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IntroductIon

Fractal dimension (Df) is a global measure of the branching pattern of complex geometric structures.

Fractal objects are self-similar structures that retain a similar level of complexity across all scales. For example, blood vessels repeatedly subdivide down-stream into smaller blood vessels with similar network patterns. Fractal dimension (Df) quantifies the degree of complexity into a single value and is particularly useful for quantifying non-Euclidean geometric shapes such as vascular networks.1,2 We recently developed two new computer software programs to measure the fractal dimension of the retinal vasculature from

Current Eye Research, 35(9), 850–856, 2010Copyright © 2010 Informa Healthcare USA, Inc.ISSN: 0271-3683 print/ 1460-2202 onlineDOI: 10.3109/02713683.2010.490628

ORIGINAL ARTICLE

retinal Vascular Fractal dimension Measurement and Its Influence from Imaging

Variation: results of two Segmentation Methods

Victoria Fay Cosatto1, Gerald Liew1, Elena Rochtchina1, Alan Wainwright1, YongPing Zhang2, Wynne Hsu3, Mong Li Lee3, Qiangfeng Peter Lau3, Haslina H Hamzah4, Paul

Mitchell1, Tien Yin Wong4,5, and Jie Jin Wang1,5

1Centre for Eye Research Australia, Department of Ophthalmology and Westmead Millennium Institute, Centre for Vision Research, University of Sydney, Australia

2School of Electronic and Information Engineering, Ningbo University of Technology, China3School of Computing, National University of Singapore, Singapore

4Singapore Eye Research Institute, National University of Singapore, Singapore5Centre for Eye Research Australia, University of Melbourne, Australia

ABStrAct

Aim: To assess the influences of imaging variation (different photographic angle) on the measurement of retinal vascular fractal dimension (Df), using two segmentation methods.Materials and methods: Nonlinear orthogonal projection segmentation (International Retinal Imag-ing Software-Fractal, termed IRIS-Fractal) and curvature-based segmentation (Singapore Insti-tute Vessel Assessment-Fractal, termed SIVA-Fractal) methods were used to measure Df and were assessed for their reproducibility in detecting retinal vessels of 30 stereoscopic pairs of optic disc color images. Each pair was taken from the same eye with slightly different angles of incidence. Each photograph of the pairs had subtle variations in brightness between areas temporal and nasal to the optic disc.Results: Intragrader reproducibility of Df measurement was similar (intraclass correlation 0.81 and 0.96, respectively) for IRIS-Fractal and SIVA-Fractal. Within-image pair Pearson’s correlation coef-ficients (r) of Df measurements were moderate for both methods (0.57 and 0.48, respectively).Conclusions: Both nonlinear orthogonal projection and curvature-based retinal vessel segmentation methods were found to be sensitive to variations in image brightness, resulting from iris shadowing associated with different angle of photographic incidence.

KEYWordS: Blue Mountains Eye Study; Fractal dimension; Methodology; Photographic angle of incidence; Retinal vasculature

Received 09 September 2008; accepted 25 April 2010

Correspondence: Dr. Jie Jin Wang, Center for Vision research, Department of Ophthalmology, and Westmead Millennium Insti-tute, Centre for Vision Research, Westmead Hospital, Hawkesbury Road, New South Wales, Australia 2145. E-mail: jiejin_wang@wmi.usyd.edu.au

09 September 2008

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digital or digitized retinal photographs. These programs identify the retinal vessels using different segmentation methods and compute the Df measure with minimum manual input. Our research team has documented the reliability of Df measures using one of the programs (International Retinal Imaging Software-Fractal, termed IRIS-Fractal) and shown that persons with hypertension have reduced Df compared with persons without hyper-tension.3 This supports the premise that retinal vascular Df may be a marker for alterations in microvascular architecture that results from elevated blood pressure, and may therefore be useful, along with other retinal vascular measures (e.g., retinal vessel caliber), to predict the risk of various ocular and systemic cardiovascular diseases.4,5

Little is known, however, about how retinal vessel Df measures vary depending on the quality of images, or whether the segmentation method used to detect reti-nal vessel lines from images is sensitive to variations in image quality, such as photographs taken from the same eye but with a slightly different angle of incidence within a few seconds apart. Precise measure of retinal vessel Df may be able to detect small but meaningful differences between normal and diseased groups.

