Structure-based level set method for automatic retinal vasculature segmentation
- Bekir Dizdaroğlu^{1, 2}Email author,
- Esra Ataer-Cansizoglu^{2},
- Jayashree Kalpathy-Cramer^{3},
- Katie Keck^{4},
- Michael F Chiang^{4, 5} and
- Deniz Erdogmus^{2}
https://doi.org/10.1186/1687-5281-2014-39
© Dizdaroğlu et al.; licensee Springer. 2014
Received: 27 February 2014
Accepted: 30 July 2014
Published: 11 August 2014
Abstract
Segmentation of vasculature in retinal fundus image by level set methods employing classical edge detection methodologies is a tedious task. In this study, a revised level set-based retinal vasculature segmentation approach is proposed. During preprocessing, intensity inhomogeneity on the green channel of input image is corrected by utilizing all image channels, generating more efficient results compared to methods utilizing only one (green) channel. A structure-based level set method employing a modified phase map is introduced to obtain accurate skeletonization and segmentation of the retinal vasculature. The seed points around vessels are selected and the level sets are initialized automatically. Furthermore, the proposed method introduces an improved zero-level contour regularization term which is more appropriate than the ones introduced by other methods for vasculature structures. We conducted the experiments on our own dataset, as well as two publicly available datasets. The results show that the proposed method segments retinal vessels accurately and its performance is comparable to state-of-the-art supervised/unsupervised segmentation techniques.
Keywords
Color retinal fundus images Phase map Segmentation of retinal vasculature Structure and texture parts of retinal fundus image Structure-based level set method1 Introduction
Published ophthalmology studies reveal that there are often significant differences in clinical diagnosis of retinal diseases among medical experts[1]. Some of these approaches involve tedious processes. Manual segmentation has become more and more time consuming with the increasing amount of patient data. An automatic retinal vasculature segmentation method may become an integral part of a computer-based image analysis and diagnosis systems with improved accuracy and consistency[2].
Considering the conducted research, literature is full of examples[3–10] on vasculature segmentation, detection, and other kinds of analysis employing especially supervised/unsupervised classification of pixels in retinal fundus images[11–19]. Marin et al.[14] and Soares et al.[15] presented two different supervised methods for segmentation of retinal vasculature by using moment invariant-based features and 2-D Gabor filters, respectively. Staal et al.[16] proposed a retinal vasculature segmentation method using centerlines of a vessel base that are extracted by using image ridges. Budai et al.[17] presented an improved approach using Frangi’s method[18]. Other studies have employed centerline tracing methods and principal curves[19, 20]. The reader may refer to[21] for more related studies in the literature.
Level set-based methods have been widely used for image segmentation[22–34]. In general, these methods can be classified under two categories: (i) edge-based[22–30] and (ii) region-based[31–34] methods. However, level set-based methods have not been extensively employed in retinal vasculature segmentation. To the best of our knowledge, there have been only a few studies in the literature proposing methods based on level sets to trace vasculature in retinal fundus images. This is due to challenges of vessel shapes in level set-based image segmentation methods[24]. Major challenges posed by the very thin and elongated structure of retinal vessels are further compounded by poor contrast in regions of interest for level set-based segmentation methods. In one of those studies[24], the level set-based method is applied only on a selected region of images by implementing a non-automatic initialization of zero-level contours. These regions do not have any non-uniform intensity values. The method in[24] also employs edge information based on phase map and uses a re-initialization process to regularize the level set function, which is a problem in level set-based framework[25]. Moreover, this process requires complex discretization especially for re-initialization of the level set function. In addition, the method employs fixed filter coefficients to generate image features such as edges by using the log-Gabor filter, which does not generate a proper output to trace extremely thin retinal vessels in fundus images smoothly. The level set segmentation method[26] proposed by Pang et al. requires the selection of initial contour in the form of long strips in the vertical direction, and this is not an optimal selection. This selection leads to an increase in the number of iterations to generate the results. According to the accuracy metric, the method produces poor results quantitatively on a non-pathological fundus image. Although they claim to present a fully automated method, the system requires mask images from the user. There are other level set approaches[27–29, 31–34] that focus on segmenting other vasculature structures in different image modalities such as ultrasound images and magnetic resonance images (MRIs). However, these region-based methods[32, 33] cannot be used extensively in segmentation of retinal fundus images due to the form of vascular structures. Another method presented for retinal vessel segmentation[34] employs region-based level sets and region growing approaches, simultaneously.
In this paper, we present an improved and automatic level set-based method for retinal vasculature segmentation. The presented method utilizes a robust phase map to determine image structures and seed points around the vessels in the initialization of the level set function. The performed tests on pathological and non-pathological fundus images demonstrate that the proposed method performs better than the existing approaches based on level sets.
The organization of the paper is structured as follows. 'Section 2’ introduces the general information about retinal fundus images and level set-based methods developed for segmentation. 'Section 3’ explains the proposed method and compares it with the existing approaches in the literature. Experimental results are given in 'Section 4.’ Finally, 'Section 5’ presents a conclusion and possible future work in the field.
2 Background
Let I: Ω → ℝ^{3} be a color image defined on domain Ω → ℝ^{2}, and let I_{ i }: Ω → ℝ represent the i th color channel of the image I. Let p = (x, y) ∈ Ω, denote any point in Ω. Digital images have two additive components: structure part and texture part. These can be visualized as the cartoon version with sharp edges and noisy/textured version of the original image, respectively[35–37].
