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line-like structures or segments. We mitigated this by applying a three-point moving average filter to the exported coordinates prior to calculating tortuosities.

NeuronJ is a semiautomated tracing method, as it requires the user to guide the vessel tracing. However, it has major advantages in that there is no need to preprocess the images (e.g., by histogram equalization) nor is segmentation required (i.e., the tracing can be performed on a grayscale image (usually the green plane of an RGB color image) directly).

12.5.2 Other Software Packages

Hessian-based detectors are computationally expensive. HCA-vision is a software platform for the automated detection and analysis of linear features based on multidirectional nonmaximum suppression (MDNMS). HCA-vision has been successfully applied to a number of applications including neurite tracing for drug discovery and functional genomics [60], quantifying astrocyte morphology [61], and separating adjacent bacteria under phase contrast microscopy [62]. It is discussed in detail in Chapter 8. The software can be downloaded after completing a request at http://www.hca-vision.com/product download hca vision.html. The large noise content in our images precluded us from utilizing the program successfully.

Retinal vessel centerline extraction can also be achieved using multiscale matched filters, with a vessel confidence measure defined as a projection of a vector formed from a normalized pixel neighborhood on to a normalized ideal vessel profile [54]. Vessel boundary measures and associated confidences are computed at potential vessel boundaries. A training technique is used to develop a mapping of this vector to a likelihood ratio that measures the “vesselness” at each pixel. Results comparing this vesselness measure to matched filters alone and to measures based on the Hessian of intensities have shown substantial improvements both qualitatively and quantitatively. Binary executables of the code are available at http://www.sofka.com/LRV.html.

This represents a possible route for fully automated tracing of retinal vessels. A typical tracing is shown in Fig. 12.6. This is a promising result, although it was difficult to avoid breaks in the tracings without adding spurious vessels. It may be possible to achieve a more acceptable result with an optimal choice of tracer sensitivity, and judicious preprocessing of the image to remove background variation and reduce noise.

12.6 Experimental Results and Discussion

The grades associated with the Messidor project database (and all other databases) are rather coarse. To explore changes in the vessels with the severity of retinopathy, we need a finer grading scheme. The number of detected microaneurysms has been

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Fig. 12.6 The result of a fully automated tracing of retinal vessels using Sofka’s program on the same image as in Fig. 12.5. The traced vessels are shown in green, with the bifurcations subsequently colored red

used as a surrogate for the severity of retinopathy in its early stages [12, 13]. This information was available in the marked database (of 82 unique images) supplied by MINES ParisTech.

Figure 12.7 shows that the tortuosity (per cm) increases steadily with the number of manually identified microaneurysms from images in the marked database. The correlation coefficient (r = 0.4159, n = 46) corresponds to a probability, p, for the null hypothesis of 0.004.4 This suggests that tortuosity is related to microaneurysm count, and that the tortuosity increases with the severity of retinopathy.

The number of microaneurysms detected by the Waikato Automated Microaneurysm Detector did not match the numbers manually counted by experts for images from the marked database. Despite the normalization of the images prior to segmentation, the number of microaneurysms detected is still somewhat dependent on the threshold probability used in the Bayes classifier. Useful thresholds normally lie between 10−5 and 10−7 (Cree, private communication). The key is to select a threshold which is high enough to detect all the microaneurysms but small enough not to count noise as aneurysm, but this optimum threshold depends on the particular image. We investigated two methods for finding the optimum value of the threshold.

4http://faculty.vassar.edu/lowry/VassarStats.html.

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Fig. 12.7 The tortuosity/length for 46 vessels from the marked database. The best-fitted line is superimposed

For both methods, we plotted the number of microaneurysms detected in an image for a series of thresholds between 10−5 and 10−7. The higher the threshold, the smaller the number of aneurysms detected. We considered the optimum threshold to be a balance between the microaneurysm count changing too fast with threshold and it hardly changing at all with threshold. In our first method (method 1), we considered this be the value where the plot of microaneurysm counts was furthest from a straight line connecting the two extreme thresholds (Fig. 12.8). In our second method (method 2), we calculated the local curvature of datapoints (by calculating the local tortuosity using five points centered on the datapoint of interest) in the plot of microaneurysm counts vs. threshold, and considered the largest value to indicate the position of the optimum threshold.

We tested both methods on the marked database, for which we know the microaneurysm counts (viz., the “gold standard” counts from manual counting by three experts). Table 12.1 shows the number of microaneurysms in the images, assessed by the various methods. Probability thresholds of 10−5, 10−6, and 10−7 are included, although microaneurysm counts for 100 different thresholds were computed. The correlation coefficient for these fixed values with the “gold standard” values varied between 0.4696 and 0.6805, depending on the value of the threshold. Although it is possible to achieve a correlation of 0.6805 with a fixed threshold, it would be highly unlikely that this particular value of the threshold would be chosen a priori. The correlation coefficient for the number of microaneurysms found by method 1 with the “gold standard” counts was 0.6458, while the correlation coefficient for the number of microaneurysms found by method 2 with the “gold standard” counts was higher at 0.7303. (This corresponds to p < 0.001 (n = 82)

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Fig. 12.8 (a) Image (MA Originaux 09, from the marked database) and (b) a plot showing how the optimum threshold is obtained from this image using method 1

for the null hypothesis). In the light of these findings, we consider that method 2 is particularly well suited for finding the optimum threshold for use with the Waikato Automated Microaneurysm Detector.

