection of the cup edge pixel closest to the temporal zone, taking into account the fact that due to glaucoma the vascular bundle is always displaced towards the nasal zone. This zone was selected because it is where the excavation is farthest from the center of the optic disc. We assumed that the displacement of the vessel bundle to the left (nasal zone) is a consequence of the growth of the excavation located to the right of the optic disc (in the case of the left eye). In the case of the right eye, the situation is the opposite. The steps for the segmentation of the excavation from Fig. 2(a) appears in Fig. 3, where Fig. 3(a) shows the segmented excavation by Otsu threshold; (b) the segmented excavation after the morphological Opening and Closing operations; (c) the excavation border obtained with the external border morphological operation; and finally, (d) the reference point farthest toward the temporal region in (c) superimposed to the optic disc (Fig. 2(d)), marked with a cross enclosed by a circle in Fig. 3(d), and denoted by the capital letter A. The exact location of point A is simple, since it is the point on the far right of the outline of the excavation shown in Fig. 3(c). 3.5. Detection of centroids of three zones of the vascular bundle The main objective of this work was to analyze and measure the displacement of blood vessels located within the optic disc. For this, we took into account reference points in the vascular bundle that describe the growth in size of the excavation towards the
Fig. 2. Details of the optic disc region: (a) the ROI containing the optic disc in the RGB color model of the normalized-size image; (b) the optic disc without arterioles and venous; (c) segmented optic disc; (d) AND logic operation of the area shown in (c) with the image shown in (a).
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Fig. 3. Details of reference point detection in the excavation (left eye): (a) Otsu threshold; (b) morphological Opening and Closing operations; (c) excavation border through the morphological operation called the external border; (d) reference point denoted by the capital letter A in Fig. 2(d).
Fig. 4. Masks used for segmenting the blood vessels located in different zones of the optic disc.
Fig. 5. Masks of Fig. 4 when coupled with optical disc center of Fig. 2(d). (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
temporal zone of the optic disc and the displacement of the vascular bundle within it, which is always displaced to the nasal zone. This step begins with the segmentation of blood vessels located within the optic disc (the vascular bundle). For this, the central point (centroid) of the optic disc is obtained (see Fig. 2(d)), which
serves as the reference for coupling it to the three triangular masks shown in Fig. 4, where Fig. 4(a) shows the mask for the superior zone, 4(b) for the inferior zone, and 4(c) for the nasal zone, when the image to be analyzed is from the left eye. If the image to be analyzed is from the right eye, then the last mask would be the mirror image of that shown in Fig. 4(c). The central point of each mask must match the central point of the optic disc even when the masks protrude from the ROI as is shown in Fig. 5, with the purpose of selecting the correct choice of the target zone. The segmentation is carried out in the red plane of the image in the RGB color model, since it was the channel where the best results were achieved, probably due to the common orange– reddish color of the optic papilla. The blood vessel segmentation algorithm uses a morphologic Black-top-hat operator and the technique of Otsu for thresholding [13,20,32,33] The Black-tophat is a morphologic transformation that depends on the shape of the objects in the papilla and extracts the regions having lower intensities than their neighboring regions; it is effective for identifying the sections where the vascular bundle is located. It is defined as the residue between the image processed by morphological closing (a dilation followed by an erosion operation using a flat disc structuring element of six pixels of diameter) and the original image. This operation allows us to highlight the elements deleted by the closing that, in this particular case, are the blood vessels located within the optic disc (the vascular bundle). The blood vessel segmentation is carried out individually in each zone covered by the corresponding mask (Fig. 4) as shown in Fig. 5. The result of the blood vessel segmentation in different zones is shown in Fig. 6(a) superior zone; 6(b) inferior zone; and 6 (c) nasal zone.
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Fig. 6. Segmentation of blood vessels located in the different zones of the optic disc: (a) superior zone; (b) inferior zone; (c) nasal zone.
Fig. 7. Centroid of blood vessels located in the different zones of the optic disc. B: Superior zone; C: nasal zone, and D: inferior zone.
To find the reference point that describes the trend in the position of vessels being analyzed, the centroid of vessels is calculated in each zone shown in Fig. 6. The centroid of a body coincides with the center of mass if the object density (area) is isotropic or when the material distribution is radially symmetrical; however, if an area has irregular borders defined by relative complex mathematical expressions (this is the case of the vascular bundle), the simplest method is to divide the object (vessels of each zone shown in Fig. 6) in small finite elements to calculate its centroid with the help of the individual summations described in (1) in order from left to right [24]. n
A ¼ ∑ ΔAi ; i¼1
n
Q x ¼ ∑ yi ΔAi ; i¼1
n
Q y ¼ ∑ xi ΔAi ; i¼1
Qy x¼ ; A
Q y¼ x A ð1Þ
where ΔAi is the area (number of pixels) of the ith element belonging to the foreground (the vascular bundle pixels); n is the number of finite elements in which the figure was divided; Qx and Qy are the static moments of the area with respect to the axes, respectively; yi is the coordinate y (ordinate) of the centroid of the ith element belonging to the foreground; xi is the coordinate x (abscissa) of the centroid of the ith element belonging to the foreground; and finally, x is the coordinate x of the centroid of the object and y is the coordinate y of the centroid of the object. The coordinates of the centroid of the object (x,y) do not always coincide with the foreground pixels.
Fig. 8. Distances d1, d2, and d3 between the centroids denoted by B, C, and D and the reference point A.
The centroid position of each region is shown in Fig. 7. The centroids are marked by a cross enclosed in a circle, and denoted by capital letters B, C, and D, in Fig. 2(d). The letter B represents the centroid of vessels in the superior zone; the letter C represents the centroid of vessels in the nasal zone; and the letter D represents the centroid of vessels in the inferior zone.
3.6. Measurement of the distance between the reference point of the cup to the three centroids In this stage of the process, the blood vessel displacements are calculated with respect to the excavation growth, which is carried out by using the reference point of the cup (A in Fig. 3(d)) and the vessels centroids (Fig. 7) in the different zones defined by the masks of Fig. 4. The displacements are measured by the calculation of the distances d1, d2, and d3 from the centroids B, C, and D, respectively, to the reference point A located in the temporal part of the excavation, as shown in Fig. 8. Since normally the vessel displacement is in the horizontal direction, distances are measured using the chessboard metric defined by Eq. (2) [29]: dc ¼ maxðjx2 x1 j; jy2 y1 jÞ
ð2Þ
where (x1, y1) are the coordinates of the first point and (x2, y2) are those of the second point.
