Microaneurysms are the first ophthalmoscopic sign of diabetic retinopathy [1]. Over and above that, their number is an indication of the progression of the disease. Their detection is therefore crucial for the diagnosis of diabetic retinopathy, for the mass screening, and for the monitoring of the disease.

Microaneurysms are tiny dilations of the capillaries. They appear as small reddish isolated patterns of circular shape in color fundus images of the human retina [1]. Their diameter normally lies between 10 and 100 ^m, but it is always smaller than 125 ^m. As they come from capillaries, and as capillaries are not visible in color fundus images, they appear as isolated patterns, i.e. disconnected from the vascular tree.

Microaneurysms are sometimes hard to detect: Their contrast is often very low and sometimes, they are hardly visible and difficult to distinguish from noise. Their reddish color can hardly be used for their detection, because it is far from being constant in different images (see Fig. 7.24).

The first algorithm for the detection of microaneurysms has been presented Lay [19]. The author introduced the radial opening ysup = (J yLi, i.e. the supremum

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Figure 7.24: Microaneurysms in color images. (a) Sure microaneurysms; (b) doubtful cases. Figure 7.25: The principle of the algorithm for microaneurysm detection. Figure 7.25: The principle of the algorithm for microaneurysm detection. of openings with linear structuring elements Li in different directions in order to remove the microaneurysms but to preserve the piecewise linear vessels. This technique has been used by nearly all the authors working on the automatic detection of microaneurysms; important improvements have been proposed in [20,21]. ## 7.6.1.4 The AlgorithmThe algorithm presented in this section is based on the strategy shown in Fig. 7.25. First, the shade correction method described in section 7.4 is applied, and then candidates are detected by means of the diameter closing and an automatic threshold; features calculated for these candidates allow their classification into real microaneurysms and false positives. A first version of this algorithm has been presented in [22]. Prefiltering and shade correction: The objective of this step is to attenuate the noise, to enhance the contrast, and to correct the nonuniform illumination. As it has been stated in section 7.2, microaneurysms—like all blood containing elements—appear best contrasted in the green channel. First, the shade correction operator described in section 7.4 is applied to the green channel. It is crucial that this algorithm does not introduce new dark regions which would cause a lot of false positives. Besides the shade correction, the operator SCnorm enhances the contrast of structures in the image depending on their size. In order to privilege small vessels and microaneurysms more than larger hemorrhages and large vessels, an adapted size of the window used in SCnorm can be chosen. A small gaussian filter attenuates the noise, but enhances microaneurysms; it can be seen as a matched filter [20]. With G a gaussian filter, we obtain the prefiltered image by (see also Fig. 7.26): (a) A detail of a fundus image containing microaneurysms image (b) Detail of the prefiltered (a) A detail of a fundus image containing microaneurysms image (b) Detail of the prefiltered Figure 7.26: Prefiltering step. The detection of dark isolated details by means of the diameter closing: The next step is to find the "candidates," i.e., allfeatures that may possibly correspond to microaneurysms. Microaneurysms are characterized by their diameter; in the green channel of a color image, they correspond to dark details—"holes"—with a maximal diameter of X (with X depending on the image resolution). As in the top-hat transformation used for vessel detection in section 7.5.1, the main idea is to first construct a closing $ that removes the details from the image and then calculate the difference to the original image. However, a morphological closing cannot be used in our case because it fills not only the holes but also the ditches (vessels). One possibility to fill only the holes without filling the ditches is to determine the infimum of openings with linear structuring elements in different directions, because they do fit into the vessels in at least one direction. However, this is only an approximative solution of the problem; a tortuous line for example will be closed as well. We will now present the diameter closing which removes all dark details of a diameter smaller than X. First, we define the diameter a of a connected set X as its maximal extension, i.e. the maximal distance between two points of the set: with d(x, y) the distance between two points x and y. For simplicity, we use the block distance: If x = (x1; x2), y = (y1, y) € Z2 are two points and x1, x and y1, y their coordinates, respectively, the block distance can be written as d(x, y) = |x1 - y11 v |x - ml (a) A binary image (b) The result of a diameter opening Figure 7.27: The diameter opening of abinary image: all connected components with a diameter inferior to 15 pixels are removed. With this definition of the diameter of a set, we can define a trivial opening. Let X be an arbitrary binary image and Xi its connected components, i.e. X = (J Xi and Xi n Xj for i = j. The diameter opening is the union of all connected components Xi with a diameter greater or equal to X (see Fig. 7.27): As the applied criterion a(Xi) > X is increasing, i.e., X c Y implies that if X fulfills the criterion, Y also does, the operation yA°(X) is an opening. It can be shown that the diameter opening is the supremum of all openings with structuring elements with a diameter greater than or equal to X [8]: It is, therefore, a generalization of the approximative method proposed in [16] used by the majority of authors, where only linear structuring elements fulfilling the criterion are used. The diameter closing removes all holes Xic (connected components of the background Xc) with a diameter inferior X. Furthermore, it can be written as the infimum of all morphological closings with structuring elements whose diameter is equal or superior to X: We have now defined the diameter opening and closing for the binary case. In order to pass from binary to gray-level images, we can apply the binary operator to all level sets (the results of threshold operations for all gray levels t g T). Let Cx(X) be the connected opening, i.e., the connected component of X containing x if x g X and the empty set if x g X. Furthermore, let X+ (f) be the section of f at level t, i.e., the set of all pixels for which f (x) > t and X-( f) the section of the background (the "lakes," see Fig. 7.28): Then, the gray scale diameter opening and closing can be defined respectively: $Kf) = inf {s > f (x) | a (Cx [X-(f)]] > X} (7.36) Of course, Eq. (7.36) cannot be used for implementation of this algorithm because it would be highly inefficient. Instead of calculating the diameter opening for each threshold, we use hierarchical queues in order to simulate a flooding of the image. We explain this technique for the diameter