The microaneurysms in the Messidor project database are not so clearly delineated. We detected and counted them with the Waikato Automated Microaneurysm Detector using method 2 (Fig. 12.9). Only images with a microaneurysm count of five or greater were considered, since we had greatest confidence that these corresponded to actual microaneurysms. The correlation

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Table 12.1 The number of microaneurysms detected for the images of the marked database using various thresholds, and our methods 1 and 2, compared with the actual “gold standard” counts

	“Gold
	standard”	Threshold	Threshold	Threshold
Image ID	counts	= 10−5	= 10−6	= 10−7	Method 1	Method 2
1	2	0	1	11	1	2
2	3	2	3	11	3	4
3	2	1	1	4	1	2
4	1	3	4	16	3	4
5	4	2	4	19	4	4
6	16	5	17	34	11	16
7	3	1	6	11	2	7
8	8	3	7	12	4	7
9	9	8	15	36	11	11
10	19	7	20	39	16	16
11	14	4	15	41	11	9
12	3	2	3	11	3	4
13	3	2	4	11	4	5
14	4	0	4	7	1	4
15	1	3	4	16	3	4
16	5	2	4	19	4	4
17	11	3	10	22	10	11
18	16	7	17	29	13	15
19	7	2	8	21	4	4
20	0	1	1	7	1	3
21	2	0	1	4	1	1
22	3	1	6	11	2	7
23	6	2	7	11	4	5
24	7	3	13	25	11	10
25	0	1	1	3	1	3
26	0	0	1	6	0	1
27	6	3	10	39	8	6
28	10	8	17	48	14	14
29	11	0	3	12	2	3
30	5	5	13	20	5	15
31	2	1	7	21	5	6
32	8	4	13	36	9	7
33	7	0	6	13	3	6
34	5	4	7	33	6	8
35	3	1	3	15	1	3
36	0	1	2	43	2	2
37	1	0	6	34	2	2
38	18	5	12	24	10	10
39	18	1	13	34	8	14
40	22	5	17	42	11	17
41	7	3	9	25	9	9
42	17	3	8	31	5	8
43	10	5	18	57	10	10
						(continued)

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Table 12.1	(continued)
	“Gold
	standard”	Threshold	Threshold	Threshold
Image ID	counts	= 10−5	= 10−6	= 10−7	Method 1	Method 2
45a	4	2	6	11	7	4
46	4	1	4	22	3	3
47	1	0	1	10	5	2
48	18	4	9	25	1	9
49	2	1	2	14	9	2
50	13	5	15	42	2	12
51	10	4	9	30	12	8
52	7	1	8	23	9	4
53	1	0	1	4	2	1
54	0	1	4	11	1	4
55	3	1	3	6	1	3
56	12	3	5	36	2	5
57	14	3	17	52	5	11
58	8	2	5	8	11	6
59	0	0	2	5	3	2
60	2	2	3	12	2	3
61	4	1	2	9	3	3
62	11	3	11	22	2	9
63	21	4	11	25	9	12
64	5	5	12	27	6	14
65	14	8	21	36	12	13
66	5	1	2	17	16	4
67	2	0	2	17	2	2
68	0	1	2	22	0	2
69	0	0	0	3	2	3
70	2	3	7	24	0	7
71	1	1	2	5	6	2
72	1	1	1	14	1	2
73	13	9	26	61	1	14
74	12	15	22	93	14	20
75	6	3	15	50	22	13
76	0	0	1	4	11	3
77	0	0	1	3	0	1
78	4	10	37	111	1	20
79	2	1	3	7	25	3
80	1	0	1	4	3	1
81	1	0	8	39	1	8
82	15	5	15	32	3	16
83	6	5	15	8	9	7

aNo ID 44 exists because the image is identical to ID 43

of microaneurysm count with tortuosity is not as strong (r = 0.2236 (n = 34), corresponding to a probability value for the null hypothesis of 0.1018) as with the marked database. Although we optimized the counting within the Waikato

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Fig. 12.9 The tortuosity/length for 34 vessels from the Messidor project database. The best-fitted line is superimposed

Fig. 12.10 The tortuosity of the first quintile length compared to the tortuosity of the entire vessel, for 46 vessels from the marked database

Automated Microaneurysm Detector, we do not expect the number of counts to be completely accurate. Despite this, the level of correlation supports our earlier finding with the marked database that tortuosity is related to microaneurysm count, and that tortuosity increases with severity of retinopathy.

A complicating factor in the use of vessel tortuosity as an indicator of the severity of retinopathy would be a change in tortuosity along an individual blood vessel. We measured the tortuosity of vessels along the quintiles of their length. Figure 12.10