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So that the method can be used in retinal images of different sizes, the distances are normalized with respect to the horizontal diameter of the optic disc Dh. The normalized distance dn is obtained by Eq. (3). dn ¼
100 d Dh
ð3Þ
where Dh is the horizontal diameter of the optic disc and d is the distance to normalize. The final result of the blood vessel displacement with respect to the proportional growth of the excavation is calculated using the average of the three normalized distances just measured. We need a decision point pre-diagnosing to decide if an optic disc is suspect to suffer glaucoma or not. Tests were carried out
Table 1 Range of the metrics (m s, m þ s) of the displacement of the vascular bundle in normal images and in images suspect of glaucoma. Distribution
l
r
lr
lþ r
Normal images Glaucoma suspect images
41.19 48.67
3.44 3.75
37.75 44.91
44.63 52.42
with 67 images. The cut-off point p was selected at a normalized distance of 45 pixels obtained empirically from our experiments. This threshold was determined on the basis of the pre-diagnostic carried out previously by the specialist and the standard deviation (s1 Normal images, s2 Glaucoma suspect images) as a measure of dispersion of the data relative to the average value of the distribution (μ1 Normal images, μ2 Glaucoma suspect images). Making use of the standard deviation, the variability of the distributions (dispersion) obtained as a result of measuring the displacement of the vascular bundle in healthy and diseased patients was calculated. In this way it was possible to calculate the range of the metrics (m s, m þ s) of the displacement of the vascular bundle in normal images and in images suspect of glaucoma. The values obtained are shown in Table 1. The range of dispersion of the normal image metrics was from 37.75 to 44.63, and the range of images with glaucoma ranges was from 44.91 to 52.42. Then, rounding the maximum value (m1 þ s1) of 44.63 of the normal images and the minimum value (μ2 s2) of 44.91 of the images suspect of glaucoma, we got the cut-off point p at a distance of 45 pixels to classify images into one of the two groups: normal and suspect of glaucoma. If the average of distances p calculated was less than the cut-off point (45), then the retina was pre-diagnosed as normal; otherwise the retina was pre-diagnosed as suspect of glaucoma.
Fig. 9. Detail of the region of interest of the optic disc with the centroids of three regions denoted by B, C, and D and the reference point of the excavation A. Images (a)–(f) have suspect excavation; images (g)–(i) have normal excavation.
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4. Discussion of results Fig. 9 shows several sample images from the collection of 67 images of human retina that were analyzed using the proposed method. The image population for the discussion of results was divided into two groups corresponding to normal and suspect excavation. The factors taken into account to select the test images were images with glaucoma suspect excavation; images with generalized thinning of the neuroretinal rim (a), (d), and (f); images having wide excavation and ostensible scleral holes (b) and (e); images with decreased neuroretinal rim and superior dislocation; images with nasal displacement of the vessels and its denudation (c) and (f). Images with normal excavation: images with circular excavation, concentric and small (g) and (i); images that meet rule ISNT and have normal cup/disc ratio (cup diameter lesser than 0.4 optic disc diameter) (h). Images show in detail the region of interest ROI with the centroids B, C and D of three zones and the reference point A marked by a cross enclosed by a circle. Results achieved in these test images were correct in all cases. The method proved to be able to pre-diagnose images with an advanced stage of development of glaucoma, even when the optic disc presented some morphological degeneration in the basic structure. This method has the advantage that even if the structures are degenerated (in the case of the disc and excavation) or moved partially out of the optic disc (in the case of the vascular bunch), there always exist vestiges of the anatomic structures, which allow the method to continue detecting the reference point without any problem, as is the case in (d)–(f) of Fig. 9. With the application of the proposed methodology in 67 retinal images, 93.02% images (40 retinas) were classified within the class of diseased, with 6.98% (3 retinas) classified incorrectly, and 91.66% images (22 retinas) classified within the class of healthy, with 8.4% (2 retinas) classified incorrectly, achieving a global accuracy in the pre-diagnosis of 92.34%. The method was evaluated by means of the Receiver Operating Characteristic (ROC) curve [25]. The ordinate of the ROC curve is the sensitivity, i.e., the ability of the method to classify the object within the correct class, and the abscissa is related to the specificity, i.e., the inability to classify correctly the objects within the correct class. The values of the sensitivity and the specificity have been obtained by Eq. (4) and the value of the area under the ROC curve (AUC) by Eq. (5), where ΔAi is the area of the ith element and n is the number of elements under the curve. The values achieved are shown in Table 2 and the ROC curve is shown in Fig. 10. Sensitivity ¼
TP 100; TP þ FN
Specificity ¼
TN 100 TN þ FP
Table 2 Results of the proposed method applied to 67 retinal images of real patients from which 24 were normal images and 43 were suspect to have glaucoma. Diagnosis
Result
True positive (TP) True negative (TN) False Positive (FP) False negative (FN) Sensitivity Specificity Area under the ROC curve Global accuracy
40 22 2 3 93.02% 91.66% 92.3% 92.34%
ð4Þ
Fig. 10. ROC curve plotted from the values achieved in Table 2.
n
AUC ¼ ð0:01Þ ∑ ΔAi i¼1
ð5Þ
The ROC curve was created with definitely positive and definitely negative results; for that reason the curve shows only a single operating point off the (0,0) and (100,100) corners (see Table 2). According to Ref. [30], an area of value from 90% to 100% represents an excellent test, from 80% to 90% a good test, from 70% to 80% a fair test, from 60% to 70% a poor test, and from 50% to 60% represents a fail test. The proposed work is a novel method for the analysis of the correlation found between the displacement of the blood vessels and the growth of the excavation present within the optic disc, Table 3 shows our results and some other published methods related to other state-of-the-art solutions, followed by the number of samples and the origin of the database of retina images used in the studies, respectively. As shown in Table 3, the sensitivity and the specificity in the pre-diagnosis of our proposed method are within the results achieved in the related state-of-the-art solutions. Analyzing the results in detail, in images where our method failed, it was observed that the expert pre-diagnosis was questionable because apart of the growth characteristics of the excavation, there were also the presence of nicks, notches and localized loss of optical fibers. On this basis, we can say that the effectiveness of the method presented is high. This paper represents the complete and updated version of the work presented in the 12th Mexican International Conference on Artificial Intelligence (MICAI 2013) held in November 2013 in Mexico City [34].