2.1 Characteristics of retinal fundus images
2.2 Edge-based level set segmentation approach
Iterations of level set evolution are adversely affected by numerical errors and other factors that cause irregularities. Therefore, a frequent re-initialization process, formulated as ∂Φ/∂t = sign(Φ_{0}) (1 - ||∇Φ||), could be included to restore the regularity of the level set function, establishing a stable level set evolution. Here, Φ_{0} is the level set function to be re-initialized and sign(.) stands for signum function. Re-initialization is performed by interrupting the evolution periodically and correcting irregularities of the level set function using a signed distance function. Even with a re-initialization process, in most of the level set methods such as the geodesic active counters (GAC) model[23], irregularities can still emerge[25]. Therefore, Li et al. introduced a new energy term called level set function regularization[25].
- 1.Initialization with a signed distance function, d(.) (GAC model [23]) (Figure 3a,b,c):$\begin{array}{c}{\mathrm{\Phi}}_{\mathrm{initial}}\left(\mathbf{p}\right)=\left\{\begin{array}{c}\hfill -d\left(\mathbf{p},C\right)\phantom{\rule{1.75em}{0ex}}\mathrm{in}\phantom{\rule{0.5em}{0ex}}{\mathrm{\Omega}}_{0}\phantom{\rule{0.50em}{0ex}}\mathrm{where}\phantom{\rule{0.25em}{0ex}}{\mathrm{\Omega}}_{0}\phantom{\rule{0.25em}{0ex}}(\mathrm{marked}\phantom{\rule{0.25em}{0ex}}\mathrm{by}\phantom{\rule{0.25em}{0ex}}\mathrm{the}\hfill \\ \hfill 0\phantom{\rule{5.5em}{0ex}}\mathrm{on}\phantom{\rule{0.25em}{0ex}}C\phantom{\rule{0.25em}{0ex}}\mathrm{user}\phantom{\rule{0.25em}{0ex}}\mathrm{or}\phantom{\rule{0.5em}{0ex}}\mathrm{selected}\mathrm{automatically}\hfill \\ \hfill d\left(\mathbf{p},C\right)\phantom{\rule{0.75em}{0ex}}\mathrm{in}\phantom{\rule{0.5em}{0ex}}\mathrm{\Omega}\backslash {\mathrm{\Omega}}_{0}\mathrm{is}\phantom{\rule{0.25em}{0ex}}\mathrm{an}\phantom{\rule{0.25em}{0ex}}\mathrm{initial}\phantom{\rule{0.25em}{0ex}}\mathrm{region}\phantom{\rule{0.25em}{0ex}}\mathrm{in}\phantom{\rule{0.25em}{0ex}}\Omega .\hfill \end{array}\right.\end{array}$
- 2.
Initialization with a binary function (distance regularized level set evolution (DRLSE) model [25]) (Figure 3a,d,e): ${\mathrm{\Phi}}_{\mathrm{initial}}=\left\{\begin{array}{c}\hfill -{c}_{0}\phantom{\rule{2em}{0ex}}\mathrm{in}\phantom{\rule{0.37em}{0ex}}{\mathrm{\Omega}}_{0}\phantom{\rule{0.25em}{0ex}}\hfill \\ \hfill {c}_{0}\phantom{\rule{1.5em}{0ex}}\mathrm{in}\phantom{\rule{0.37em}{0ex}}\mathrm{\Omega}\backslash {\mathrm{\Omega}}_{0}\hfill \end{array}\right.\phantom{\rule{2em}{0ex}}$, where c _{0} is a small valued constant.
- 3.
Initialization with a constant function (adaptive regularized level set (ARLS) model [28]) (Figure 3f,g): Φ_{initial} = ∓ c _{0} in Ω.
Edge-based level set methods have some drawbacks. Sometimes, a global minimum cannot be found and the methods tend to be slower than other segmentation methods. The global minimum can be correctly obtained if the initial contour is set properly. Level set-based methods also run faster when a narrow band approach is employed in the segmentation process.
3 The proposed method
- 1.
Preprocessing
- 2.
Modified phase map estimation
- 3.
Structure-based level set segmentation
More details about these steps are given in the following subsections of 3.1, 3.2, and 3.3.
3.1 Preprocessing for correction of non-uniform intensity
- 1.
If the input image does not have intensity inhomogeneity, only the histogram-equalized green channel image in the previous step is taken into account as a corrected image.
- 2.
Otherwise, the corrected image is produced by division of those generated images.
- 1.
If λ ^{+} ≅ λ ^{-} ≅ 0, then the point may be in a homogenous region.
- 2.
If λ ^{+} ≫ λ ^{-}, then the point may be on an edge.
- 3.
If λ ^{+} ≅ λ ^{-} ≫ 0, then the point may be on a corner.
- 1.
To process pixels on image edges along the φ ^{-} direction (anisotropic smoothing)
- 2.
To process pixels on homogeneous regions on all possible directions (isotropic smoothing). In this case, T ≅ identity matrix and then the method behaves as a heat equation
where H_{ i } is the Hessian matrix of I_{ i }:${\mathbf{H}}_{i}=\left[\begin{array}{cc}\hfill {\partial}^{2}{I}_{i}/\partial {x}^{2}\hfill & \hfill {\partial}^{2}{I}_{i}/\partial x\partial y\hfill \\ \hfill {\partial}^{2}{I}_{i}/\partial y\partial x\hfill & \hfill {\partial}^{2}{I}_{i}/\partial {y}^{2}\hfill \end{array}\right].$
Here, s^{+}: ℝ^{2} → ℝ, s^{+}(.) = (1 + λ^{+} + λ^{-})^{-0.5} is a decreasing function, and sub-indexes b and f stand for backward and forward finite differences, respectively.
