Fig 1.
Retinal blood vessels are segmented and their centerlines are detected, followed by junction removal to extract segments which are then smoothed. Cross-section intensity profiles are extracted perpendicularly to the centerlines and model fitting is performed on smoothed profiles. Based on the best-fit model parameters, vessel width is estimated through regression.
Fig 2.
Blood vessel segmentation, centerline detection, and segment extraction and smoothing.
Top row: example of vessel segmentation; second row: example of removal of junctions from a thinned vessel image and vessel segment smoothing through spline fitting. A: image from REVIEW dataset (CLRIS001); B: segmented image [24]; C: region from [A]; D: region from [B]; E: thinned vessels for a region of [D]; F: vessel segments, after junction removal; G: vessel segments of [F], labeled with different colors; H: vessel segments of [G] after spline approximation. Colors are used for better distinguishing between vessel segments.
Fig 3.
Blood vessel segments obtained for CLRIS001 image (REVIEW dataset).
Segments are numbered, colored and overlapped with the green channel of the RGB image (note that different segments may be represented in the same color). White marks along some blood vessel edges represent ground truth points.
Fig 4.
Vessel intensity profile determination and smoothing, for one segment from Fig 3.
A: profile directions; B: segment intensity profiles stacked in parallel; C: top view of [B]; D: smoothed intensity profiles; E: top view of [D]. Colors in the plots are representative of the intensity values: warmer colors represent higher intensity whilst cooler colors represent lower intensity. The white marks in [A] and the black marks in [C] and [E] represent the ground truth annotations.
Fig 5.
Typical shape of a blood vessel with and without central light reflex (CLR).
A: blood vessel without CLR; B: blood vessel with CLR. The extreme point positions are also shown.
Fig 6.
Typical shape of a vessel with CLR and cases where the conditions imposed for CLR detection are violated.
A: typical shape of a vessel with CLR, along with its extreme point positions; B: the lowest maximum of the profile is not the correct CLR center; C: the found minima positions are too close to each other to constitute a CLR region; D: the two bumps of the CLR have an intensity difference larger than the acceptable; E: the distances between the maxima and the vessel center are too different; F: the elevation in the CLR center has larger intensity than the vessel limits. The arrows indicate the locations of the peaks that would define the CLR region, if one of the conditions had not been violated.
Fig 7.
Examples of profile length determination results.
Top row: successful cases; bottom row: non-successful cases, for which the conditions were not restrict enough. Curve: smoothed mean intensity profile; triangular marks: detected maxima; square marks: detected minima; orange vertical lines: detected vessel limits; yellow vertical line: center of the profile. A and B: CLR correctly rejected due to the big difference in the depth of the two depressions; C: left limit symmetric to the right, since it was too far away from the center; D and E: CLR wrongly detected (conditions not restricted enough); F: profile region overestimated (lack of peaks near the vessel limits).
Fig 8.
Examples of curves of the Hermite model as defined in Eq 1, but in 1D.
A: effect of the amplitude of the main Gaussian (h); B: effect of the spread of the Gaussians (σ); C: effect of the amplitude of the two other Gaussians (β); D: effect of the CLR asymmetry (δ). A profile length of 20 pixels was set to the vessel. In each plot a parameter is varied at a time, with the remaining parameters fixed, in order to evaluate the influence of that parameter in the overall model shape (t = 1, h = −0.588, β = 0.2, μ = 10, δ = 0.2, σ = 2.5).
Fig 9.
Examples of fitting of the Hermite, DoG-L7 and DoG-L8 models to smoothed and non-smoothed real vessel profiles.
Profiles from 11 adjacent profiles are used. Black dots: profile data points; orange curve: fitted curve through Trust-Region-Reflective method; vertical yellow line: center of the profile; vertical purple lines: ground truth. A: original data, Hermite model (Eq 1); B: original data, DoG-L7 model (Eq 3); C: original data, DoG-L8 model (Eq 4); D: smoothed data, Hermite model; E: smoothed data, DoG-L7 model; F: smoothed data, DoG-L8 model.
Fig 10.
Examples of curves of the DoG-L7 (A-E) and DoG-L8 models (F), but in 1D.
A: amplitude of the 1st Gaussian (h1); B: spread of the 1st Gaussian (σ1); C: amplitude of the 2nd Gaussian (h2); D: spread of the 2nd Gaussian (σ2); E: slope of the multiplying line (λ); F: center of the 2nd Gaussian (μ2). A profile length of 20 pixels was set to the vessel. In each plot a parameter is varied (inside a established range) at a time, with the remaining parameters fixed (t = 0.5, h1 = −0.5, μ = 10, σ1 = 3, h2 = −0.33, σ2 = 1, λ = 0.02), in order to evaluate the influence of that parameter in the overall model shape.
Table 1.
REVIEW subsets characteristics.
HRIS: The high resolution image set; VDIS: The vascular disease image set; CLRIS: The central light reflex image set; KPIS: The kick point image set (px: pixels; FOV: field of view; im: images; seg: segments; prof: profiles).
Fig 11.
Example of fitting of the models to a vessel intensity profile.
Black dots: profile; orange curve: best-fit model. A: Hermite model; SSE = 0.0586, R2 = 0.9329, , RMSE = 0.0128; B: DoG-L7 model; SSE = 0.01524, R2 = 0.9825,
, RMSE = 0.0065; C: DoG-L8 model; SSE = 0.0030, R2 = 0.9965,
, RMSE = 0.0029.
Table 2.
Goodness-of-fit metrics obtained for the DoG-L7, DoG-L8 and Hermite models.
The results shown are the mean of the values from all the profiles of each dataset. The best results for each dataset are highlighted.
Table 3.
Results of the proposed method for retinal vessel width estimation using the DoG-L7, DoG-L8, and Hermite models in the CLRIS and HRIS datasets from REVIEW.
Four evaluation schemes are presented: cross-validation in each dataset (Cv_d) and in the whole REVIEW (Cv_R) and leave-one-segment-out in each dataset (Lso_d) and in the whole REVIEW (Lso_R). O1, O2 and O3 are the observers, and G.T. is the ground truth, i.e., mean of the 3 observations. SR is the success rate, μmeas and σmeas are the mean and standard deviation of the width measurements, respectively, and μerror and σerror are the mean and standard deviation of the measurement errors. * SR values are negatively influenced by errors found in the observers’ annotations.
Table 4.
Results of the proposed method for retinal vessel width estimation using the DoG-L7, DoG-L8, and Hermite models in the KPIS and VDIS datasets from REVIEW.
Four evaluation schemes are presented: cross-validation in each dataset (Cv_d) and in the whole REVIEW (Cv_R) and leave-one-segment-out in each dataset (Lso_d) and in the whole REVIEW (Lso_R). O1, O2 and O3 are the observers, and G.T. is the ground truth, i.e., mean of the 3 observations. SR is the success rate, μmeas and σmeas are the mean and standard deviation of the width measurements, respectively, and μerror and σerror are the mean and standard deviation of the measurement errors. * SR values are negatively influenced by errors found in the observers’ annotations.
Fig 12.
Bland-Altman plots of the ground truth and measured diameters, using the DoG-L7 model for fitting.
Results for both 10-fold cross-validation and leave-one-segment-out validation, in each dataset (CLRIS, HRIS, KPIS and VDIS) and in the whole REVIEW, are shown (in the xx axis the ground truth diameters are plotted instead of the mean between the ground truth and measured diameters). A: cross-validation in each dataset; B: cross-validation in the whole REVIEW; C: leave-segment-out validation in each dataset; D: leave-segment-out validation in the whole REVIEW.
Fig 13.
Example of poor width measurements due to a false central light reflex (CLR) detection.
A: HRIS vessel segment (labeled as 1), that at a given point runs next to another segment (labeled as 2); B: smoothed profile extracted from region X; C: smoothed profile extracted from region Y, where the presence of another vessel close to the main vessel simulates the presence of CLR. Profiles as the one in [C] were wrongly measured by our algorithm when leave-one-segment-out validation in the whole REVIEW is performed, being retrieved a diameter that is approximately two times the real diameter. Black points in [B] and [C]: intensity profiles; orange curves: best-fit models, yellow vertical lines: centers of the profiles; purple vertical lines: ground truth locations; white marks in [A]: ground truth points.
Table 5.
Correlation between the segments of each dataset.
μcorr and σcorrr are the mean and standard deviation of the correlations of all pairs of segments, maxcorr is the maximum correlation and #comb is the number of combinations of 2 segments found in the dataset.
Table 6.
Standard deviation of the width errors for each of the four REVIEW datasets.
The width errors are the point-by-point differences between the ground truth and the width measurements (pixels). Cv_d, Cv_R, Lso_d and Lso_R stand for cross-validation in the dataset and in the whole REVIEW, and leave-one-segment-out validation in the dataset and in the whole REVIEW, respectively. The score is the mean of the values of all datasets. The 3 best scores at highlighted.