5. Conclusion This paper presents a methodology for detecting the optic disc suspect of glaucoma by measuring the displacement of the vascular bundle caused by the growth of the excavation or cup. The method was successful in 62 images out of 67, achieving 93.02% sensitivity, 91.66% specificity, and 91.34% global accuracy. This shows that the methodology is effective, and it could be used to develop new medical systems for the pre-diagnosis of glaucoma by computer.
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Table 3 Result of some other methods related to other state-of-the-art solutions. #
Type of analysis
Sensitivity
Specificity
1 2 3 4 5 6
Cup/disc ratio [12]a, [16]b, [18]c, [19]d Cup/disc ratio used pairs of stereo retinal images [17]e Cup/disc ratio and vessel bends [21]f, [23]g Cup/disc ratio and ISNT rule [26]h, [27]i, [28]j Defects of retinal nerve fiber layer [31]k The proposed methodl
60–94% 87% 18.6–81.3% 97.6–100% 80–90% 93.02%
82–94.7% 82% 45–81.8% 80–99.2% 54–75% 91.66%
a
107 images from the Center for Computing Research of IPN database. 140 images from the Singapore Eye Research Institute database. c 90 images from the Manchester Royal Eye Hospital database. d 45 images from the Gifu University Hospital database. e 98 images pairs from the Gifu University Hospital database. f 138 images from the Aravind Eye Hospital database. g 27 images from the Singapore Eye Research Institute database. h 61 images from the Kasturba Medical College database. i 550 images from an Aravind Eye Hospital database. j 36 images from an Aravind Eye Hospital database. k 249 images from residents of Akita, Japan, participating in a community health checkup. l 67 images from the Center for Computing Research of IPN database. b
Conflict of interest statement Authors do not have any conflict of interest.
Acknowledgments The authors of this paper wish to thank the Centro de Investigación en Computación (CIC), Mexico; Secretaría de Investigación y Posgrado (SIP), Mexico, and Instituto Politécnico Nacional (IPN), Mexico, for their economic support to develop this research. References [1] P. Gili-Manzanaro, F.C. Carrasco, J.C. Martín Rodrigo, J. Yangüela-Rodilla, A. Arias-Puente, Análisis digital de la papila con cámara de fondo de ojo convencional: estudio de variabilidad, Arch. Soc. Esp. Oftalmol. de Madrid 79 (3) (2004) 125–130. [2] Consejo de Salubridad general, Aspectos Generales. Centro Nacional de Excelencia Tecnológica en Salud: Diagnóstico y tratamiento del paciente adulto con glaucoma de ángulo abierto, México Secretaría de Salud, CENETEC, 2009. [3] R. Elolia, J. Stokes, Monograph series on aging-related diseases: XI. Glaucoma, Chronic Dis. Can. 19 (4) (1998) 157–169. [4] E.M. Felipe-Riverón, S.L. Morales-Güitrón, S. Ortiz-Yánez, Detección automática de la normalidad de las retinas humanas, Tesis de Maestría en Ciencias de la Computación CIC-IPN, México, 2004. [5] N. Harizman, C. Oliveira, A. Chiang, C. Tello, M. Marmor, R. Ritch, J. M. Liebmann, The ISNT rule and differentiation of normal from glaucomatous eyes, Arch. Ophthalmol. 124 (11) (2006) 1579–1583. [6] W.T. Jackman, J.D. Webster, On photographing the retinal of the living human eye, Philadelphia Photographer 23 (275) (1886) 275–276. [7] S. Ansari-Shahrezaei, N. Maar, R. Biowski, M. Stur, Biomicroscopic measurement of the optic disc with a high-power positive lens, Invest. Ophthalmol. Vis. Sci. 42 (1) (2001) 153–157. [8] L. Fernández-Argones, I. Piloto-Díaz, M. Coba-Peña, B. Pérez-Tamayo, M. Domínguez-Randulfe, K. Trujillo-Fonseca, Sistemas de análisis digital de imágenes en el glaucoma, Rev. Cubana Invest. Biomédica 28 (3) (2009) 102–111. [9] C.E. Mendoza-Santiesteban, R. Santiesteban-Freixas, A. González-García, L. González-Hess, E. Mesa-Hernández, Y. Perdomo-Trujillo, E. AlemañyRubio, F. Eguia, S. Vidal-Casalís, La tomografía de coherencia óptica en el diagnóstico de enfermedades de la retina y el nervio óptico, Rev. Cubana Oftalmol. 18 (2) (2005) 5, Tema de Revisión, 5 páginas, julio-diciembre de. [10] S. Duch-Tuesta, O. Buchacra-Castellano, Tomografía de coherencia óptica en glaucoma, Thea Innovation 43 (2006). http://www.laboratoriosthea.com/ archivos/publicaciones/00072.pdf (accesed 27.01.2014). [11] J.A. de la Fuente-Arriaga, E. Garduño-Calderón, F.J. Cuevas-de la Rosa, Estado actual de las técnicas computacionales para la valoración del disco óptico en glaucoma, 1er Congreso Mexiquense CTS þ I 2011, Memorias del Congreso Mexiquense CTS þ I, Alfaomega, México (2011) 155–161 (1a ed.).
