and topography) the UltraSound BioMicroscopy (UBM) allow a direct inspection of the cornea, eventually freezing to memory the ultrasound images. Recently it ...
Estimating the Keratoconus Index from ultrasound images of the human cornea Filippo Castiglione
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and Francesco Castiglione
Abstract | The keratoconus index (KI) is a valuable measure to make diagnosis of the keratoconus in human eyes. Using images from an ultrasound biomicroscope, we show a method to automatically compute the KI and, ultimately, to make diagnosis of the keratoconus. Keywords | keratoconus, cornea, ultrasound biomicroscope, image analysis.
I. Introduction
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II. Data and methods
As in [1] we used images taken by means of a commercial version of the Ultrasound BioMicroscope 1 equipped with a 50-MHz probe that allow a resolution of 50m. The images come directly from the equipment in PCX graphics format. Each image is a 256 256 pixels in 256 gray levels. The scale factor is 1 mm = 51.2 pixels so that every image represent a square of 5mm per side of the cornea (see g 1). Starting from such images we used common image analysis techniques ([4]) to calculate the thickness of the portion of the cornea freezed in the image. Good image are characterized by three factors: (a) pick up the corneal apex, (b) keep the probe as much as possible perpendicular to it and (c) stay in the ultrasound focus area (focus line). As a result the images can vary according to the luminosity, contrast and other parameters; thus we have to consider the images as patterns produced by a noisy source and develop a statistical method to take care about the unavoidable variances in image quality which natually a ect our processing. The main part of the procedure is to determine the thinnest corneal thickness point (TCT); for this purpose we need to nd a numeric expression for the upper and lower contour of the cornea. For this purpose we used third order splines to interpolate the corneal borders ([4], [5]). Choosing di erent knots (spline interpolants) we obtain di erent contours leading to di erent results. The nal KI is then computed as a statistical average of all these values (although only those KI with TCT and PCT values that are considered valid corneal thikness (i.e. in the range 0.385 to 0.661 mm) are not rejected). The method proceeds as it follows: 1. Apply an image lter to reduce noise; 2. Determine knots for the spline that approximate the borders of the cornea (f1 superior and f2 inferior); 3. nd the thinnest thickness points TCT; 4. compute the thickness at 2.5mm from the TCT (i.e. the PCT); 5. compute the ratio KI=TCT/PCT.
The keratoconus is a corneal dystrophy evidenced by a progressive asymmetric increment of the corneal curvature and by a thickness reduction in the central area. Among other methods to identify keratoconic (sick) eyes (ultrasound pachimetry, cheratoscopy, photocheratoscopy and topography) the UltraSound BioMicroscopy (UBM) allow a direct inspection of the cornea, eventually freezing to memory the ultrasound images. Recently it has been introduced the keratoconus index, KI, as a valuable measure to make diagnosis of the keratoconus in human eyes ([1], [2]). While in keratoconic eyes the central thickness is reduced signi catively, the peripheral thickness is not really a ected in normal eyes ([3]). From these facts the KI is de ned as the ratio between the peripheral and central thickness of the human cornea. It is important to note that the thickness of the cornea varies from individual to individual, so the peripheral thickness was de ned as the corneal thickness at 2.5mm from the central area of the cornea. Formally the keratoconus index is de ned as KI = P CT=T CT where TCT is the Thinnest Corneal Thickness and PCT is the Peripheral Corneal Thickness. The TCT is taken in the central part, which, in keratoconic eyes, is the area with reduced thickness, while, in normal eyes, the TCT is comparable to the peripheral thickness PCT. The methods was proposed making the evaluation of the corneal thicknesses manually ([1]). This results in a non objective measurement of the index as the choice on the reference points is up to the observer. Here we focus on the problem to automatize the compu- A. Cubic spline interpolation of corneal contours The procedure computes the thickness of the cornea (i.e. tation of the KI directly from the ultrasound images, thus achieving a twofold goal: speed up the evaluation of the KI TCT, PCT) according to the borders which, in turn, are approximated by the splines. Then, we run the computaand make it objective. tion of KI over di erent contours of the cornea just changing the position of the interpolants. The knots are varied y Zentrum fur Paralleles Rechnen (Universitat zu Koln) Weyertal in the x-position giving a set of spline approximation. The 80, D - 50931 Koeln, GERMANY z Institute of Ophtalmology, (University of Catania) via Bambino, 1 c UBM System, model 840; Zeiss-Humprey Instruments, San Lean32, 95124 Catania, ITALY dro, CA, U.S.A.