closing. The flooding starts with the lowest local minima in the image (i.e. with the global minima). We determine the diameter of all the lakes with gray level s. Ifthe diameter of a lake exceeds X, the output image takes the value s for all the points belonging to this lake ("the flooding stops for this lake"). Then s is incremented, the new local minima at this level are added, and the existing lakes are extended until there is no more pixel x in the image with f (x) < s not belonging to a lake. If two lakes meet, they fuse and it is considered as one lake from now on. Then, when the flooding has been finished for this level, the diameter of all lakes are calculated. If the diameter of a lake exceeds X, but has not exceeded X for the previous level, the output image is set to s for all the pixels of this lake. In this way, we flood the whole image until there is no more lake with a diameter inferior to X. This algorithm can be implemented very efficiently with hierarchical queues. See [8] for details. In Fig. 7.29, we show the application of the diameter closing to the detection of microaneurysms. The prefiltered image is shown in Fig. 7.29(a); its closing by diameter in Fig. 7.29(b). We note that the distinction of holes and ditches (microa-neurysms and vessels) works very well: The microaneurysms are completely filled whereas the vessels are not touched. The associated top-hat 4>l f — f is shown in Fig. 7.29(c). The small details visible in this image and not corresponding to microaneurysms are "parasite holes" and are due to irregularities and noise in the image. From this image, it is easy to get the candidates by a threshold. The applied threshold technique is shown in the next paragraph. (a) The prfiltered and (b) The diameter clos- (c) The associated top- shade corrected image ing hat transformation Figure 7.29: Detection of dark details by means of the diameter closing. (a) The prfiltered and (b) The diameter clos- (c) The associated top- shade corrected image ing hat transformation Figure 7.29: Detection of dark details by means of the diameter closing. The automatic threshold: The threshold can be seen as the minimal contrast a detail must have in order to be considered as a candidate. If the threshold is chosen manually, we lose the main advantages of an entirely automatic analysis. If a fix threshold is applied, we have to deal with a lot of false positives or with poor sensitivity, because the contrast of microa-neurysms may be very different from one image to another. If it depends exclusively on the histogram of the top-hat image, it is supposed that the image contains microaneurysms. Hence, we have to find a compromise between a fix a histogram-dependent threshold. In order to find an automatic method for the determination of an automatic threshold, we have analyzed 10 retinal images. For all these images, we have chosen an "optimal" threshold using ROC-analysis, i.e., a threshold that gives the best compromise between sensitivity and number of false positives. This optimal threshold has then been compared to statistical properties of the top-hat image (standard deviation, amount of noise, volume of the top-hat image, etc.). The most obvious relation has been found between the volume of the top-hat image and the optimal threshold. This relation is shown in Fig. 7.30. This result is not really surprising. The volume of the top-hat image depends on two image properties: the contrast and the amount of noise. On the one hand, 19 18 17 0 JZ CO 1 16 ra E 15 14 13 80000 90000 100000 110000 120000 130000 140000 volume of tophat Figure 7.30: Optimal threshold versus volume of top hat. optimal threshold vs. volume of tophat image the better the contrast is, the higher the threshold can be chosen. On the other hand, the higher the amount of noise is, the higher the threshold must be chosen. However, some "fix" information must be incorporated by using lower and upper bounds for the threshold: The candidate regions are determined by a double threshold technique (see [6] for details). This technique allows one to apply a lower threshold without accepting a higher number of candidates: This improvement in the determination of the candidate region is important, because the features that are calculated for the candidates depend a lot on this region, as we will see in the following paragraph. Elimination of the candidates situated on the vessels: Before calculating the features, we can exclude all candidates situated on the vascular tree. As we have seen, a top-hat transformation associated to a morphological closing extracts all dark details that cannot contain the structuring element, i.e., all "holes" and all "ditches," and as a consequence all microaneurysms and all vessels. Comparing the morphological top-hat transformation with the one associated to the diameter closing of the same size, we can identify the false candidates situated on vessels and hemorrhages: For candidates not situated on vessels, we can assume that the values of the two top-hat images are approximately the same: This is not the case for candidates situated on the vessels. We can write the modified candidate image CA as CA = {x e CA | [V«>(P)] (x) < 2 • (P)] (x)} (7.40) Candidates situated on the optic disk can be easily removed using the segmentation result from section 7.5.2. Feature extraction and classification: With the top-hat transformation and the automatic threshold, we have found candidates, i.e. possible microa-neurysms, using just a size criterion and a contrast measure (threshold). However, there are still many false positives, and the result is not acceptable. But there are still other properties to be exploited. We used the following features in order to classify the candidates into true microaneurysms and false positives: • The surface: Fundus images are often corrupted by noise (high frequency gray level variations). Hence, there are many small "holes" and "peaks" in the image; therefore, the surface of the candidate regions is an important feature: • The circularity: We have used the maximal extension as a feature. That means that small linear features are also extracted. The circularity may help excluding them: Surf(Ci) • The maximal value of the top-hat image: In the threshold operation, we have already used this feature. On the other hand, it may be important to combine it with other features. xeCi X • The dynamic: The dynamic is a measure of "deepness" of a minimum. If a minimum is very deep or in contrary very shallow, it is probably not a microaneurysm. • The outer mean value: It is also important to take into consideration the absolute gray level values on the outside of the candidate. The mean on the external gradient can help finding false positives due to exudates or hemorrhages (see Fig. 7.31): • The contrast measure: The maximal value of the top-hat image is a contrast measure: It is the difference between the local minimum and the level for which the flooding stops. Another contrast measure is the difference between the mean value on the external gradient of the candidate region and the mean value on the candidate region itself: |

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