[12] E.M. Felipe-Riverón, M. del Toro-Cespedes, Measurement of parameters of the optic disk in ophthalmoscopic color images of human retina, 17th Iberoamerican Congress on Pattern Recognition (CIARP 2012), Lecture Notes Comput. Sci. LNCS 3287 (2004) 661–668. [13] C. Muramatsu, T. Nakagawa, A. Sawada, Y. Hatanaka, T. Hara, T. Yamamoto, H. Fujita, Automated segmentation of optic disc region on retinal fundus photographs: comparison of contour modeling and pixel classification methods, Comput. Methods Programs Biomed. 101 (1) (2010) 23–32. [14] A. Osareh, M. Mirmehdi, B. Thomas, R. Markham, Colour morphology and snakes for optic disc localization. In: Proceedings of the 6th Medical Image Understanding and Analysis Conference, pp. 21–24, 2002. [15] D. Welfer, J. Scharcanski, C.M. Kitamura, M.M. Dal-Pizzol, L.W.B. Ludwig, D. Ruschel-Marinho, Segmentation of the optic disk in color eye fundus images using an adaptive morphological approach, Comput. Biol. Med. 40 (2010) 124–137. [16] J. Liu, D.W.K. Wong, J.H. Lim, H. Li, N.M. Tan, T.Y. Wong, ARGALI: an Automatic Cup-to-Disc Ratio Measurement System for Glaucoma Detection and Analysis Framework, SPIE 7260, 72603K-8, 2009. [17] C. Muramatsu, T. Nakagawa, A. Sawada, Y. Hatanaka, T. Yamamoto, H. Fujita, Automated determination of cup-to-disc ratio for classification of glaucomatous and normal eyes on stereo retinal fundus images, J. Biomed. Opt. 16 (9) (2011) 7, http://dx.doi.org/10.1117/1.3622755. [18] A. Abdel-Ghafar, A. Morris, B. Ritchings, C. Wood, Detection and characterization of the optic disk in glaucoma and diabetic retinopathy. In: Proceedings of the 8th Medical Image Understanding Analysis Conference, pp. 23–24, 2004. [19] Y. Hatanaka, A. Noudo, A. Sawada, T. Hara, T. Yamamoto, H. Fujita, Automated measurement of cup to disc ratio based on line profile analysis in retinal images. In: Proceedings of the 33rd Annual International Conference of the IEEE Engineering in Medicine and Biology Society, IEEE Engineering in Medicine and Biology Society, pp. 3387–3390, 2011. [20] T. Nakagawa, Y. Hayashi, Y. Hatanaka, A. Aoyama, Y. Mizukusa, A. Fujita, M. Kakogawa, T. Hara, H. Fujita, T. Yamamoto, Recognition of optic nerve head using blood-vessel-erased image and its application to production of simulated stereogram in computer-aided diagnosis system for retinal images, IEICE Trans. Inf. Syst. J89-D 11 (2006) 2491–2501. [21] G.D. Joshi, J. Sivaswamy, S.R. Krishnadas, Optic disk and cup segmentation from monocular color retinal images for glaucoma assessment, IEEE Trans. Med. Imag. 30 (6) (2011) 1192–1205. [22] J.A. de la Fuente-Arriaga, E.M. Felipe-Riverón, E. Garduño-Calderón, Segmentación del disco óptico en imágenes de retina mediante la transformada de Hough y los contornos activos, 12th International Congress on Computer Science (CORE 2012), Res. Comput. Sci. 58 (2012) 117–131. [23] J. Liu, D.W.K. Wong, J.H. Lim, H. Li, N.M. Tan, T.Y. Wong, Automated detection of kinks from blood vessels for optic cup segmentation in retinal images, SPIE 7260, 2009 (72601J-1–72601J-8). [24] J.M. Gere, B.J. Goodno, Repaso de centroides y momentos de inercia, Cervantes-González, S.R: Mecánica de materiales, Latin Am. Cengage Learn. (2009) 901–927. [25] M.J. Burgueño, J.L. García-Bastos, J.M. González-Buitrago, La curva ROC en la evaluación de las pruebas diagnósticas, Med. Clin. (Barcelona) 104 (1995) 661–670. [26] J. Nayak, R. Acharya, Automated diagnosis of glaucoma using digital fundus images, J. Med. Syst. 33 (2009) 337–346. [27] S. Kavitha, K. Duraiswamy, An efficient decision support system for detection of glaucoma in fundus images using ANFIS, Int. J. Adv. Eng. Technol. 6 (1) (2012) 226–240.
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[28] K. Narasimhan, K. Vijayarekha, An efficient automated system for glaucoma detection using fundus image, J. Theor. Appl. Inf. Technol. 33 (1) (2011) 104–110. [29] R.C. Gonzalez, R.E. Woods, Digital Image Processing, 3rd ed., Pearson Education, Inc., Pearson Prentice Hall, Upper Saddle River, NJ 07458, USA, 2008. [30] University of Nebraska, Medical Center, Department of Internal Medicine, The Area Under an ROC Curve. 〈http://gim.unmc.edu/dxtests/roc3.htm〉, 2013 (accessed 19.08.13). [31] Y. Hayashi, C. Muramatsu, A. Sawada, T. Hara, T. Yamamoto, H. Fujita, Glaucoma risk assessment based on clinical data and automated nerve fiber layer defects detection, In: Proceedings of the IEEE Engineering in Medicine and Biology Society, pp. 5963–5966, 2012.
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[32] N. Otsu, A threshold selection method from gray-level histograms, IEEE Trans. Syst. Man Cybern. 9 (1) (1979) 62–66. [33] P. Soille, Morphological Image Analysis: Principles and Applications, 2nd ed., Springer-Verlag Berlin Heidelberg, 2010. [34] J.A. de la Fuente-Arriaga, E.M. Felipe-Riverón, E. Garduño-Calderón, Detection of human retina images suspect of glaucoma through the vascular bundle displacement in the optic disc. In: Proceedings of the 12th Mexican International Conference on Artificial Intelligence, MICAI 2013, Lecture Notes in Artificial Intelligence LNAI 8265, pp. 520–531, 2013.
Contents lists available at ScienceDirect
Computers in Biology and Medicine journal homepage: www.elsevier.com/locate/cbm
Application of vascular bundle displacement in the optic disc for glaucoma detection using fundus images José Abel de la Fuente-Arriaga a, Edgardo M. Felipe-Riverón b,n, Eduardo Garduño-Calderón c a
Tecnológico de Estudios Superiores de Jocotitlán, Jocotitlán, Mexico Centro de Investigación en Computación, Instituto Politécnico Nacional, México City (D.F.), Mexico c Centro Oftalmológico de Atlacomulco, Atlacomulco, Mexico b
art ic l e i nf o
a b s t r a c t
Article history: Received 4 July 2013 Accepted 14 January 2014
This paper presents a methodology for glaucoma detection based on measuring displacements of blood vessels within the optic disc (vascular bundle) in human retinal images. The method consists of segmenting the region of the vascular bundle in an optic disc to set a reference point in the temporal side of the cup, determining the position of the centroids of the superior, inferior, and nasal vascular bundle segmented zones located within the segmented region, and calculating the displacement from normal position using the chessboard distance metric. The method was successful in 62 images out of 67, achieving 93.02% sensitivity, 91.66% specificity, and 91.34% global accuracy in pre-diagnosis. & 2014 Elsevier Ltd. All rights reserved.
