Global increases in the age of the population and the prevalence of diabetes are bringing a concomitant increase in diabetic retinopathy. On the heels of that increase is a mounting need for accessible, early, and effective identification of proliferative changes and monitoring of disease progress and treatment outcomes. Practical and effective quantitative indices of DR are therefore essential, and may be found in fractal analysis. In general, our results showed that the Dconn, an objective and readily obtainable measure, distinguishes between images of more severe and less severe pathology of the retina, where the μDconn is higher for pathological as compared to nonpathological retinal branching patterns in skeletonised automated images and both skeletonised and nonskeletonised manually drawn images.
Automated procedures should aim to be comparable to the results obtained by ophthalmologists. Using an automated method that can detect changes in the eye associated with diabetes with a minimum sensitivity of 60% is therefore a useful advancement as it would lessen the burden on ophthalmologists during initial population screening. (Daxer 1993a
) For clinical use, however, the methods should exceed 80% accuracy. (BDA 1994
; NHMRC 2001
) Overall, our work suggests that CWT-based segmentation and Dconn
analysis can provide the required levels of sensitivity and accuracy.
These findings are encouraging, but further work (eg, using a larger sample) is required, and several points about our results need to be discussed, including the point that none of the other fractal analysis methods we assessed yielded significant results.
The global DF
of the retinal vasculature has been studied for some time (Family et al 1989
; Masters 1989
). Several research groups have demonstrated that the normal retinal vasculature has fractal-like properties with a global DF
generally falling between 1.60 and 1.88 (Daxer 1992
; Landini et al 1993
; Cesar and Jelinek 2003
; Jelinek et al 2005
). Our results suggest that the manually segmented images we analyzed were a valid representation inasmuch as the global DB
was within this usually reported range (), but the same conclusion cannot be drawn for the automatically segmented images, because the mean global DB
for that group fell below the range reported in the literature. Reasons we identified for this include that the entire sample was pushed to a consistently lower DB
by an overall relative insensitivity to the finest level of branching in the segmenting method, and that certain images were further affected by factors such as uneven signaling and scarring.
The μDconn values were also lower than the reported range for the global DB, in this case for both the manually and automatically segmented sets of images. This does not reflect the limitations of the segmentation method described above, however. Rather, it highlights differences between global and local connected analyses. Whereas global dimensions sample entire images at once, the μDconn for an image is calculated from a sampling at each pixel of a pattern (ie, it is comparable to an average of averages). Moreover, each pixel’s Dconn considers scaling only over a contiguous area (refer to ), and in our analysis, we further limited those areas to relatively small parts of the image in order to better capture local variation in scaling.
The first study that reported automated segmentation of blood vessels combined with fractal analysis used 30 mm SLR photographs of the retinal posterior pole that were scanned into a computer and segmented by the CWT. (Cesar and Jelinek 2003
) Automated segmentation of fluorescein-labeled retinal vessels and analysis using the CD has also been reported in a study of digital images of the posterior pole with automated vessel segmentation followed by using 8 feature patterns including the CD, which was able to differentiate proliferative changes. (Jelinek et al 2005
) However the CDs did not contribute significantly to our outcome. This is reflected again in .
The CWT is a powerful and versatile tool that has been applied in many different image processing problems, including shape analysis (Costa and Cesar Jr 2001
). We found in pilot work for our study (results not shown) that selecting only images that convey what are considered the essential patterns associated with neovascularization and comparing these with control images that have no visible retinopathy improves the discerning ability of the Dconn
and indeed of any feature parameter. To be practical, however, DR screening methods will have to be able to address all the possibilities that will arise in retinal imaging scenarios. Thus, our test sample was deliberately not idealized; rather, we included images with various commonly encountered complicating factors.
As was discussed above, these factors, such as laser scars, vessel drop out, microaneurysms, and hemorrhage, probably did affect the absolute results for each image and may have been a major reason why segmentation using the CWT was unsuccessful except when followed by analysis with the Dconn
. Reasons the Dconn
but not other methods were successful in distinguishing PDR may also be linked to at least some of the reasons behind the range in values reported in the literature. That range reflects a host of additional methodological issues known to influence the absolute results of fractal analyses including the type of DF
, image size and resolution, feature extraction methods such as variation in the use of skeletonisation (eg, unlike skeletonised images, nonskeletonised images preserve differences in vessel diameter in the final pattern), and whether red free or fluorescein images are used (Masters 2004
In addition to such factors, previous studies using DF
s have found various types of local differences within the retinal vascular tree. Differences have been reported between DF
s for arteries and veins, for example (Mainster 1990
; Landini et al 1993
). Different investigators have also found contradictory trends in the DF
associated with an increase in pathological status. Avakian and collaborators, for example, applied fractal analysis to region-based vascular changes in non-proliferative retinopathy (Avakian et al 2002
). They found that the DF
was significantly higher in the normal macular region compared to the NPDR macular region, although not elsewhere in the retina. Daxer also used fractal analysis of region-based vascular changes, but applied to proliferative retinopathy, using a method which requires that neovascularization be identified in the first instance. More in keeping with the results we found, Daxer reported that the DF
was significantly higher for vessel patterns with neovascularization at the disk than without (Daxer 1993b
Such variable and sometimes contradictory results can be reconciled using the Dconn. To elaborate, if vessels disappear from an extracted pattern for any reason, such as from being occluded or by being obscured to the camera by hemorrhage, the local DFs calculated in that area of the pattern would be expected to decrease. Conversely, if vessels increase over some area, as seen in PDR, the local DFs in that area would be expected to increase. Global fractal dimensions smooth away such variety, but the Dconn is likely to capture and quantitate the interplay without conflict because it quantifies complexity over the entire branching pattern but also locally within it, thus, does not lose important details inherent in that local variation. This was illustrated in shown earlier, which compared the distribution of the Dconn over two automatically segmented, skeletonised patterns. The patterns shown in the figures were extracted from, respectively, one image of PDR with extensive capillary closure and one of normal retinal vasculature. The two images differ significantly in the frequency distribution of the Dconn, which, as was discussed, can provide both a single objective index and various types of objective graphic representations (histograms and color-coded maps of the original retinal images) of the relative differences in the distributions of pathology between them.