The methods based on color information are compatible with all local geometric properties expressed above: I_{(t + 1)} = I_{(t)} + τ_{1}∂I_{(t)}/∂t, where τ_{1} is an adapting time step. The adapting time step τ_{1} is set by the following inequality: τ_{1} ≤ 20/max(max_{ p }(∂I_{(t)}(p)/∂t), min_{ p }(∂I_{(t)}(p)/∂t)).
3.2 Modified phase map estimation
Here, (r, θ) stands for the polar coordinates, f_{0} is the center frequency, θ_{0} is the orientation angle (direction), σ_{ r } = log(υ/f_{0}) defines the scale bandwidth, and σ_{ θ } defines the angular bandwidth. In order to keep the shape ratio of the filter constant, the term υ/f_{0} must also be kept constant for varying f_{0}[40].
3.3 Structure-based level set segmentation method
A novel structure-based variational method is proposed in this study in order to trace retinal vasculature. The level set function in[25] can be discretized more easily compared to other methods in the literature since it has a level set regularization term. The discretization process uses center/forward difference model instead of other complex discretization schemes[23, 24]. For instance, in the GAC model in[23], the upwind method is used for the calculation of the gradient norm of the level set function Φ, and for the re-initialization of the level set function Φ, essentially non-oscillatory (ENO) scheme is employed. Therefore, the same level set function regularization term of the DRLSE method[25] is used in the proposed method.
where, in general, the parameter ϵ is set to 1.5.
- 1.
For ||∇Φ|| > 1, the diffusion rate μD(.) is positive and the diffusion is forward, which decreases the term ||∇Φ||
- 2.
For ||∇Φ|| < 1, the diffusion is backward, which increases the term ||∇Φ||
In our method, iso-contours automatically shrink when the contour is outside the object due to the functional of A(.) returning a positive contribution, or they automatically expand with a negative value in A(.) when the contour is inside, regardless of the sign of α values as in the existing method[25] (Figure 9j,k).
where$s\left(\left|\left|\widehat{q}\right|\right|\right)={\left(1+\left|\right|\widehat{q}{\left|\right|}^{2}\right)}^{-1}$, Φ_{ ζζ } = ζ^{ T }H ζ, Φ_{ ηη } = η^{ T }H η, and H is the Hessian of Φ. The unit vectors η and ζ are represented by the gradient direction and the tangential (its orthogonal) direction, respectively. Here, η = ∇Φ/||∇Φ|| and ζ = η^{⊥}. s(.) depends on the value of the strength of the image structure$\left|\right|\widehat{q}\left|\right|$, which is generated from phase map. So, along the zero-level contour, the oriented Laplacian flow has a strong smoothing effect. As a result, our approach is more efficient compared to the PBLS method[24] to regularize zero-level contours.
3.4 Proposed segmentation method
The proposed method accepts a retinal fundus image in RGB color space as input. Firstly, a simple mask is obtained to exclude the exterior parts of the fundus where the color is in the 0-U interval in all three channels (generally very dark regions). Also, an iterated erosion operator whose structure element is$\mathbf{B}={\left[\begin{array}{ccc}\hfill 0,\phantom{\rule{0.25em}{0ex}}1,\phantom{\rule{0.25em}{0ex}}0;\hfill & \hfill 1\phantom{\rule{0.25em}{0ex}},1,\phantom{\rule{0.25em}{0ex}}1;\hfill & \hfill 0,\phantom{\rule{0.25em}{0ex}}1,\phantom{\rule{0.25em}{0ex}}0\hfill \end{array}\right]}^{T}$ is applied on the mask for proper execution. Secondly, a preprocessing step is employed to obtain a corrected image in terms of intensity inhomogeneity. Thirdly, we compute the phase map by using the corrected image as input. Afterwards, to eliminate some small non-blood vessels region, Otsu’s method[43] is applied on the processed image. As a result of these processes, a skeleton-based image giving the centerlines of the vasculature is generated with the following steps: (i) remove disconnected pixels, (ii) obtain skeleton-based image, (iii) find junctions, (iv) trace lines (centerlines) and label them, and (v) clean short lines. Here, a threshold value is used to eliminate tiny little short lines called artifacts.
Note that values of the edge indicator function g, used in[25], are in the [0,1] interval. In the proposed method, the sign of the coefficient α in the level set energy functional can always remain positive in contrast to the earlier method[25] since the function$\Re \left(\widehat{q}\right)$ obtained from the phase map has a different sign around object boundaries.
The proposed level set evolution equation culminates in Φ_{(t + 1)} = Φ_{(t)} + τ_{2}∂Φ_{(t)}/∂t where τ_{2} is a time step, which is set by τ_{2} ≤ (4 μ)^{-1} based on Courant-Friedrichs-Lewy (CFL) condition with 4-neighbor connectivity[25, 44].The initialization of level set function is important. If the seed points are selected away from the vessel centers and close to pathological regions, the proposed method can fail (wrongly segmenting the pathological region, as well) as shown in Figure 10d.