Keywords: Glaucoma detection Vascular bundle displacement Excavation detection Optic papilla segmentation Chessboard distance metric
1. Introduction Application of noninvasive techniques in automatic retina analysis is an important area in medicine [1]. The information extracted from the analysis of digital images can be used to determine the existence of ocular diseases, such as glaucoma [2]. The optic disc (or optic papilla) yields the clearest area in images of the rear pole of the retina. Anatomically in a normal papilla, the vascular network emerges from the choroids through the center of the nervous fibers that constitute the optic nerve. In turn, the optic nerve passes through a tube-like structure toward the brain. Glaucoma, an ocular asymptomatic neuropathy, creates excessive intraocular pressure and an increase in size of the excavation (or cup) in the papilla. This excavation produces a thickening of the wall of the papilla, which then pushes the blood vessels (arterial and venous) located within the optic disc boundary (called also the vascular bundle) toward the nasal side of the affected eye(s). In time, the increased size of the cup and the displacement of the vascular bundle, damages the optic nerve. If left untreated, glaucoma causes first a progressive irreversible loss of peripheral vision and finally leads to blindness. Glaucoma occurs only in the optic disc of the retina.
n
Corresponding author. Tel.: þ 52 55 5729 6000x56515. E-mail addresses: [email protected] (J.A.d.l. Fuente-Arriaga), [email protected] (E.M. Felipe-Riverón), [email protected] (E. Garduño-Calderón). 0010-4825/$ - see front matter & 2014 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compbiomed.2014.01.005
Between 12% and 15% of the total world population suffering from various stages of blindness is affected by glaucoma in its different stages [2,3]. In Mexico, glaucoma represents the second cause of blindness [4]. Consequently, it is important to develop new methods for the effective early detection of glaucoma. The clinical procedures that contribute to the pre-diagnosis of glaucoma by the ophthalmologists are (a) analysis of the clinical history of the patient; (b) measurement of the intraocular pressure; (c) analysis of alterations in the optic disc; and (d) functional study of the visual field (called a Campimetry test). Some important changes of the optic disc resulting from glaucoma are [2] excavation growth; localized and generalized thinning of the optic nerve; presence of notches in the excavation perimeter; loss of nerve fibers; asymmetry of the excavation in both eyes; blood vessels bayonet; deep excavation with visible scleral holes; and neuroretinal rim thickness. In arriving at a diagnosis, ophthalmologists make significant use of the so-called cup/disc ratio and the ISNT Rule (in normal retinas the neuroretinal rim generally is thicker in the inferior zone, followed by the superior, nasal, and temporal zones) [5]. If the diameter of the cup (or its equivalent in area) exceeds 0.4 of the diameter of the optic papilla, then the eye has a high probability of becoming glaucomatous. It is easier for specialists to estimate at a glance qualitatively the cup/disc ratio than to measure the displacement of the vascular bundle towards the nasal zone. This work presents a new method for the detection and classification of retinal images that depicts various stages of glaucoma. The method analyzes morphological alterations detected
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within the optic disc. The approach is based on the close relationship found between the vascular bundle displacement and the excavation growth within the optic disc in the superior, inferior, and nasal zones. It is possible using the proposed method to classify physiologically normal versus suspect excavations, even when they are in their initial stages of development.
2. Background A medical procedure used in the detection of glaucoma consists of evaluating the morphological alterations in the optic disc, visible with the help of instruments such as a slit lamp; highpower convex lenses [7]; optical photographs of the retina [6]; retinal confocal tomography [8,9]; laser polarimetry tomography [8,9]; and optical coherence tomography [8,10]. The performance and reproducibility of papillary measurements in glaucomatous retinas have been successfully evaluated and compared in numerous investigations [11]. The analysis of glaucoma begins with the detection and evaluation of some parts of the retina, mainly the optic disc (or optic papilla), the excavation, and the blood vessels located within it (vascular bundle). The characteristics most frequently analyzed are the measurement of the cup/disc ratio and the neuroretinal rim thickness. The latter shows in normal eyes a characteristic configuration that generally is thicker in the inferior zone, followed by another feature, known as the ISNT rule, which is related to the distribution of blood vessels in the superior, nasal, and temporal zones. Current methods for the automatic detection of glaucoma have difficulties in segmenting the disc and cup. Segmentation is a crucial step in automatic analysis that ultimately determines the accuracy of the results. In the present application, segmentation is affected mainly by the presence of blood vessels in images of the optic disc [12–15,22] This difficulty affects detection of the exact contour of the optic disc, as well as the detection of possible excavations. Despite this, many reported results on glaucoma detection methods are based on the cup/disc ratio [12], such as [16,18,19]; they show results between 60% to 94% sensitivity and 82% to 94.7% specificity in pre-diagnosis. Other works measure this same characteristic using pairs of stereo retinal images to find the disparity of the corresponding points of both images [17] achieving results of 87% sensitivity and 82% specificity. However, the accuracy and actual effectiveness of reported results remain a subject of much controversy. Other authors have employed combined approaches, using the cup/disc ratio and the analysis of vessel bends or kinks (small
vessels emanating from the excavation) that provide physiological validation for the boundary cup [21,23]. These methods have been reported to yield results between 18.6% to 81.3% sensitivity and 45.5% to 81.8% specificity. When combined with the ISNT rule [26– 28], where, instead of measuring the neuroretinal rim thickness, they measure the proportion of the blood vessels in the inferior, superior, nasal, and temporal disc zones, have been reported between 97.6% to 100% sensitivity and 80% to 99.2% specificity. When adding the detection of defects of retinal nerve fiber layer [31], results of 80% to 90% sensitivity and 54% to 75% specificity in the pre-diagnosis have been reported.