Fig. 2. The rst gure (up) shows the points for the computed TCT and PCT. The second gure (down) shows the approximating splines f1 and f2 (curves in black) and the corneal pro le fm (curve in white) relative to the rst gure. The TCT-PCT Fig. 1. Ultrasound BioMicroscope image. It represents a vertical distance is also evidenced by a 2.5mm long segment. section of the cornea. It is up to the observer to pick up the correct coordinates of the \central" area of the cornea. Note that if the section is not centered onto the apex area of the cornea, the g 2). The third spline fm interpolates the knots comkeratoconus in sick patients cannot be observed.
method compute the KI for each of these di erent contour approximations. We used 7 knots (interpolating points) to compute the spline (as much knots to interpolate the upper border of the cornea as for the lower border). Determining the knots for the spline that approximate the contours of the cornea, is the crucial part of the algorithm. Naturally the interpolating points have to lie on the borders of the cornea, i.e. the limit of the white predominant area of the image (see g 1). We identify the upper border proceeding top-down onto the image to determine the upper contour and analogously down-top for the low contour, identifying the knots as the rst pixel in the white colored area (corresponding to high pixel value). To determine the \gradient" of pixel intensity we proceed as follows: calculate the average gray intensity and the standard deviation relative to the vertical section x of the image (x and x ); the knot is then chosen as the rst pixel px;y which satis es the inequality px;y > x + S x. Beyond changing the x-position (17 values) for the knots, the procedure is reiterated over the parameter S (assuming values 1/2, 1, 1+1/2) and giving back three di erent knots for the spline approximation. This results in 51 di erent contours approximations.
puted as the middle points between pairs of upper and lower knots. As corneal pro le, fm give the angular coecient for the perpendiculars to the cornea. The TCT is the minimum among all the perpendicular segments lengths. Then we compute the peripheral corneal thickness (PCT) as usual, following a straight line 2.5mm long, along the endotelial border from the TCT and compute the thickness at the destination point. For every contours approximation we compute the KI thus ending with 51 (17 di erent knots x-position and 3 values for S ) estimate of KI per image even if some of them are considered invalid (for example because the TCT or PCT are not valid corneal thickness, i.e. statistically too small or too big) and not used in the computation of the average KI. III. Results
To validate the eciency of the automatic procedure, we considered a sample test composed by 30 images of keratoconic and not keratoconic eyes on which the KI was calculated manually. As in most image analysis algorithms the quality of the image play a big discriminating role for the success of the method; infact there is no lower limit on the bad quality of an image and no algorithm can eliminate an arbitrary amount of noise. In our case a good image depends basically on the operator who must be trained to use the B. Compute thickness echograph and he must know all the function for the conThe thickness of the cornea is the length of the seg- trast variation (Transfer Function, TF) and focalization of ments perpendicular to the corneal pro le. To determine the ultrasound bundle. Over good images the algorithm is the corneal pro le we used the same knots computed for f1 more likely to give objective and precise results. It must and f2 as it can be approximated by a third spline fm (see then
Reject bad images obliging the operator to repeat the examination; Give acceptable values for the KI on good images; For the validation procedure we submitted to the algorithm two distinct group of images taken from the UBM equipment according to light intensity, contrast, position and focalization of the ultrasound: group A = 10 bad images; group B = 20 good images. Group A. This group is intended to test the ability of the algorithm to reject bad quality images. The algorithm correctly rejects 90% (9/10) of the images informing the operator to repeat the scan; just in one case it gave a misunderstandable result. For this group we don't consider if they come from sick or healthy patients. Group B. The second test group is composed by 10 images for healthy patients and 10 images from patients with a slight form of keratoconus. Every image has been taken randomly from the set of eight of every single patient used in our previous work ([1]). In this way we could compare the automatic results with the previous manual measurement (validation test).
For what concernes the ability to reject bad images the results were encouraging. By means of the variance analysis and the correlation coecient we have demonstrated the agreement of the automatic results with a control group of results: in 95% the statistical correlation was good. This automatic method to compute the KI represents, in our opinion, a useful tool to speed up the objective identi cation of the keratoconus classi cation based on the central corneal thinning that could be placed side by side to the already well known methodology based on the corneal topography ([7]). [1] [2] [3]
[4] [5] [6] A. Statistical evaluation Every single results have been compared with the mean [7]
value of the manual inspection of the control (test) group ([1]). The validity (level of con dence) of the automatic method has been checked by means of the variance analysis (P ) which gives the agreement between two groups by a test F for the repeated measurement and by means of the coecient of variation (rij ) which quantify the correlation among the groups; a P > 0:05 and rij 1 are considered indices of validity of the measurements ([6]). The algorithm was able to distinguish sick patients from healthy ones in almost 95% of the cases. For those images it has computed a KI pratically overlapping the control values. The observation of the variance (P) and the correlation coecient (rij ) have demonstrated that the values given by the algorithm are statistically meaningful in 85% of the cases (P < 0:05 and rij 1), while for 3 images P > 0:05. IV. Discussion
The UBM, di erently from the ultrasound pachimetry, allow the dynamic visualization of the central part of the cornea and the localization of the conus apex in keratoconic patients. The de nition of the Keratoconus Index, using ultrabiomicroscopic measurements of the central and periperal corneal thickness, allow to quantify the corneal thinning and gives to the ophtalmologist a new and useful tool for the follow-up of these patients ([1]). Moreover it has been recently proposed the possibility of a new keratoconus classi cation by means of the progressive corneal thinning computed by the UBM ([2]). To reduce the subjective interpretation and limiting the personal action of the observer we developed an automatic method to compute the keratoconus index.
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