4 Experimental results
Formulas of some variational image segmentation methods
Group | Method | Formula |
---|---|---|
Edge-based | GAC[23] | $\vartheta ||\nabla \mathrm{\Phi}||\mathrm{div}\left(\mathrm{g}\frac{\nabla \mathrm{\Phi}}{||\nabla \mathrm{\Phi}||}\right)+\phantom{\rule{0.25em}{0ex}}\alpha \mathrm{g}||\nabla \mathrm{\Phi}||$ |
PBLS[24] | $\vartheta \left|\right|\nabla \mathrm{\Phi}\left|\right|\mathrm{div}\left(\frac{\nabla \mathrm{\Phi}}{\left|\left|\nabla \mathrm{\Phi}\right|\right|}\right)-\alpha \left|\right|\nabla \mathrm{\Phi}\left|\right|\Re \left({\widehat{q}}_{\mathrm{PBLS}}\right)$ | |
DRLSE[25] | $\mu \mathrm{div}\left(D\left(\left|\left|\nabla \mathrm{\Phi}\right|\right|\right)\nabla \mathrm{\Phi}\right)+\vartheta {\delta}_{\u03f5}\left(\mathrm{\Phi}\right)\mathrm{div}\left(\mathrm{g}\frac{\nabla \mathrm{\Phi}}{\left|\left|\nabla \mathrm{\Phi}\right|\right|}\right)+\phantom{\rule{0.25em}{0ex}}\mathit{\alpha}\mathrm{g}{\delta}_{\u03f5}\left(\mathrm{\Phi}\right)$ | |
ARLS[28] | $\mu \left({\nabla}^{2}\mathrm{\Phi}-\mathrm{div}\left(\frac{\nabla \mathrm{\Phi}}{||\nabla \mathrm{\Phi}||}\right)\right)+\vartheta {\delta}_{\u03f5}\left(\mathrm{\Phi}\right)\mathrm{div}\left({||\nabla \mathrm{\Phi}||}^{s\left(\nabla \left(I*{G}_{\sigma}\right)\right)-2}\nabla \mathrm{\Phi}\right)+\phantom{\rule{0.25em}{0ex}}\alpha {\delta}_{\u03f5}\left(\mathrm{\Phi}\right){\nabla}^{2}\left(I*{G}_{\sigma}\right)$ | |
Region-based | RBLSE[33] | $\mu \mathrm{div}\left(D\left(\left|\left|\nabla \mathrm{\Phi}\right|\right|\right)\nabla \mathrm{\Phi}\right)+\vartheta {\delta}_{\u03f5}\left(\mathrm{\Phi}\right)\mathrm{div}\left(\frac{\nabla \mathrm{\Phi}}{\left|\left|\nabla \mathrm{\Phi}\right|\right|}\right)-\alpha {\delta}_{\u03f5}\left(\mathrm{\Phi}\right)\left({e}_{1}-{e}_{2}\right),$ |
Parameter values of the methods
Method | Parameters |
---|---|
Proposed preprocessing | Amplitude of the trace-based filter is 30, amplitude of the shock filter is 45, τ_{1} = updated at each iteration, other parameters of these filters are kept as in the related study[39], and kernel size of median filter is 25 × 25. |
Log-Gabor filter[40] and modified phase map | $\begin{array}{l}{f}_{0}\left(x\right)={\left(3\times {2.1}^{\left(x-1\right)}\right)}^{-1},\phantom{\rule{0.25em}{0ex}}1\le x\le S=3\phantom{\rule{.25em}{0ex}},\phantom{\rule{.25em}{0ex}}{\sigma}_{r}=log\left(0.55\right),\\ {\sigma}_{\theta}=1.2,\phantom{\rule{0.15em}{0ex}}{\theta}_{0}\left(x\right),\phantom{\rule{0.25em}{0ex}}1\le x\le O=8\phantom{\rule{0.5em}{0ex}},\phantom{\rule{0.12em}{0ex}}\beta =1\phantom{\rule{0.12em}{0ex}},\phantom{\rule{0.37em}{0ex}}\mathrm{and}\phantom{\rule{0.36em}{0ex}}{\sigma}_{q}=3\cdot \end{array}$ |
GAC[23] | $\begin{array}{l}{\tau}_{2}=0.2,\phantom{\rule{0.12em}{0ex}}\vartheta =1,\phantom{\rule{0.24em}{0ex}}\mathrm{and}\phantom{\rule{0.12em}{0ex}}\alpha =0.3\end{array}$ |
PBLS[24] | τ_{2} = updated at each iteration, ϑ = 0.07, and α = 1 |
DRLSE[25] | τ_{2} = 5, σ = 1.5, μ = 0.04, ϑ = 5, α = ± 1.5, and c_{0} = 2 |
ARLS[28] | τ_{2} = 5, σ = 1.4, μ = 0.04, ϑ = 2.7, α = ± 1, and c_{0} = ±1 |
Proposed segmentation | τ_{2} = 1, μ = 0.2, ϑ = 0.6, α = 3, and c_{0} = {2, 5} |
RBLSE[33] | τ_{2} = 0.1, σ = 4, μ = 1, ϑ = 0.01 × 255^{2}, and c_{0} = 1 |
Statistical results of our method for test images of 1 to 20 from DRIVE dataset