3. Methodology This work presents a new method for the automatic classification of retinal images suspect of depicting glaucoma conditions. The method relies only on the analysis of morphological alterations that can be detected within the optic disc, even when the size of the excavation is in the initial stage of glaucoma. The method proposes a different way of glaucoma detection based on the analysis of the vascular bundle displacement within the optic disc caused by the excavation. This approach is motivated by a high degree of correlation between excavation growth and the blood vessel displacement in the inferior, superior, and nasal zones of the optic disc. The proposed method consists of the following steps: (1) RGB image acquisition; (2) segmentation of the optic disc region; (3) detection of a reference point in the excavation or cup; (4) detection of centroids of three zones of the vascular bundle; and (5) measurement of the distance between the reference point of the cup to the three centroids. 3.1. Data used The data used for evaluating the method were 67 retina JPEG and BMP color images of 720 576 pixels. Of these, 24 are retinal images from 20 normal patients, and the remaining 43 images consists of 21 isolated images and 11 pairs of images from 23 patients (22 images had advanced stage of glaucoma development). These images were acquired with a conventional eye fundus camera [6] and were previously selected from a greater collection of images acquired from 51 patients evaluated by an ophthalmologist that specializes in glaucoma. The images used in the research were chosen based on their clarity and the quality of the parts of the retina to be analyzed. Other images from the collection are related to other diseases, not to glaucoma. This
Fig. 1. Optical color eye fundus image from a left eye classified in an advanced stage of development of glaucoma showing the following anatomic parts: a. optic disc; b. excavation or cup; c. vascular bundle; d. neuroretinal rim, and the zones of the optic disc: I, inferior zone; S, superior zone; N, nasal zone; and T, temporal zone.
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group of images is a part of the private collection of retinal images that belongs to the Center for Computing Research of the National Polytechnic Institute, Mexico. 3.2. RGB image acquisition The proposed method was evaluated in retina images with all visible anatomic parts of the eye fundus. Fig. 1 shows an eye fundus image from our collection with the anatomic parts indicated: a. optic disc; b. excavation or cup; c. blood vessels within the optic disc (vascular bundle); d. neuroretinal rim, and the different zones of the optic disc (image is from a left eye): I, inferior zone; S, superior zone; N, nasal zone; finally, T, temporal zone. The image shown was classified as glaucomatous in an advanced stage of development, due to the excessive size of the excavation with respect to the size of the optic disc. 3.3. Segmentation of the optic disc region The objective of the optic disc area segmentation is to limit the region of interest for detecting and segmenting the anatomic elements that are described in the next steps, as well as to obtain approximately the diameter of the disc to be used in the process of normalization. In this paper we use the technique developed in Ref. [22] for optic disc segmentation. This technique consists of six steps from which we use only the first five (the sixth step deals with contour segmentation, which is not required in our procedure). The segmentation steps we used are as follows: (1) Technique uses human retinal images acquired in the color model RGB. (2) Normalization of images in size in case the images are provided from different sources. (3) Localization of the region of interest (ROI) of the optic disc using individual points (named seeds) through the Fourier transformation and P-Tile for thresholding. (4) Elimination of the arterioles and venous for segmenting the optic disc more accurately using the red plane and the morphological Closing and Opening operations with a flat disc structuring element (SE) whose diameter was set to the thickness of the largest blood vessel in the normalized image (six pixels of diameter). (5) Segmentation of optic disc area is carried out in the red plane with the combination of the circular Hough transform and active contours. The segmentation technique was tested in 80 color retina images with low contrast, high levels of noise, and discontinuities in the edges, achieving the exact segmentation in 74 images corresponding to 92.5% accuracy on the basis of the prediagnosis carried out previously by the specialist. Finally, the segmented optic disc area is superposed on the ROI image, while at the same time zeroing the pixels of the background (AND logic operation). The segmentation of the image shown in Fig. 1 appears
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in Fig. 2, where Fig. 2(a) shows the ROI of the optic disc of the normalized-size image; (b) the optic disc zone without arterioles and venous (morphological Closing and Opening operations); (c) segmented optic disc area (the circular Hough transform and active contours); (d) the segmented area shown in (c) superimposed onto the image shown in (a). 3.4. Detection of a reference point in the excavation or cup This step begins with the approximate detection of the excavation by the technique developed in Ref. [12] on images similar to in Fig. 2(a), which uses the green plane of the image and a strategy that combines: (a) thresholding based on method of Otsu [32]; (b) the sequential application of binary Opening and Closing using a flat disc structure element of 5 and 43 pixels of diameter, respectively, to eliminate the isolated small spurious components; and (c) so-called external border morphological operation to extract the external border of the excavation. This procedure is named OOCE (Otsu, Opening, Closing, External border) rule in [12]. There, an accuracy of 92.52% was reported. Then, so that the vascular bundle displacement manifests itself as large as possible, a reference point toward the temporal region farthest to the optic disc center is located in the segmented cup by means of the automatic selection of the cup edge pixel closest to the temporal zone, taking into account the fact that due to glaucoma the vascular bundle is always displaced towards the nasal zone. This zone was selected because it is where the excavation is farthest from the center of the optic disc. We assumed that the displacement of the vessel bundle to the left (nasal zone) is a consequence of the growth of the excavation located to the right of the optic disc (in the case of the left eye). In the case of the right eye, the situation is the opposite. The steps for the segmentation of the excavation from Fig. 2(a) appears in Fig. 3, where Fig. 3(a) shows the segmented excavation by Otsu threshold; (b) the segmented excavation after the morphological Opening and Closing operations; (c) the excavation border obtained with the external border morphological operation; and finally, (d) the reference point farthest toward the temporal region in (c) superimposed to the optic disc (Fig. 2(d)), marked with a cross enclosed by a circle in Fig. 3(d), and denoted by the capital letter A. The exact location of point A is simple, since it is the point on the far right of the outline of the excavation shown in Fig. 3(c). 3.5. Detection of centroids of three zones of the vascular bundle The main objective of this work was to analyze and measure the displacement of blood vessels located within the optic disc. For this, we took into account reference points in the vascular bundle that describe the growth in size of the excavation towards the
Fig. 2. Details of the optic disc region: (a) the ROI containing the optic disc in the RGB color model of the normalized-size image; (b) the optic disc without arterioles and venous; (c) segmented optic disc; (d) AND logic operation of the area shown in (c) with the image shown in (a).
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Fig. 3. Details of reference point detection in the excavation (left eye): (a) Otsu threshold; (b) morphological Opening and Closing operations; (c) excavation border through the morphological operation called the external border; (d) reference point denoted by the capital letter A in Fig. 2(d).
Fig. 4. Masks used for segmenting the blood vessels located in different zones of the optic disc.