In this study, we aimed to assess whether subtle variation in image quality affects the measurement of retinal vessel Df, and to compare the performance in this regard of two software programs that use different segmentation methods to detect retinal vessel skeleton lines: IRIS-Fractal, which uses nonlinear orthogonal projection segmentation,6 and Singapore Institute Vessel Assessment-Fractal (SIVA-Fractal), which uses before curvature-based segmentation method.7 We assessed their reproducibility in detecting retinal vessels from 30 stereoscopic pairs of optic disc color images; each photograph of a pair was taken from the same eye with slightly different angles of incidence and within a few seconds apart.

MEthodS

Study Population

We obtained retinal images from the Blue Mountains Eye Study (BMES), a population-based study of vision, common eye diseases, and other health outcomes in an urban population aged 49 years or older. The Western Sydney Area Health Service Human Research Ethics Committee granted approval for this study and written informed consent was obtained from all study partici-pants. The study was carried out in accordance with the guidelines set down in the Declaration of Helsinki. At the baseline examinations (1992–1994), 3654 partici-pants had 30° stereoscopic retinal photographs taken

of the macular, optic disc, and other retinal fields of both eyes, using a Zeiss FF3 fundus film camera (Carl Zeiss, Oberkochen, Germany), following pupil dila-tion.8 For the current study, we selected a sample of 30 stereoscopic pairs of right eye photographs of the optic disc field taken from BMES baseline participants who were free of hypertension, diabetes, and other systemic diseases. Each of the two photographs of the stereo pair, A (the first photograph of the pair) and B (the second photograph of the pair) were taken a few sec-onds apart. In order to obtain the desired stereoscopic view from the paired images, the camera was manu-ally shifted laterally, with photograph A shot with the camera shifted temporally, and photograph B shot with the camera shifted nasally with a distance between the two positions of approximately a few centimeters.

Poor quality or out-of-focus images could reduce the ability of the fractal computer program to detect ves-sel structures.9 For this report, we therefore purposely selected retinal disc photographs with the sharpest images.

The photographs were initially developed on 35 mm color transparencies that were digitized into JPG for-mat using a CanoScan FS2710 (Canon, Tokyo, Japan) film scanner set to automatic exposure and focus, with 24-bit color and a maximum resolution of 2720 dpi without enhancement. Each image was stored in JPG format, as we previously found comparable Df mea-surements for TIFF and JPG formats of the same retinal vascular images (unpublished data). Each photograph of the pairs had subtle variations in brightness in dif-ferent areas (comparing nasal with temporal sides of the optic disc) (Figure 1A and 1B).

dEVEloPMEnt oF IMAgE ProgrAMS For thE ASSESSMEnt oF rEtInAl VASculAr FrActAl

dIMEnSIon

The IRIS-Fractal program uses a nonlinear orthogonal projection segmentation method to capture the features

A B

FIGURE 1 A stereo pair of images A and B taken from the same eye.

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of retinal vascular networks, with a derived algorithm of local adaptive threshold for the detection of retinal vessels.6 The SIVA-Fractal program, on the other hand, employs a curvature-based segmentation method7 to extract the centerline of the vascular structure. A major difference between these two segmentation methods is that SIVA-Fractal computes the fractal dimension from a skeletonized image, whereas the IRIS-Fractal uses the entire vessel thickness to derive the fractal dimension. These images can capture up to the fourth branching order of the retinal vasculature.

ASSESSMEnt oF rEtInAl VASculAr FrActAl dIMEnSIon

Retinal vascular Df of both images of each stereo pair was quantified using the IRIS-Fractal (version 1.4) program on a PC workstation with twin 17-in. digital LCD monitors allowing image displays at a resolu-tion of 1280 × 1024 pixels. Details of the segmentation procedure6 and grading protocol3 for IRIS-Fractal were previously reported. In brief, an image of the optic disc was viewed on a computer screen by a trained grader. The grader marked two points corresponding to the center and the margin of the optic disc at either 12 or 6 o’clock (excluding the optic disc halos), to obtain the maximum, vertical radius of the optic disc. This radius was then used to outline a region of 3.5 optic disc radii, from the optic disc center concentric with and including the optic disc, to be cropped, in order to define the image area being measured. IRIS-Fractal then traced the skeletonized lines of the retinal vascu-lar network. The grader used two computer screens, side-by-side, to compare the vascular skeleton network for fractal dimension assessment against the original color image, and refined the skeleton line-traced image by erasing any artifacts that were not part of the vascu-lar network, such as the outer margin of peripapillary atrophy, choroidal vessels, and pigmentary abnormali-ties. The grader needed to be careful not to remove any part of the vessel structure lines as vessel lines once deleted could not be retrieved with the IRIS method. Once the grader was satisfied with the match of the vascular skeleton with the original vascular network, IRIS-Fractal proceeded to calculate Df.

Similar grading procedures were repeated using SIVA-Fractal (version 1.0) except that the SIVA pro-gram automatically determines the optic disc radius and does not require manual plotting of two points to determine the optic disc radius before cropping the area in the image to be measured. The image of the optic disc was viewed on a single computer screen by a trained grader. The skeletonized image was super-imposed onto the original retinal image to distinguish

artifacts from retinal vessels. The grader proceeded to remove any of the artifacts that were not part of the vessel structure. If the grader accidentally removed any part of the vessel network then, unlike IRIS, it could be retrieved. Once the grader completed the process of matching the vascular skeleton with the original vascu-lar image, SIVA-Fractal continued to calculate Df.

We used the box-counting method to estimate the fractal characteristics of the retinal vasculature. Reti-nal vascular fractal dimension was evaluated within a range of six magnification levels relative to one unit of length in one direction of the image. The log–log plot exhibited a reasonable linear pattern between the log-scaled magnification magnitudes of the images (X-axis) and the log-scaled number of boxes needed to cover the vascular pattern or the skeleton lines (Y-axis) (Figure 2).

StAtIStIcAl MEthodS

Student’s t-test was used to compare mean Df between images A and B and a Bland–Altman plot to illustrate the variation in Df measurements between each ste-reo pair (B minus A) against the mean Df of images A and B. We assessed the correlations of Df measures between images A and B of the 30 stereo pairs using Pearson’s correlation coefficients (r), and compared the coefficients obtained from the measures using the IRIS-Fractal with that from measures using SIVA-Fractal.

We next regraded 30 images (one from each eye) and assessed intragrader reproducibility by comparing Df measures from the first and the second grading of the same images, performed by the same grader 3 months apart. Reproducibility was assessed using intraclass cor-relation coefficients (ICC). Data are presented as mean and 95% confidence intervals (CI). All statistical analyses were performed using SAS statistical software (version 9.1; SAS Institute, Cary, North Carolina, USA).

rESultS

Table 1 shows the characteristics of the 30 participants included in this study. Mean retinal vascular Df were 1.559 (95% CI 1.548–1.569) and 1.556 (95% CI 1.547–1.566) for images A and B, respectively, measured using IRIS-Fractal (paired t-test P = 0.64) (Table 2). The corresponding means were 1.573 (95% CI 1.558–1.588) and 1.571 (95% CI 1.557–1.584) for images A and B, respectively, measured SIVA-Fractal (paired t-test P = 0.74) (Table 2). The Pearson’s correlation coeffi-cients between Df of images A and B were r = 0.57 for measures using IRIS-Fractal and r = 0.48 for measures using SIVA-Fractal (Figure 3).

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Differences in Df measures between images A and B of the same eye were plotted against mean Df of the two images, presented as a Bland–Altman plot (Figure 4). For measures using IRIS-Fractal, the mean difference was 0.0022 (± 0.025 SD), and the range for 95% limits of agreement (−0.05, 0.05) indicated a moderate level of agreement in the Df between the two images of each pair. The degree of variability appeared to be greater for the

image pairs with low mean values of Df measurements than the image pairs with high mean values (Figure 4, IRIS-Fractal). Similarly, for measures using SIVA-Fractal, the mean difference was 0.0024 (± 0.038 SD), and the range for 95% limits of agreement was −0.08 to 0.07. The degree of variability showed a similar pattern as that observed from measures using IRIS-Fractal (Figure 4, SIVA-Fractal).

The intragrader reproducibility (intraclass correla-tion coefficient) of Df measurements between the first and second gradings of the 30 images by the same grader was 0.81 (95% CI 0.64–0.90) for IRIS-Fractal (Figure 5A). The corresponding intraclass correlation coefficient was 0.96 (95% CI 0.92–0.98) for SIVA-Fractal (Figure 5B).

dIScuSSIon

Retinal vascular Df, is a global measure of the pattern and complexity of the retinal vasculature that may be useful in studying ocular and systemic vascular diseases.2 A previous study by Daxer9 found a signifi-cant increase in retinal Df measure 2 years after the formation of retinal neovascularization in subjects with diabetic retinopathy. Furthermore, a year later the retinal Df measure was significantly less when the new vessels had partially regressed, indicating that Df is sensitive to new vessel formation and regres-sion.9 The measurement of Df may be influenced by many factors, including photographic quality varia-tions resulting from a slightly different angle of inci-dence of photography, or the size of the pupil even

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FIGURE 2 Log–log plots showing fractal behavior of retinal vascular structure of images A and B, a linear pattern between the log-scaled magnitudes of magnifica-tion (X-axis, ranging six levels) and the log-scaled number of boxes needed to cover the vascular pattern (the skeleton lines) (Y-axis). r = linear size of a box relative to linear size of the image with values between 0 and 1; 1/r = number of boxes tiled in one direction (e.g., 1/r = 1/0.125 = 8 = 23), here six different 1/r magnification values range from 2 to 64 (i.e., 2n, n = 1, 2, …, 6); N(r) = total number of boxes that cover the vascular skeleton lines of interest.

TABLE 1 Characteristics of study participants (n = 30)Characteristic Mean (range) %Age (years) 58.9 (50–86) —Systolic blood pressure (mm Hg) 123.8 (110–135) —Diastolic blood pressure (mm Hg) 75.4 (60–88) —Females — 56.7Nonsmoker — 43.3Current smoker — 13.3Ex-smoker — 43.3

TABLE 2 Comparison of mean fractal dimension (Df) between the two images (photographs A and B) of 30 image pairs, mea-sured using IRIS-fractal and SIVA-fractal (n = 30) Mean Df (95% CI) P value*

IRIS-Fractal Photograph A 1.559 (1.548–1.569) — Photograph B 1.556 (1.547–1.566) 0.64SIVA-Fractal Photograph A 1.573 (1.558–1.588) — Photograph B 1.571 (1.557–1.584) 0.74CI = confidence interval.*Paired t-test for A and B.

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after dilatation, factors that in practice are difficult to control for or to have a uniform performance. Dif-ferent algorithms for vessel segmentation may also influence program sensitivity to subtle variations in image quality (e.g., color, brightness, contrast, etc.). We found no significant differences in the mean retinal vascular Df between photographs A and B of the stereo pairs, regardless of the segmentation method used. In addition, the within-pair correlations of Df measure-ments were moderate for both curvature-based vessel segmentation7 and the nonlinear orthogonal projection segmentation methods.6

Our finding appears to suggest that both curvature-based and nonlinear orthogonal projection segmentation methods are sensitive to subtle variations in image brightness of stereo-pair photographs. Subtle variations in image quality as observed in the samples of this report occur commonly in practice, and are dif-ficult to eliminate completely even with uniform proto-cols due to differences in operational skills and patient cooperation levels during retinal photography.

We speculate that one of the likely reasons for the variations in brightness and contrast resulting from a change in photographic angle is due to the change of the location of the shadow from the iris, which subtly reduced the brightness of the area under the iris shadow. Furthermore, we speculated that, from

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FIGURE 3 Correlation between retinal vascular fractal dimensions (Df) of 30 color stereo-pair images (A and B) as mea-sured using IRIS-Fractal or SIVA-Fractal.Broken line represents ideal correlation between A and B.

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FIGURE 4 Bland–Altman plot; differences in fractal dimension (Df) measures between images A and B of each pair against the mean fractal dimension of images A and B, The 95% limits of agreement (broken lines) and mean (solid line).

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the measures using these two image programs, the difference in degree of the incident angle between photographs A and B could influence the trend seen in Figure 4 (i.e., greater within-pair variability in Df measures when the mean Df was low). This is because the greater the difference between the two angles of photographic incidence, the larger is the likely “iris shadowing,” leading to a lower mean Df and also greater variability in Df measures. In this study, the difference in photographic angle within a stereo-pair image was not standardized (due to manual opera-tion of photography) and thus varied among stereo

pairs, which could affect the size of the area under iris shadowing. In other words, the differences in degree of photographic angle between the two images of the pairs could correlate with the size of the areas with relative darkness, and thus the degree of within-pair differences in the Df. This apparent source of measure-ment error occurred regardless of the segmentation methods used (Figure 4). We did not apply shading correction algorithms to reduce the effect of iris shad-owing in order to test the sensitivity of each software program to such subtle variations in image quality.

We also found reasonably high intragrader repro-ducibility in Df measurements using either of the two image programs (ICC 0.81 and 0.96, respectively, for IRIS-Fractal and SIVA-Fractal). The ICC for IRIS-Fractal was slightly lower than our previous assessment of reproducibility of retinal vascular Df using the same image program but measuring from gray-scale images3 (intraclass correlation coefficient 0.93–0.95). This could be due to the longer interval period (3 months versus 2 weeks) between the first and second measures in this study. Furthermore, IRIS requires the grader to mark two points on the images, one at the center of the optic disc and another at the margin of the optic disc, in order to determine the disc radius that will be cropped for the measurement. This manual part of the operation could have introduced human error and variation. In contrast, the SIVA program automatically determines the optic disc radius so that there is no room for human error in this component. This could have partly explained the nearly perfect ICC of SIVA for the intragrader reproducibility.

Additional quantitative investigation of image qual-ity (i.e., brightness and contrast) required for optimal Df measurements is warranted, given that a more pre-cise measure may have a greater ability to detect small differences in microvascular structural changes associ-ated with disease. Although one may not completely eliminate all sources of random error, some factors potentially influencing the measurement of Df can be controlled for, such as the use of a fixed camera angle, standardized flash brightness, and instructing subjects to fixate at the same point during photography. Our study findings highlight the importance of image qual-ity in order to minimize potential measurement errors resulting from variations in the quality of images.

A strength of our study is the short-time interval between photography of the two stereo photos from the same eyes of same persons, which enabled us to eliminate many other potential influential factors that might otherwise introduce variations into the measure-ment, including aging, blood pressure changes,1,10 and the development of other retinal pathologies.9,11,12 The cardiac cycle may also cause variations in the measure-ment of retinal vessel caliber13; however, this would be

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FIGURE 5 Intragrader reproducibility of fractal dimension (Df) measures of color images (n = 30): (A) using IRIS-Fractal pro-gram or nonlinear orthogonal projection segmentation method (intraclass correlation coefficient (ICC) = 0.81); and (B) using SIVA-Fractal or curvature-based segmentation method (intra-class correlation coefficient = 0.96).

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likely to have only minimal impact on the measure-ment of Df, as the major determinants of Df are the number of vessels and bifurcations within a constant area, plus vessel tortuosity, all of which are unlikely to be influenced by the cardiac cycle.

A limitation was the relatively small number in the sample size. As images were converted from color film to digitized color, the transformation routine may influence measurement of Df. However, as the same routines were applied to the digitization of both images of each pair and also the same grading procedure was used for both software programs, these procedures are unlikely to have a major influence on our findings.

In conclusion, newly developed computer software programs to measure Df of the retinal vasculature appear to be sensitive to subtle changes in image quality (brightness) induced by alterations in the photographic angle of incidence. The take-home mes-sages can be summarized as the following: (1) Fractal dimension of the retinal vascular pattern obtained from stereoscopic images captured at a particular angle from the optical axis may be less precise than standard reti-nal photography taken at an angle coincident with the optical axis; (2) the quality of the image preprocessing, in particular the precise recognition of the entire and small vessel tree as input into the fractal dimension calculation process, is a key issue for optimal preci-sion of estimates for fractal dimension. Whether such subtle variation in image quality and in photographic angle of incidence will affect the utility of Df in clini-cal research is not clear. The associations of Df with systemic risk factors and ocular or systemic disease processes remain to be further understood. Methods to standardize retinal photographic techniques, image quality, and color may help to ensure high reproduc-ibility of this measurement.

AcKnoWlEdgMEntS

This work was supported by grants from the Aus-tralian National Health & Medical Research Council, Canberra Australia (Grant Nos. 153948, 211069, and 302068); Pfizer Australia (Cardiovascular Lipid Grant No. 2007); and Diabetes Australia Research Trust (Grant

No. 2007). Preliminary findings of this study were presented in part at the 2008 Annual Meeting of the Association for Research in Vision and Ophthalmology, Fort Lauderdale, Florida, USA.

Declaration of interest: The authors report no conflicts of interest. The authors alone are responsible for the content and writing of the article.

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[9] Daxer A. Characterisation of the neovascularisation pro-cess in diabetic retinopathy by means of fractal geometry: Diagnostic implications. Graefes Arch Clin Exp Ophthalmol 1993;231:681–686.

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