Dataset | Image number | Se | Sp | Ppv | Npv | Acc | κ |
---|---|---|---|---|---|---|---|
DRIVE | 1 | 0.8182 | 0.9581 | 0.7461 | 0.9723 | 0.9398 | 0.7457 |
2 | 0.7764 | 0.9654 | 0.7982 | 0.9608 | 0.9371 | 0.7502 | |
3 | 0.7387 | 0.9513 | 0.7218 | 0.9551 | 0.9202 | 0.6834 | |
4 | 0.7456 | 0.9677 | 0.7826 | 0.9607 | 0.9378 | 0.7279 | |
5 | 0.7419 | 0.9682 | 0.7878 | 0.9593 | 0.9371 | 0.7279 | |
6 | 0.7142 | 0.9726 | 0.8126 | 0.9534 | 0.9358 | 0.7233 | |
7 | 0.7507 | 0.9466 | 0.6846 | 0.9609 | 0.9204 | 0.6699 | |
8 | 0.7285 | 0.9619 | 0.7332 | 0.9610 | 0.9325 | 0.6923 | |
9 | 0.7223 | 0.9738 | 0.7880 | 0.9630 | 0.9439 | 0.7221 | |
10 | 0.7535 | 0.9656 | 0.7507 | 0.9661 | 0.9400 | 0.7179 | |
11 | 0.7456 | 0.9512 | 0.6972 | 0.9613 | 0.9243 | 0.6768 | |
12 | 0.7932 | 0.9594 | 0.7391 | 0.9697 | 0.9383 | 0.7297 | |
13 | 0.7165 | 0.9665 | 0.7811 | 0.9533 | 0.9307 | 0.7073 | |
14 | 0.7940 | 0.9573 | 0.7130 | 0.9720 | 0.9380 | 0.7160 | |
15 | 0.7867 | 0.9463 | 0.6321 | 0.9742 | 0.9296 | 0.6616 | |
16 | 0.7880 | 0.9697 | 0.7989 | 0.9677 | 0.9457 | 0.7621 | |
17 | 0.7581 | 0.9715 | 0.7900 | 0.9660 | 0.9451 | 0.7425 | |
18 | 0.8407 | 0.9517 | 0.6965 | 0.9784 | 0.9388 | 0.7271 | |
19 | 0.8696 | 0.9599 | 0.7504 | 0.9815 | 0.9489 | 0.7764 | |
20 | 0.8254 | 0.9604 | 0.7162 | 0.9785 | 0.9458 | 0.7364 |
Statistical results of our method for test images of 1 to 20 from our dataset
Dataset | Image number | Se | Sp | Ppv | Npv | Acc | κ |
---|---|---|---|---|---|---|---|
Ours | 1 | 0.4821 | 0.9905 | 0.7483 | 0.9702 | 0.9623 | 0.5676 |
2 | 0.3471 | 0.9887 | 0.6680 | 0.9586 | 0.9494 | 0.4330 | |
3 | 0.5745 | 0.9786 | 0.5802 | 0.9781 | 0.9589 | 0.5557 | |
4 | 0.5617 | 0.9695 | 0.5911 | 0.9657 | 0.9398 | 0.5437 | |
5 | 0.5699 | 0.9872 | 0.7537 | 0.9708 | 0.9602 | 0.6284 | |
6 | 0.3527 | 0.9879 | 0.6416 | 0.9613 | 0.9511 | 0.4318 | |
7 | 0.8109 | 0.9566 | 0.5234 | 0.9885 | 0.9485 | 0.6098 | |
8 | 0.3134 | 0.9887 | 0.6280 | 0.9594 | 0.9499 | 0.3950 | |
9 | 0.3966 | 0.9857 | 0.5666 | 0.9719 | 0.9591 | 0.4461 | |
10 | 0.4290 | 0.9878 | 0.5958 | 0.9764 | 0.9654 | 0.4814 | |
11 | 0.2789 | 0.9901 | 0.6119 | 0.9607 | 0.9523 | 0.3619 | |
12 | 0.5497 | 0.9840 | 0.6101 | 0.9796 | 0.9651 | 0.5602 | |
13 | 0.6942 | 0.9783 | 0.6056 | 0.9852 | 0.9653 | 0.6288 | |
14 | 0.4028 | 0.9844 | 0.5128 | 0.9759 | 0.9616 | 0.4316 | |
15 | 0.5848 | 0.9849 | 0.5977 | 0.9840 | 0.9700 | 0.5756 | |
16 | 0.3300 | 0.9877 | 0.6573 | 0.9539 | 0.9440 | 0.4133 | |
17 | 0.7426 | 0.9731 | 0.5785 | 0.9870 | 0.9622 | 0.6308 | |
18 | 0.5550 | 0.9762 | 0.5149 | 0.9797 | 0.9578 | 0.5122 | |
19 | 0.7238 | 0.9712 | 0.6101 | 0.9826 | 0.9567 | 0.6392 | |
20 | 0.6576 | 0.9680 | 0.4891 | 0.9838 | 0.9542 | 0.5373 |
Statistical results of our method for test images of 1 to 20 from STARE dataset
Dataset | Image number | Se | Sp | Ppv | Npv | Acc | κ |
---|---|---|---|---|---|---|---|
STARE | 1 | 0.6449 | 0.9731 | 0.7455 | 0.9574 | 0.9374 | 0.6570 |
2 | 0.5754 | 0.9836 | 0.7795 | 0.9584 | 0.9464 | 0.6336 | |
3 | 0.8036 | 0.9519 | 0.5973 | 0.9820 | 0.9398 | 0.6527 | |
4 | 0.3117 | 0.9972 | 0.9275 | 0.9271 | 0.9271 | 0.4376 | |
5 | 0.8084 | 0.9466 | 0.6803 | 0.9723 | 0.9296 | 0.6985 | |
6 | 0.7759 | 0.9666 | 0.6912 | 0.9781 | 0.9498 | 0.7035 | |
7 | 0.8567 | 0.9631 | 0.7412 | 0.9820 | 0.9514 | 0.7674 | |
8 | 0.7758 | 0.9644 | 0.7125 | 0.9742 | 0.9451 | 0.7121 | |
9 | 0.7814 | 0.9698 | 0.7569 | 0.9736 | 0.9495 | 0.7406 | |