Fig. 5. Masks of Fig. 4 when coupled with optical disc center of Fig. 2(d). (For interpretation of the references to color in this figure, the reader is referred to the web version of this article.)
temporal zone of the optic disc and the displacement of the vascular bundle within it, which is always displaced to the nasal zone. This step begins with the segmentation of blood vessels located within the optic disc (the vascular bundle). For this, the central point (centroid) of the optic disc is obtained (see Fig. 2(d)), which
serves as the reference for coupling it to the three triangular masks shown in Fig. 4, where Fig. 4(a) shows the mask for the superior zone, 4(b) for the inferior zone, and 4(c) for the nasal zone, when the image to be analyzed is from the left eye. If the image to be analyzed is from the right eye, then the last mask would be the mirror image of that shown in Fig. 4(c). The central point of each mask must match the central point of the optic disc even when the masks protrude from the ROI as is shown in Fig. 5, with the purpose of selecting the correct choice of the target zone. The segmentation is carried out in the red plane of the image in the RGB color model, since it was the channel where the best results were achieved, probably due to the common orange– reddish color of the optic papilla. The blood vessel segmentation algorithm uses a morphologic Black-top-hat operator and the technique of Otsu for thresholding [13,20,32,33] The Black-tophat is a morphologic transformation that depends on the shape of the objects in the papilla and extracts the regions having lower intensities than their neighboring regions; it is effective for identifying the sections where the vascular bundle is located. It is defined as the residue between the image processed by morphological closing (a dilation followed by an erosion operation using a flat disc structuring element of six pixels of diameter) and the original image. This operation allows us to highlight the elements deleted by the closing that, in this particular case, are the blood vessels located within the optic disc (the vascular bundle). The blood vessel segmentation is carried out individually in each zone covered by the corresponding mask (Fig. 4) as shown in Fig. 5. The result of the blood vessel segmentation in different zones is shown in Fig. 6(a) superior zone; 6(b) inferior zone; and 6 (c) nasal zone.
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Fig. 6. Segmentation of blood vessels located in the different zones of the optic disc: (a) superior zone; (b) inferior zone; (c) nasal zone.
Fig. 7. Centroid of blood vessels located in the different zones of the optic disc. B: Superior zone; C: nasal zone, and D: inferior zone.
To find the reference point that describes the trend in the position of vessels being analyzed, the centroid of vessels is calculated in each zone shown in Fig. 6. The centroid of a body coincides with the center of mass if the object density (area) is isotropic or when the material distribution is radially symmetrical; however, if an area has irregular borders defined by relative complex mathematical expressions (this is the case of the vascular bundle), the simplest method is to divide the object (vessels of each zone shown in Fig. 6) in small finite elements to calculate its centroid with the help of the individual summations described in (1) in order from left to right [24]. n
A ¼ ∑ ΔAi ; i¼1
n
Q x ¼ ∑ yi ΔAi ; i¼1
n
Q y ¼ ∑ xi ΔAi ; i¼1
Qy x¼ ; A
Q y¼ x A ð1Þ
where ΔAi is the area (number of pixels) of the ith element belonging to the foreground (the vascular bundle pixels); n is the number of finite elements in which the figure was divided; Qx and Qy are the static moments of the area with respect to the axes, respectively; yi is the coordinate y (ordinate) of the centroid of the ith element belonging to the foreground; xi is the coordinate x (abscissa) of the centroid of the ith element belonging to the foreground; and finally, x is the coordinate x of the centroid of the object and y is the coordinate y of the centroid of the object. The coordinates of the centroid of the object (x,y) do not always coincide with the foreground pixels.
Fig. 8. Distances d1, d2, and d3 between the centroids denoted by B, C, and D and the reference point A.
The centroid position of each region is shown in Fig. 7. The centroids are marked by a cross enclosed in a circle, and denoted by capital letters B, C, and D, in Fig. 2(d). The letter B represents the centroid of vessels in the superior zone; the letter C represents the centroid of vessels in the nasal zone; and the letter D represents the centroid of vessels in the inferior zone.
3.6. Measurement of the distance between the reference point of the cup to the three centroids In this stage of the process, the blood vessel displacements are calculated with respect to the excavation growth, which is carried out by using the reference point of the cup (A in Fig. 3(d)) and the vessels centroids (Fig. 7) in the different zones defined by the masks of Fig. 4. The displacements are measured by the calculation of the distances d1, d2, and d3 from the centroids B, C, and D, respectively, to the reference point A located in the temporal part of the excavation, as shown in Fig. 8. Since normally the vessel displacement is in the horizontal direction, distances are measured using the chessboard metric defined by Eq. (2) [29]: dc ¼ maxðjx2 x1 j; jy2 y1 jÞ
ð2Þ
where (x1, y1) are the coordinates of the first point and (x2, y2) are those of the second point.
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So that the method can be used in retinal images of different sizes, the distances are normalized with respect to the horizontal diameter of the optic disc Dh. The normalized distance dn is obtained by Eq. (3). dn ¼
100 d Dh
ð3Þ
where Dh is the horizontal diameter of the optic disc and d is the distance to normalize. The final result of the blood vessel displacement with respect to the proportional growth of the excavation is calculated using the average of the three normalized distances just measured. We need a decision point pre-diagnosing to decide if an optic disc is suspect to suffer glaucoma or not. Tests were carried out
Table 1 Range of the metrics (m s, m þ s) of the displacement of the vascular bundle in normal images and in images suspect of glaucoma. Distribution
l
r
lr
lþ r
Normal images Glaucoma suspect images
41.19 48.67
3.44 3.75
37.75 44.91
44.63 52.42
with 67 images. The cut-off point p was selected at a normalized distance of 45 pixels obtained empirically from our experiments. This threshold was determined on the basis of the pre-diagnostic carried out previously by the specialist and the standard deviation (s1 Normal images, s2 Glaucoma suspect images) as a measure of dispersion of the data relative to the average value of the distribution (μ1 Normal images, μ2 Glaucoma suspect images). Making use of the standard deviation, the variability of the distributions (dispersion) obtained as a result of measuring the displacement of the vascular bundle in healthy and diseased patients was calculated. In this way it was possible to calculate the range of the metrics (m s, m þ s) of the displacement of the vascular bundle in normal images and in images suspect of glaucoma. The values obtained are shown in Table 1. The range of dispersion of the normal image metrics was from 37.75 to 44.63, and the range of images with glaucoma ranges was from 44.91 to 52.42. Then, rounding the maximum value (m1 þ s1) of 44.63 of the normal images and the minimum value (μ2 s2) of 44.91 of the images suspect of glaucoma, we got the cut-off point p at a distance of 45 pixels to classify images into one of the two groups: normal and suspect of glaucoma. If the average of distances p calculated was less than the cut-off point (45), then the retina was pre-diagnosed as normal; otherwise the retina was pre-diagnosed as suspect of glaucoma.