10 | 0.7568 | 0.9722 | 0.7711 | 0.9700 | 0.9485 | 0.7349 | |
11 | 0.8000 | 0.9629 | 0.7004 | 0.9780 | 0.9470 | 0.7175 | |
12 | 0.8446 | 0.9665 | 0.7490 | 0.9814 | 0.9537 | 0.7679 | |
13 | 0.7743 | 0.9710 | 0.7881 | 0.9687 | 0.9470 | 0.7510 | |
14 | 0.7611 | 0.9739 | 0.8055 | 0.9663 | 0.9474 | 0.7528 | |
15 | 0.6239 | 0.9796 | 0.8031 | 0.9512 | 0.9376 | 0.6680 | |
16 | 0.4445 | 0.9916 | 0.8961 | 0.9165 | 0.9150 | 0.5528 | |
17 | 0.7238 | 0.9803 | 0.8372 | 0.9621 | 0.9488 | 0.7477 | |
18 | 0.5669 | 0.9931 | 0.8594 | 0.9685 | 0.9635 | 0.6647 | |
19 | 0.4183 | 0.9934 | 0.8001 | 0.9646 | 0.9595 | 0.5304 | |
20 | 0.8035 | 0.9512 | 0.6234 | 0.9797 | 0.9377 | 0.6679 |
Statistical average results for test images of 1 to 20 from the datasets
Dataset | Method | Se | Sp | Ppv | Npv | Acc | κ | |
---|---|---|---|---|---|---|---|---|
DRIVE | Unsupervised | PBLS[24] | 0.7754 | 0.9348 | 0.6403 | 0.9655 | 0.9140 | 0.6494 |
Jiang et al.[12] | - | - | - | - | 0.9212 | - | ||
Martinez-Perez et al.[13] | 0.7246 | 0.9655 | - | - | 0.9344 | - | ||
Proposed | 0.7704 | 0.9613 | 0.7460 | 0.9658 | 0.9365 | 0.7198 | ||
Budai et al.[17] | 0.6440 | 0.9870 | - | - | 0.9572 | - | ||
Supervised | Staal et al.[16] | 0.7194 | 0.9773 | - | - | 0.9442 | - | |
Marin et al.[14] | 0.7067 | 0.9801 | 0.8433 | 0.9582 | 0.9452 | - | ||
Soares et al.[15] | 0.7283 | 0.9788 | - | - | 0.9466 | - | ||
Ours | Unsupervised | PBLS[24] | 0.6600 | 0.9482 | 0.4380 | 0.9804 | 0.9328 | 0.4754 |
Proposed | 0.5179 | 0.9810 | 0.6042 | 0.9737 | 0.9567 | 0.5192 | ||
STARE | Unsupervised | PBLS[24] | 0.8268 | 0.9117 | 0.5227 | 0.9803 | 0.9035 | 0.5822 |
Hoover et al.[11] | 0.6751 | 0.9567 | - | - | 0.9267 | - | ||
Martinez-Perez et al.[13] | 0.7506 | 0.9569 | - | - | 0.9410 | - | ||
Proposed | 0.6926 | 0.9726 | 0.7633 | 0.9656 | 0.9441 | 0.6779 | ||
Supervised | Soares et al.[15] | 0.7103 | 0.9737 | - | - | 0.9480 | - | |
Staal et al.[16] | 0.6970 | 0.9810 | - | - | 0.9516 | - | ||
Marin et al.[14] | 0.6944 | 0.9819 | - | - | 0.9526 | - |
5 Conclusions
We present a structure-based level set method with automatic seed point selection for segmentation of retinal vasculature in fundus images. Extensive experiments employing the proposed algorithms using datasets indicate that the algorithm performs well and favorably compared to the already existing level set-based methods in the literature. Developing strategies to improve inconsistencies in clinical diagnosis is an important challenge in ophthalmology. The segmentation methods described in this study may provide a basis for the development of computer-based image analysis algorithms. Future work will involve quantitative feature extraction from segmented retinal vessels, followed by implementation of these image analysis algorithms for image-based diagnostic assistance.
We plan to extend the study in order to improve the results especially for pathological regions such as drusen, GA, etc. Moreover, we will investigate how to use all color channels of the given image interactively in an efficient manner in order to trace retinal vasculature more properly. In addition to this, we plan to do a narrow band implementation in order to accelerate the run time of the proposed method.
Declarations
Acknowledgements
This work is partially supported by grants from TUBITAK (grant no. 1059B191000548), NSF, and NIH.
Authors’ Affiliations
References
- Chiang MF, Jiang L, Gelman R, Du YE, Flynn JT: Interexpert agreement of plus disease diagnosis in retinopathy of prematurity. Arch. Ophthalmol 2007, 125: 875-880. 10.1001/archopht.125.7.875View ArticleGoogle Scholar
- Gelman R, Jiang L, Du YE, Martinez-Perez ME, Flynn JT, Chiang MF: Plus disease in retinopathy of prematurity: pilot study of computer-based and expert diagnosis. JAAPOS 2007, 11(6):532-540.Google Scholar
- Osareh A, Shadgar B: An automated tracking approach for extraction of retinal vasculature in fundus images. J. Opthalmic. Vis. Res. 2010, 5: 20-26.Google Scholar
- Wu D, Zhang M, Liu JC, Bauman W: On the adaptive detection of blood vessels in retinal images. IEEE Trans. Biomed. Eng. 2006, 53: 341-343. 10.1109/TBME.2005.862571View ArticleGoogle Scholar
- Azemin MZC, Kumar DK, Wong TY, Kawasaki R, Mitchell P, Wang JJ: Robust methodology for fractal analysis of the retinal vasculature. IEEE Trans. Med. Imaging 2011, 2(30):243-250.View ArticleGoogle Scholar
- Mahadevan V, Narasimha-Iyer H, Roysam B, Tanenbaum HL: Robust model-based vasculature detection in noisy biomedical images. IEEE Trans. Inf. Technol. Biomed. 2004, 8(3):360-376. 10.1109/TITB.2004.834410View ArticleGoogle Scholar
- Narasimha-Iyer H, Mahadevan V, Beach JM, Roysam B: Improved detection of the central reflex in retinal vessels using a generalized dual-Gaussian model and robust hypothesis testing. IEEE Trans. Inf. Technol. Biomed. 2008, 3(12):406-410.View ArticleGoogle Scholar
- Tobin KW, Chaum E, Govindasamy VP, Karnowski TP: Detection of anatomic structures in human retinal imagery. IEEE Trans. Med. Imaging 2007, 26(12):1729-1739.View ArticleGoogle Scholar
- Niemeijer M, Xu X, Dumitrescu AV, Gupta P, van Ginneken B, Folk JC, Abramoff MD: Automated measurement of the arteriolar-to-venular width ratio in digital color fundus photographs. IEEE Trans. Med. Imaging 2011, 11(30):1941-1950.View ArticleGoogle Scholar
- Wang L, Bhalerao A, Wilson R: Analysis of retinal vasculature using a multiresolution Hermite model. IEEE Trans. Med. Imaging 2007, 2(26):137-152.View ArticleGoogle Scholar
- Hoover A, Kouznetsova V, Goldbaum M: Locating blood vessels in retinal images by piecewise threshold probing of a matched filter response. IEEE Trans. Med. Imaging 2000, 19(3):203-210. 10.1109/42.845178View ArticleGoogle Scholar
- Jiang X, Mojon D: Adaptive local thresholding by verification-based multithreshold probing with application to vessel detection in retinal images. IEEE Trans. Pattern. Anal. Mach. Intell. 2003, 25(1):131-137. 10.1109/TPAMI.2003.1159954View ArticleGoogle Scholar
- Martinez-Perez ME, Hughes AD, Thom SA, Bharath AA, Parker KH: Segmentation of blood vessels from red-free and fluoresce in retinal images. Med. Image Anal. 2007, 11(1):47-61. 10.1016/j.media.2006.11.004View ArticleGoogle Scholar
- Marin D, Aquino A, Arias GME, Bravo JM: A New supervised method for blood vessel segmentation in retinal images by using gray-level and moment invariants-based features. IEEE Trans. Med. Imaging 2011, 30(1):146-158.View ArticleGoogle Scholar
- Soares JVB, Leandro JJG, Jr Cesar RM, Jelinek HF, Cree MJ: Retinal vessel segmentation using the 2-D Gabor wavelet and supervised classification. IEEE Trans. Med. Imaging 2006, 25(9):1214-1222.View ArticleGoogle Scholar
- Staal J, Abramoff MD, Niemeijer M, Viergever MA, van Ginneken B: Ridge-based vessel segmentation in color images of the retina. IEEE Trans. Med. Imaging 2004, 23: 501-509. 10.1109/TMI.2004.825627View ArticleGoogle Scholar
- Budai A, Bock R, Maier A, Hornegger J, Michelson G: Robust vessel segmentation in fundus images. Int. J Biomed. Imaging 2013., 2013:Google Scholar
- Frangi AF, Niessen WJ, Vincken KL, Viergever MA: Multiscale Vessel Enhancement Filtering (Springer. Germany, Heidelberg; 1998.Google Scholar
- You S, Bas E, Erdogmus D, Kalpathy-Cramer J: Principal curve based retinal vessel segmentation towards diagnosis of retinal diseases. Proc. Healthcare Inform, Imaging Sys. Biol. (HISB) 2011, 331-337. San Jose, California, USA, (2011)Google Scholar
- Erdogmus D, Ozertem U: Self-consistent locally defined principal surfaces. Proc. ICASSP 2007, Vol. 2: II.549-II.552. Honolulu, Hawaii, USAGoogle Scholar
- Kirbas C, Quek F Proceedings of the Third IEEE Symposium on BioInformatics and BioEngineering (BIBE’03), 238-245. In Vessel Extraction Techniques and Algorithms: a Survey. Bethesda, Maryland, USA; 2003.View ArticleGoogle Scholar
- Vese L, Chan T: A multiphase level set framework for image segmentation using the Mumford and Shah model. Int. J. Comput. Vis. 2002, 50(3):271-293. 10.1023/A:1020874308076View ArticleMATHGoogle Scholar