Fig. 9. Detail of the region of interest of the optic disc with the centroids of three regions denoted by B, C, and D and the reference point of the excavation A. Images (a)–(f) have suspect excavation; images (g)–(i) have normal excavation.
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4. Discussion of results Fig. 9 shows several sample images from the collection of 67 images of human retina that were analyzed using the proposed method. The image population for the discussion of results was divided into two groups corresponding to normal and suspect excavation. The factors taken into account to select the test images were images with glaucoma suspect excavation; images with generalized thinning of the neuroretinal rim (a), (d), and (f); images having wide excavation and ostensible scleral holes (b) and (e); images with decreased neuroretinal rim and superior dislocation; images with nasal displacement of the vessels and its denudation (c) and (f). Images with normal excavation: images with circular excavation, concentric and small (g) and (i); images that meet rule ISNT and have normal cup/disc ratio (cup diameter lesser than 0.4 optic disc diameter) (h). Images show in detail the region of interest ROI with the centroids B, C and D of three zones and the reference point A marked by a cross enclosed by a circle. Results achieved in these test images were correct in all cases. The method proved to be able to pre-diagnose images with an advanced stage of development of glaucoma, even when the optic disc presented some morphological degeneration in the basic structure. This method has the advantage that even if the structures are degenerated (in the case of the disc and excavation) or moved partially out of the optic disc (in the case of the vascular bunch), there always exist vestiges of the anatomic structures, which allow the method to continue detecting the reference point without any problem, as is the case in (d)–(f) of Fig. 9. With the application of the proposed methodology in 67 retinal images, 93.02% images (40 retinas) were classified within the class of diseased, with 6.98% (3 retinas) classified incorrectly, and 91.66% images (22 retinas) classified within the class of healthy, with 8.4% (2 retinas) classified incorrectly, achieving a global accuracy in the pre-diagnosis of 92.34%. The method was evaluated by means of the Receiver Operating Characteristic (ROC) curve [25]. The ordinate of the ROC curve is the sensitivity, i.e., the ability of the method to classify the object within the correct class, and the abscissa is related to the specificity, i.e., the inability to classify correctly the objects within the correct class. The values of the sensitivity and the specificity have been obtained by Eq. (4) and the value of the area under the ROC curve (AUC) by Eq. (5), where ΔAi is the area of the ith element and n is the number of elements under the curve. The values achieved are shown in Table 2 and the ROC curve is shown in Fig. 10. Sensitivity ¼
TP 100; TP þ FN
Specificity ¼
TN 100 TN þ FP
Table 2 Results of the proposed method applied to 67 retinal images of real patients from which 24 were normal images and 43 were suspect to have glaucoma. Diagnosis
Result
True positive (TP) True negative (TN) False Positive (FP) False negative (FN) Sensitivity Specificity Area under the ROC curve Global accuracy
40 22 2 3 93.02% 91.66% 92.3% 92.34%
ð4Þ
Fig. 10. ROC curve plotted from the values achieved in Table 2.
n
AUC ¼ ð0:01Þ ∑ ΔAi i¼1
ð5Þ
The ROC curve was created with definitely positive and definitely negative results; for that reason the curve shows only a single operating point off the (0,0) and (100,100) corners (see Table 2). According to Ref. [30], an area of value from 90% to 100% represents an excellent test, from 80% to 90% a good test, from 70% to 80% a fair test, from 60% to 70% a poor test, and from 50% to 60% represents a fail test. The proposed work is a novel method for the analysis of the correlation found between the displacement of the blood vessels and the growth of the excavation present within the optic disc, Table 3 shows our results and some other published methods related to other state-of-the-art solutions, followed by the number of samples and the origin of the database of retina images used in the studies, respectively. As shown in Table 3, the sensitivity and the specificity in the pre-diagnosis of our proposed method are within the results achieved in the related state-of-the-art solutions. Analyzing the results in detail, in images where our method failed, it was observed that the expert pre-diagnosis was questionable because apart of the growth characteristics of the excavation, there were also the presence of nicks, notches and localized loss of optical fibers. On this basis, we can say that the effectiveness of the method presented is high. This paper represents the complete and updated version of the work presented in the 12th Mexican International Conference on Artificial Intelligence (MICAI 2013) held in November 2013 in Mexico City [34].
5. Conclusion This paper presents a methodology for detecting the optic disc suspect of glaucoma by measuring the displacement of the vascular bundle caused by the growth of the excavation or cup. The method was successful in 62 images out of 67, achieving 93.02% sensitivity, 91.66% specificity, and 91.34% global accuracy. This shows that the methodology is effective, and it could be used to develop new medical systems for the pre-diagnosis of glaucoma by computer.
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Table 3 Result of some other methods related to other state-of-the-art solutions. #
Type of analysis
Sensitivity
Specificity
1 2 3 4 5 6
Cup/disc ratio [12]a, [16]b, [18]c, [19]d Cup/disc ratio used pairs of stereo retinal images [17]e Cup/disc ratio and vessel bends [21]f, [23]g Cup/disc ratio and ISNT rule [26]h, [27]i, [28]j Defects of retinal nerve fiber layer [31]k The proposed methodl
60–94% 87% 18.6–81.3% 97.6–100% 80–90% 93.02%
82–94.7% 82% 45–81.8% 80–99.2% 54–75% 91.66%
a
107 images from the Center for Computing Research of IPN database. 140 images from the Singapore Eye Research Institute database. c 90 images from the Manchester Royal Eye Hospital database. d 45 images from the Gifu University Hospital database. e 98 images pairs from the Gifu University Hospital database. f 138 images from the Aravind Eye Hospital database. g 27 images from the Singapore Eye Research Institute database. h 61 images from the Kasturba Medical College database. i 550 images from an Aravind Eye Hospital database. j 36 images from an Aravind Eye Hospital database. k 249 images from residents of Akita, Japan, participating in a community health checkup. l 67 images from the Center for Computing Research of IPN database. b
Conflict of interest statement Authors do not have any conflict of interest.
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