- Caselles V, Kimmel R, Sapiro G: Geodesic active contours. Int. J. Comput. Vis. 1997, 22(1):61-79. 10.1023/A:1007979827043View ArticleMATHGoogle Scholar
- Lathen G, Jonasson J, Borga M: Blood vessel segmentation using multi-scale quadrature filtering. Pattern Recogn. Lett. 2010, 31: 762-767. 10.1016/j.patrec.2009.09.020View ArticleGoogle Scholar
- Li C, Xu C, Gui C, Fox MD: Distance regularized level set evolution and its application to image segmentation. IEEE Trans. Image Process. 2010, 19(12):3243-3254.MathSciNetView ArticleGoogle Scholar
- Pang KY, Iznita L, Fadzil A, Hanung AN, Hermawan N, Vijanth SA: Segmentation of Retinal Vasculature in Colour Fundus Images. Conference on Innovation Technologies in Intelligent Systems and Industrial Applications (CITISIA, Malaysia; 2009:398-401.Google Scholar
- Zhou B, Mu C: Level set evolution for boundary extraction based on a p-Laplace equation. Appl. Math. Mod 2010, 34(12):3910-3916. 10.1016/j.apm.2010.04.003MathSciNetView ArticleMATHGoogle Scholar
- Meng L, Chuanjiang H, Yi Z: Adaptive regularized level set method for weak boundary object segmentation. Math. Probl. Eng 2012, 2012(369472):16. doi:10.1155/2012/369472MathSciNetMATHGoogle Scholar
- Belaid A, Boukerroui D, Maingourd Y, Lerallut J-F: Phase based level set segmentation of ultrasound images. IEEE Trans. Inform. Tech. Biomed 2011, 15(1):138-147.View ArticleGoogle Scholar
- Dizdaroğlu B, Ataer-Cansizoglu E, Kalpathy-Cramer J, Keck K, Chiang MF, Erdogmus D 2012 IEEE International Workshop On Machine Learning For Signal Processing. In Level Sets for Retinal Vasculature Segmentation Using Seeds from Ridges and Edges from Phase Maps. Santander, Spain; 2012.Google Scholar
- Yu G, Lin P, Li P, Bian Z: Region-based vessel segmentation using level set framework. Int. J. Control. Autom. Syst. 2006, 4(5):660-667.Google Scholar
- Li C, Kao C, Gore JC, Ding Z: Minimization of region-scalable fitting energy for image segmentation. EEE Trans. Image Proc. 2008, 17(10):1940-1949.MathSciNetView ArticleGoogle Scholar
- Li C, Huang R, Ding Z, Gatenby C, Metaxas DN, Gore JC: A level set method for image segmentation in the presence of intensity inhomogeneities with application to MRI. IEEE Trans. Image Proc. 2011, 20(7):2007-2016.MathSciNetView ArticleGoogle Scholar
- Zhao YQ, Wang XH, Wang XF, Shih FY: Retinal vessels segmentation based on level set and region growing. Pattern Recognition. 2014, 47(7):2437-2446. 10.1016/j.patcog.2014.01.006View ArticleGoogle Scholar
- Bertalmio M, Vese L, Sapiro G, Osher S: Simultaneous structure and texture image inpainting. IEEE Trans. Image Process. 2003, 12: 882-889. 10.1109/TIP.2003.815261View ArticleGoogle Scholar
- Buades A, Le TM, Morel J-M, Vese LA: Fast cartoon + texture image filters. IEEE Trans. Image Process. 2010, 19(8):1978-1986.MathSciNetView ArticleGoogle Scholar
- Dizdaroğlu B: An image completion method using decomposition. EURASIP J. Advanc. Signal Proc 2011, 2011(831724):15. doi:10.1155/2011/831724Google Scholar
- Black MJ, Sapiro G, Marimont DH, Heeger D: Robust anisotropic diffusion. IEEE Trans. Image Process. 1998, 7(3):421-432. 10.1109/83.661192View ArticleGoogle Scholar
- Tschumperlé D: PDE’s based regularization of multi-valued images and applications, PhD thesis. Université de Nice-Sophia Antipolis, France; 2002.Google Scholar
- Kovesi P: Phase congruency: a low-level image invariant. Psychological Research 2000, 64(2):136-148. 10.1007/s004260000024View ArticleGoogle Scholar
- Blomgren P, Chan TF, Wong CK: Total variation image restoration: numerical methods and extensions. Proc. IEEE Int. Conf Image Proc 1997, 3: 384-387.View ArticleGoogle Scholar
- Kornprobst P, Deriche R, Aubert G: Image Restoration via PDE’s. First Annual Symposium on Enabling Technologies for Law Enforcement and Security - SPIE Conference 2942: Investigative Image Processing, Boston, Massachusetts, USA; 1996.MATHGoogle Scholar
- Otsu N: A threshold selection method from gray-level histogram. IEEE Trans. Syst. Man Cybern 1979, 9(1):62-66.MathSciNetView ArticleGoogle Scholar
- Courant R, Friedrichs K, Lewvy H: Über die partiellen Differenzengleichungen der mathematischen Physik. Math. Ann. 1928, 100(1):32-74. 10.1007/BF01448839MathSciNetView ArticleMATHGoogle Scholar
- Landis J, Koch G: The measurement of observer agreement for categorical data. Biometrics 1977, 33: 159-174. 10.2307/2529310MathSciNetView ArticleMATHGoogle Scholar
Copyright
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited.