1 Introduction

The analysis of the retina is frequently used in many relevant diagnostic procedures as useful information can be obtained for diseases such as hypertension or diabetes. Computer-aided diagnosis (CAD) systems can thus be of the utmost importance in assisting clinicians in the different diagnostic processes, facilitating and simplifying their work.

The retinal vessel tree is one of the most widely examined structures as it represents the most direct and least invasive way to observe the human circulatory system. Hence, analysis of the retinal vasculature has proved extremely useful due to its relation with a number of pathologies. In this regard, some works have stated that retinal vasculature calibers are a significant biomarker for diabetes [16, 23]. Smith et al. [29] also identified retinal vasculature caliber as a relevant sign in the analysis of hypertension as small vessel changes can anticipate the presence of severe hypertension. Other studies [7, 26] have also defined calculations on the microcirculation of the retina as possible indices for cerebrovascular disease as well as for other cardiovascular illness events related to retinal vasculature calibers [32, 35]. The retinal vasculature has also demonstrated its usefulness in other problems as is the case, for example, in biometrics, where vessel intersections are used in a similar manner to fingerprints [25].

The most widely used image modalities in this respect are angiography and retinography, which give a 2D representation of the real layout of the eye fundus. Most of the proposals in the literature were made using these image modalities, providing only a partial representation of the vessel tree. Some surveys have described the various proposals that have been put forward in the matter [12], and representative examples of the principal paradigms employed will now be described.

Thresholding is one of the methodologies used in the problem, as in the works of Zhang et al. [43] or Yong et al. [42] where adaptive thresholds were designed in processes that aimed for the localization and segmentation of the vessels. Xiaoyi and Mojon [38] designed a sophisticated framework that includes adaptive local thresholding in an approach combining hypothetical thresholds and a posterior verification step.

Tracking approaches have also been implemented, as in the work of Wink et al. [34], who designed a semi-automatic method that starts from a set of user-defined points in the image and retrieves the central axis of tubular structures. For that purpose, a vectorial multiscale feature image was included for wave front propagation, a process that adapts perfectly to the problem of multiscale vessels. Mendonça and Campilho [21] presented a methodology that combines the extraction of the centerline of the vasculature with the subsequent application of region growing to construct the final vessel segmentation. Lazar and Hajdu [18] implemented a region-growing process that integrates a hysteresis thresholding scheme including the response vector similarity of adjacent pixels.

Different edge detector approaches have also been used to deal with the issue, including specific improvements since they normally present certain drawbacks in the detection of vessels in noisy scenes or blurred contours. Dhar et al. [8] studied the robustness of the Canny and Laplacian of Gaussian detectors, demonstrating that the Canny filter offers a more stable behavior in a variety of image conditions. Xiaolin et al. [37] modified Canny with a bilateral filter to remove noisy artifacts and facilitate vessel detection.

As in many other medical imaging procedures, Wavelet transform has shown its potential in this particular application, as demonstrated in the proposal by Fathi et al. [10], which provided satisfactory results integrating the information over multiple classification scales. Nayak et al. [22] also employed the Wavelet transform for the purpose of vessel identification in a context of patients that presented diabetic retinopathy. Soares et al. [30] designed a methodology that used a 2D Gabor Wavelet over multiple scales as the feature for a classification process with a Bayesian classifier.

Chen et al. [4] used graph-cuts in an unsupervised approach to identify the vessels, as did Xu et al. [40], where vessel width is derived in a segmentation process using a graph-theoretic method.

Of all the strategies employed, Artificial Neural Networks (ANNs) is one of the most widely referenced in many different medical imaging procedures, as they usually provide correct results in largely complex problems. ANNs appear frequently in the ophthalmological research field, as in the work by Sinthanayothin et al. [28], where neural networks extract the main structures of the eye fundus such as the optic disk, the fovea, or the blood vessels. Li et al. [19] approached the problem as a modality data transform, using a neural network that discriminates vessel pixels in the image. In the work of Alonso-Montes et al. [1], the proposed method included a Convolutional Neural Network (CNN) with the aim of optimizing vascular tree extraction in order to meet real-time requirements. Jiang et al. [15] used ANNs characterizing the pixels with a 8D vector composed of intensity descriptors and pixel strength features and subsequently trained the network to achieve the segmentation. Vega et al. [33] developed an elaborate network they refer to as a Lattice Neural Network with Dendritic Processing (LNNDP) to extract the vessels with successful results. Other classifiers were also considered, such as random forest in the work by Cheng et al. [5], where the authors defined a large and heterogeneous set of features combined with the abovementioned classifier.

Approaches that exploit different kinds of pattern analysis have also appeared in the literature. Staal et al. [31] searched for ridges to detect the lines which match with vessel centerlines. The line elements are then partitioned in patches to extract features and perform the final vessel detection using a K-NN classifier. Kovacs and Hajdu [17] designed a process of template matching using generalized Gabor function-based templates to detect the centerlines and subsequently applying a reconstruction step to obtain the final segmentation. Chakraborti et al. [3] implemented a self-adaptive matched filter combining vesselness filtering with a high degree of sensitivity for the detection of vessels in retinographies. Yin et al. [41] constructed an orientation aware-detector based on the principle that the vessels are locally oriented and have linearly elongated structures. Imani et al. [14] used a morphological component analysis (MCA) algorithm in a method that overcomes the difficulties of the problem in retinographies with lesions, facilitating the discrimination between vessels and lesions.

More recently, Optical Coherence Tomography Angiography (OCTA) has emerged as an image modality that uses the spectral domain for a non-invasive visualization of the retinal and choroidal vasculature [6]. The use of OCTA is not yet widespread in health services due to its recent appearance and the high cost of acquiring this type of technology.

Optical Coherence Tomography (OCT) imaging is widely used in clinical services. It offers additional depth information instead of the classical 2D layouts provided by angiographies and retinographies. This information is crucial for obtaining the real 3D layout of the retinal vessels and enabling clinicians to perform an analysis that comes closer to reality. Only a small number of works have appeared that use OCT images to deal with the issue of vasculature segmentation. Moreover, these few proposals consist of limited methodologies that still offer 2D representations of the retinal vasculature. In this regard, Niemeijer et al. [24] presented an approach that segments the retina in multiple layers with the vessel projections and performs a classification stage in the projected image to extract the vessels. Xu et al. [39] implemented a 3D boosting learning to detect the vessels, after which the method applies a post-processing to remove false-positive detections. In the work of Pilch et al. [27] statistical shape models were considered with manually segmented vessels. This vessel set was then used for a subsequent training stage. Once trained, the resulting model is used to identify the final contours of the vessels in the axial direction. Guimaraes et al. [13], in a study of abnormal retinal vascular patterns, identified the vessel depths at all the positions using the OCT images. In the work of Wu et al. [36] Coherent Point Drift was included in an approach for the segmentation of the vessel points. These points are established as landmarks in a context of image registration.

In such a context, this work presents a complete methodology for 3D extraction of the retinal vessel tree and its 3D reconstruction using OCT images. Hence, a more complete vasculature representation permits a more reliable analysis of the retinal microcirculation that is needed in many diagnostic processes.

This paper is organized as follows. Section 2 presents the proposed methodology and the characteristics of all the stages. Section 3 presents some practical results and the validation of key steps of the proposal, compared to the manual annotations of a clinician. Finally, Sections 4 and 5 include the discussion and conclusions of this proposal as well as possible future work.

2 Methods

The proposed method receives, as input, a set of OCT images. The images correspond to consecutive OCT sections that represents the morphology of the retinal layers. This technique provides tomographic images of the biological tissue with high resolution in progressive scans over the eye fundus of the patient. These images are complemented with the corresponding near-infrared reflectance retinography that is provided in combination with the OCT sections. Both sources of information, the consecutive OCT sections and the corresponding near-infrared retinography, are directly provided by the capture machine. Figure 1 illustrates an OCT scan composed of the near-infrared reflectance retinography and the consecutive OCT sections.

Fig. 1
figure 1

Set of OCT sections in combination with the near-infrared reflectance retinography

Full size image

The method is organized in a set of progressive stages. Firstly, the arteriovenous tree is extracted in the near-infrared reflectance retinography, constructing the set of segments that represents the vessels and correcting all the detected misrepresentations at the intersections. Subsequently, diameters over the detected points are calculated. The vessel segments are then mapped in the input OCT sections with the aim of identifying the depth, z, coordinates. The 3D segmentation is finally constructed with the obtained coordinates. For this purpose, an interpolation using splines of the extracted vasculature is calculated to provide a smooth representation. Figure 2 describes the general scheme of the proposed methodology, each stage of which will be detailed in the following subsections.

Fig. 2
figure 2

Scheme of the proposed methodology

Full size image

2.1 2D vessel extraction

The vessels are initially segmented in the near-infrared reflectance retinography to obtain the first (x,y) coordinates, given its simplicity and well-established techniques. We used an approach that involves different morphological operators [2] to obtain an initial representation of the vessels. The segmentation process is performed in two main stages: vascular structure enhancement and extraction of the arteriovenous tree.

Firstly, a top-hat filter [9] is used to enhance the biggest and darkest structures in the image, corresponding to the vessels. Then, the noise and vascular reflex is minimized with a median filter, thus facilitating the extraction of a more precise segmentation.

Vessel enhancement is done using the eigenvalues, λ 1 and λ 2, of the Hessian matrix [11], these being combined to enhance tubular structures of variable size and therefore identify vessels at different scales. Thus, a function B(p) is formulated as:

$$ B(p) = \left\{\begin{array}{ll}0 & \lambda_{2} > 0\\ exp(\frac{-{R^{2}_{B}}}{2\beta^{2}}) (1- exp(-\frac{S^{2}}{2c^{2}})) & otherwise\end{array}\right. $$
(1)

where R B = λ 1/λ 2, c is half of the max Hessian norm and S measures the “second order structures.” Pixels that belong to vessels are normally represented by small λ 1 values and higher positive λ 2 values. This way, we reinforce the robustness of the method by minimizing the influence of the input image characteristics in the parameters of the system.

After this enhancement, vascular segmentation is achieved in two steps: an initial segmentation and the subsequent removal of isolated structures. The initial segmentation is done by means of a hysteresis-based thresholding. A hard threshold (T h ) obtains pixels with a high confidence of being vessels while a weak threshold (T w ) keeps all the pixels of the tree, including the spurious ones. The final vessel segmentation is formed by all the pixels included by T w that are connected to at least one pixel obtained by T h . The values for T h and T w are calculated from two image properties: the percentage of image representing vessels and the percentage of image representing fundus. The gap between both percentages will include all the non-classified pixels. The values for the thresholds are easily derived after calculating the percentiles with:

$$ P_{k} = L_{k} + \frac{k(n/100) - F_{k}}{f_{k}} \times c, ~~~ k=1,2,...,99 $$
(2)

where L − k is percentile lower limit k, n indicates the size of the set, F k is the accumulated frequency for k − 1, f k measures the frequency of percentile k and c is the size of the percentile interval (1 in this case).

As the images can include noisy artifacts due to capture devices or pathologies, a cleaning step is then applied. All isolated detections smaller than a given size are removed from the results. Finally, as this strategy can produce discontinuity inside the vessels, a final dilation process is applied with the result that vessel borders grow towards the center, filling the existing gaps. This dilation process is done using a modified median filter. In order to avoid an erosion when the filter is applied to the external border of the vessels, the resulting value will only be set if it is a vessel pixel. To “fill” as many white gaps as possible the dilation process is applied iteratively, repeated N times to guarantee the filling of the vessels. Figure 3 illustrates this vessel segmentation approach with an example.

Fig. 3
figure 3

Segmentation process of the vessel tree. a Original image. b Result after pre-processing, enhancement, hysteresis thresholding and cleaning of small structures. c Final result after dilation step

Full size image

2D segmentation methodologies typically present cumulative errors as they misrepresent the edges of the vessels. For that reason, their direct use for vasculature reconstruction is not recommended. Instead, proposals that identify the centerline of the vessels are desired to correct possible deviations in the detections. Firstly, our proposal identifies the vessels as a set of segments that identify the approximate centerlines. We used the strategy explained in [25] where curvature level curves are used to identify the creases (crest and valley lines) that identify the vessels. In particular, Level Set Extrinsic Curvature (LSEC) was implemented in this work, Eq. 3, given its invariant properties. The result of this method identifies the entire centerline of the vessels, a kernel structure that is subsequently used in the 3D vessel reconstruction. Given a function \(L:\mathbb {R}^{d} \rightarrow \mathbb {R} \), the level set for a constant l consists of the set of points x|L(x) = l. For 2D images, L can be considered as a topographic relief or landscape and the level sets as its level curves. Negative minima of the level curve curvature k, level by level, form valley-like curves and positive maxima ridge-like curves.

$$ k = (2L_{x}L_{y}L_{xy} - {L_{y}^{2}}L_{xx}-{L^{2}_{x}}L_{yy})({L_{x}^{2}}+{L_{y}^{2}})^{-\frac{3}{2}} $$
(3)

where

$$ L_{\alpha}=\frac{\partial L}{\partial \alpha}, L_{\alpha \beta} = \frac{\partial^{2} L}{\partial \alpha ~ \partial \beta}, \alpha, \beta \in {x,y} $$
(4)

However, the usual discretization of LSEC is ill-defined in a number of cases, giving rise to unexpected discontinuities at the center of elongated objects. Due to this, the Multilocal Level Set Extrinsic Curvature with Structure Tensor, MLSEC-ST operator, originally defined [20] for 3D landmark extraction of CT and MRI volumes, is used:

$$ k = -div(\bar{w}) = - \sum\limits_{i=1}^{d} (\frac{\partial \bar{w}^{i} }{\partial x^{i}} ), d=2; $$
(5)

where \(\bar {w}^{i}\) is the component at the position i of \(\bar {w}\), the normalized vector field of \(L : \mathbb {R}^{d} \rightarrow \mathbb {R}\). This last is defined by Eq. 6, where O d is the d-dimensional zero vector.

$$ \bar{w} = \left\{ \begin{array}{c l l} \frac{w}{\Vert w \Vert}, & if &\Vert w \Vert > 0 \\ O_{d}, & if & \Vert w \Vert = 0 \end{array} \right. $$
(6)

Although the method finds the approximate centerline, it detects more than 1-pixel width vessel segmentations as the vessels present different degrees of creaseness over their structure. All the detected pixels are subsequently assigned to a particular segment to guarantee that all of them only belong to a single one. In this way, we obtain a skeletonized vessel tree, organized by a set of segments that are represented by two end points and a list of consecutive pixels. Finally, small segments are filtered from the results considering that these detections belongs to other noisy structures that can appear in the eye fundus, as shown in Fig. 4a–c.

Fig. 4
figure 4

2D vessel tree extraction process. a Input retinography. b 2D Vessel tree segmentation. c Skeletonized segments. d Detected end points. e Bifurcations to be corrected. f Crossings to be corrected

Full size image

2.2 Intersections correction

The crease procedure presents a significant limitation due to the many problems it experiences in correctly identifying vessels at intersections. This occurs because the method is unable to identify the crease directions in these areas, as shown in (Fig. 4d). All these intersections are revised to correct any wrong detection. The main objective consists of recovering, by joining segments, the information lost in the crease extraction phase. Hence, all detected end points are categorized as either belonging to a bifurcation, belonging to a crossing or being correctly identified as an end.

  • Bifurcations. For each end point, the closest distance to any other segment is calculated and those under a given threshold are marked for joining in a bifurcation of a single vessel. The identified end point is connected to this closest segment by interpolation using its own continuity. Figure 5 illustrates the situation with an example of a bifurcation and the correction that was performed in the intersection.

  • Crossings. Two end points that are significantly close to a crossing segment. When a pair of end points is within a given threshold, the continuity between them is considered. In this case, the points are connected by interpolation and belong, as a result, to a single segment. Figure 6 presents an example of crossing and the corresponding correction.

Fig. 5
figure 5

Example of a detected bifurcation and the corresponding correction made

Full size image
Fig. 6
figure 6

Example of a detected crossing and the corresponding correction made

Full size image

The end points that are neither marked as bifurcations nor crossings are directly considered as correctly detected end points. Figure 4d–f shows an example of the process of analysis and correction of end points.

2.3 Caliber estimation

In addition to vessel coordinates, we also need to determine their calibers for the 3D reconstruction. The orientation of a vessel at a coordinate, 𝜃, is calculated as the angle between consecutive vessel points P 1(x 1,y 1) and P 2(x 2,y 2) as:

$$ \theta = arctan \left( \frac{y_{2} - y_{1}}{x_{2} - x_{1}} \right) $$
(7)

The caliber is then estimated in the perpendicular directions of 𝜃, as Fig. 7a illustrates. We analyze the initial vessel segmentation image was previously obtained by the crease method to find the width at each point. Hence, the method looks for the edges (limits of the vessel) in each perpendicular direction, an easy process in a binary image. Finally, two distances, r 1 and r 2, are calculated as the distance from the centerline to the edges. Their sum indicates the final caliber at the point in question:

$$ d = r_{1} + r_{2} $$
(8)

Vessel caliber is searched in both directions as the detected centerlines are not always exactly placed in the center of the vessels, as is the case of the example shown in Fig. 7b. Therefore, the sum of both distances produces a more accurate estimation of a vessel’s caliber.

Fig. 7
figure 7

Diameter estimation. a Representation of the analyzed direction at each point of a segment. b Example of a segment overlapping the vessel

Full size image

2.4 Mapping in the OCT images

The depth position of the vessels, z, is calculated using the depth information that is provided in the OCT sections.

In the OCT images, any structures that appear in the eye fundus, in our case vessels, block the transmission of light and therefore leave a shadow proportional to their size. Figure 8 includes an OCT image where the shadows of several vessels are delimited.

Fig. 8
figure 8

Example of the shadow projection caused by a set of vessels

Full size image

Each OCT section corresponds to a band in the 2D retinography. The positions of the vessels in the OCT sections are represented by the intersections of the band and the vessel tree in the 2D retinography. These intersections identify the columns of the band where the vessels are located, and are mapped in their corresponding OCT sections. A search is made for intersections in the retinography in all the bands that correspond to the OCT sections, making it possible to identify all the columns of the OCT sections in which vessels are to be be found. This process is repeated for all the bands in the 2D retinography that correspond with the OCT sections. Then, a rectangle with the same size as the calculated caliber is constructed, r 1 + r 2, that matches with the projection zone, or in other words with the shadow produced by the vessel. This process is illustrated in Fig. 9.

Fig. 9
figure 9

Mapping process of vessel coordinates in OCT. Identification of the projection zone

Full size image

This projection zone, delimited by the constructed rectangle, contains the vessel location. By identifying its position we can derive the corresponding depth z of the vessel coordinate. Figure 10 includes the location of a vessel inside the projection zone of the OCT section.

Fig. 10
figure 10

Vessel location inside its projection zone in a OCT band

Full size image

2.5 Vessel depth estimation

The method calculates the depths, z, in three progressive stages:

Identification of the ILM and RPE layers

Inside the projection zone, we can restrict the search region to the retinal layers that delimit the possible vessel location. This search space is enclosed by the Inner Limiting Membrane (ILM) and the Retinal Pigment Epithelium (RPE) retinal layers. Figure 11 identifies the ILM and RPE inside an OCT section of an OCT image.

Fig. 11
figure 11

ILM and RPE layers inside the section of an OCT image

Full size image

Firstly, a Gaussian filtering is applied to smooth the image and remove noise. As both ILM and RPE show the edges with the largest contrast of all the layers, Canny edge detector is then applied to find these limits. A horizontal gradient is used to obtain the strongest and clearest detections of both layers. As a result, the upper and lower connected lines delimit both ILM and RPE layers. Figure 12 includes the results of the detection of both layers.

Fig. 12
figure 12

Identification process of the ILM and RPE layers in a OCT section

Full size image

Vessel location

The vessels appear in the OCT images as dark elliptic areas. Therefore, we search for the darkest neighborhood between ILM and RPE layers. The darkest point of the darkest neighborhood is marked as the vessel center (Fig. 13). To reinforce the detection, a mean filter of 3 × 3 size is previously used to remove possible noisy dark pixels and minimize the risk of wrong detections.

Fig. 13
figure 13

Vessel detection in an OCT section inside the search region between ILM and RPE layers

Full size image

Final depth estimation

Finally, the depth coordinate z is derived using the RPE layer as baseline and calculating the distance from it to the detected location of the vessel:

$$ z = \lvert C_{v} - P_{i} \rvert $$
(9)

where C v measures the the vessel location in the OCT section and P i the baseline of the RPE layer.

2.6 3D vasculature reconstruction

The vessels are represented by segments S, where each point P i of a segment S is represented by the 3D coordinates (x,y,z) and its diameter d, parameters that were previously calculated. Interpolation by splines is used with the entire set of points of S connecting them in a curve. This permits a smooth representation to be visualized, minimizing abrupt transitions between vessel coordinates of consecutive OCT sections in images with low OCT image resolution.

The vasculature is reconstructed as tubular shapes (due to the tubular structure of the vessels) centering on the centerline points P i with a diameter size equivalent to the calibers, d. Figure 14 illustrates this 3D representation process over a curve.

Fig. 14
figure 14

Representation of a 3D tubular structure associated to a curve

Full size image

3 Results

The proposed method was validated with an image dataset of 991 OCT sections from 21 patient scans. The local ethics committee approved the study and the tenets of the Declaration of Helsinki were followed. These images were captured with a Spectralis ®; OCT confocal scanning laser ophtalmoscope from Heidelberg Engineering. The image acquisition was done by selecting the dense volume scan type over a scan angle of (20∘× 20∘, roughly 6 mm × 6 mm) consisting of 49 B-mode scans acquired utilizing Automatic Real-Time (ART Mean) = 16 (number of scans averaged). B-mode scans are separated by 120 μm between each other and composed of 1024 A-mode scans, with a separation of 5.5 μm. Each A-mode scan has 496 pixels with 3.8 μm resolution. The system acquires the images at a given frame-rate (8.8 frames/second) and with a given bit depth (32-bits). The images, all centered on the macula, were taken from both eyes. OCT scans centered on the macula are widely used since clinicians employ this imaging modality to study this specific region of the eye fundus in the context of different pathologies.

Given the complexity of the manual segmentation of the entire vessel tree, we did not carry out a global analysis of the entire vasculature automatic segmentation process. Instead, specific tests of key steps of the methodology were performed to provide a more insightful idea of the robustness of the defined stages.

Intersections represent one of the most difficult structures of the vasculature. For that reason, we analyzed the performance of the intersections correction process to determine the extent to which the method is capable of correctly representing these complex vasculature regions. Eighty-seven crossings and 222 bifurcations were manually annotated by a specialist from within the image dataset. Then, we analyzed whether the method identified them correctly using the manual labeling as a reference. The metrics obtained are presented in Table 1, including the accuracy, sensitivity, specificity and the Matthews correlation coefficient (MCC). As we can see, satisfactory results were achieved. Figure 15 includes different examples of intersections that were correctly handled by the methodology. In particular, Fig. 15 Row 1 includes four complex crossings, with vessels that are significantly close to each other, including a highly complicated case of a multiple crossing involving several vessels. Figure 15 Row 2 shows a heterogeneous set of bifurcations including a double chained intersection and another bifurcation with a close crossing that could interfere with the correct identification of this junction.

Table 1 Results of the intersections correction process
Full size table
Fig. 15
figure 15

3D visualization of intersections correctly managed. Row 1: examples of crossings. Row 2: examples of intersections

Full size image

Another crucial stage is that of vessel caliber estimation. In order to measure the performance of our method in this respect, we constructed a test set with 220 random points from 24 segments , also randomly selected. Again, a specialist annotated the diameters of the selected points to use as a reference to test the performance of this automatic stage of the proposal. At each point, the corresponding error is calculated as:

$$ Error = d_{e} - d_{c} $$
(10)

whereas the relative error is:

$$ Relative\_Error = \frac{d_{e}-d_{c}}{d_{e}} $$
(11)

where d e is the annotated diameter and d c is the diameter resulting from the method. Table 2 presents the errors obtained by the caliber estimation process.

Table 2 Errors obtained by the caliber estimation process
Full size table

The next step is vessel mapping in the OCT sections. We conducted another experiment to quantitatively validate the vessel mapping process. A set of 1,348 mapped points randomly taken from the entire image dataset was selected for validation. In this case, a success is considered to be where a point is mapped by the method within the annotated projection zone. The results, shown in Table 3, indicate an accuracy of over 86%. Figure 16 shows four successful mapping examples including the corresponding projection zones in the OCT sections.

Table 3 Results obtained for the vessel mapping and depth calculation stages of the methodology
Full size table
Fig. 16
figure 16

Vessel mapping in the OCT sections. a Near-infrared reflectance retinography with the intersection of vessels at the band of an OCT section. b Identification of the projection zone of a mapped vessel point

Full size image

A further test was designed to validate the robustness of the depth estimation. An expert clinician segmented the vessels in the OCT images, constructing a set of 1,561 annotated vessel points that were randomly selected. The gold standard establishes that a success is considered to be when the location result falls inside the manual segmentation. As presented in Table 1, a success rate of 91.80% was obtained, demonstrating the robustness of the proposal. Figure 17 presents eight examples of correct vessel identifications inside the projection zones. Figure 18 includes three examples of final 3D reconstructions. They illustrate the potential of the 3D extraction and reconstruction of the arteriovenous tree with respect to classical 2D segmentations for further analysis and diagnostic processes. In general terms, and in the opinion of the experts, the method offers correct and promising results, providing an innovative 3D vasculature view that constitutes a better representation of the real layout of the vessels than that given by classical 2D representations.

Fig. 17
figure 17

Examples of correct vessel depth identifications. Row 1: vessels to be located. Row 2: obtained detections

Full size image
Fig. 18
figure 18

Final 3D reconstructions of the vessel tree. 1st column: original images. 2nd column: final 3D reconstructions

Full size image

4 Discussion

The identification of the vasculature in the near-infrared reflectance retinography guarantees the use of a robust and proven methodology to identify the locations of the vessels, even in the case of the identification of small vessels, a typical situation in the macular region. This way, we only map the vascular profiles in the OCT sections and calculate their depth, using the spatial coordinates and their caliber. The support of the near-infrared reflectance retinography, provided directly by the capture machine in combination with the OCT sections, greatly facilitates this work, with only those areas in the sections that belong to real vessels being analyzed.

This methodology takes OCT images focused on macula as its input. The macular region includes the smallest and most tenuous vasculature of the retina, and for this reason we consider that the tests were carried out in one of the most complex scenarios available. In other areas the vessels are thicker and more visible, presenting a higher contrast that facilitates their detection.

The method was tested under a set of images that were captured from healthy individuals and patients presenting diabetic retinopathy or hypertension, proving the capability of the method to identify the vasculature under a large variability of conditions. These conditions may produce changes mainly in the vascular calibers (thickening, narrowing or appearance of small protuberances) or in the vascular structure (increased tortuosity or neovascularization). These changes do not alter the vessel visualization in the retinography as well as the shadow projection in the OCT sections. In addition, the three-dimensional visualization of the real layout of the vasculature that this method provides facilitates the analysis and identification of these changes.

As no other complete 3D methods have been published to date we are unable to perform any kind of comparison with other proven approaches. Instead, we used the opinion of expert clinicians to identify the relevant stages of the method and test its performance, validating its accuracy as compared to manual annotations by the experts at key stages of the methodology.

Most of the errors came from complex intersections more often than not involving more than two segments. Examples of this can be found in Fig. 19, where two intersections that were not correctly included are presented. The columns represent the original vessel detection, the final results of the method and the desired results, respectively. In the case of Fig. 19 Row 1, as we can see from the desired result, the analyzed region belongs to a junction of 3 different vessels. Two of them constitute an intersection but the third belongs to the end of a vessel, with no real final connection. However, given the proximity of this end point, the method interprets that another intersection exists. Figure 19 Row 2 shows a particular case where the method interprets two different bifurcations instead of a crossing.

Fig. 19
figure 19

Examples of intersections incorrectly managed. 1st row, bifurcation. 2nd row, crossing. a Vessel detection before intersection correction. b Corrected vasculature. c Desired result

Full size image

Normally, methodologies for retinal vasculature identification omit tiny vessels in the image. In the case of our method, we consider it important to mention the high rate of detection of vessels appearing in the macular region, a region of the eye fundus where vessels are smaller than in the rest of the retina. The errors in caliber estimation are presented in Table 2. Given the complexity of the images, with a significant noise level and blurred vessel contours, it is often highly complicated to exactly detect the limits. For this reason, a relative error rate in the estimation of vasculature calibers of about only 4% can be considered to be more than acceptable.

Figure 20 includes two incorrect mapping examples. Most of the failures tend to occur when the detected vessel is elongated in parallel to the band of the OCT sections. In these cases, the method is not capable of correctly matching the exact point of the intersection. This situation could be minimized through the use of higher resolutions, which could help to discriminate the exact intersection points. Alternatively, OCT sections in the perpendicular direction or radial directions, as provided by some capture machines, could also help to minimize these errors.

Fig. 20
figure 20

Examples of incorrect vessel mappings in the corresponding OCT sections. a Near-infrared reflectance retinography with the intersection of vessels at the band of a OCT section. b Identification of the projection zone of a mapped vessel point

Full size image

We also present a number of incorrect detections in the vessel location phase, as shown in Fig. 21. In this case, although the method finds the darkest spot between the ILM and RPE layers, it belongs to noisy artifacts or overlapping vessels, not to the target vessel. Incorrect detections are on the whole mainly due to (1) noisy artifacts or vessels that are too close to and appear in the same region of the OCT section as the target vessel position; (2) alterations of a particular layer producing dark regions that can be confused with a vessel; and (3) the impossibility of detecting the dark spot of a vessel. In the latter case, this is because vessels are at times located in parallel to the OCT section and thus do not produce the typical dark spot that identifies a vessel.

Fig. 21
figure 21

Examples of wrong vessel depth identifications. 1st column, vessels to locate. 2nd column, results: red circle, the obtained vessel location: green circle, real vessel location

Full size image

5 Conclusions

This work presents a new fully automatic methodology to obtain the 3D segmentation and reconstruction of the retinal arteriovenous tree using OCT images. A 3D representation offers a more complete set of information for the analysis of the retinal microcirculation, in contrast to the 2D visualizations of classical retinographies, enabling more accurate analysis and diagnosis in different clinical procedures. Vessel tree analysis is crucial for the early diagnosis of several relevant diseases such as nicking (AV nicking) or retinal vascular tortuosity. AV nicking is the situation where a small arteriole is swollen or dilated and crosses over a vein compressing it and is a highly relevant indicator in prevalent conditions that alter the caliber of vessels. For its part, retinal vascular tortuosity indicates the degree of elongation or bending of the retinal vasculature. Both are signs of hypertension, arteriosclerosis or other vascular conditions and a 3D representation of the vessels can lead to more accurate identifications and measurements of both indicators.

The proposed method covers the entire automatic segmentation process: initial 2D vasculature identification, caliber estimation and mapping in the OCT images to calculate the depth coordinates. Finally, the method uses the resulting (x,y,z) vasculature coordinate set combined with their calibers d to reconstruct the entire vessel tree. The proposed approach was validated with 21 patient scans summing an image dataset of 991 OCT sections with their corresponding near-infrared reflectance retinographies. Key stages of the methodology were tested, providing coherent and promising results.

In future works, we plan to analyze and improve the different stages to achieve higher success rates. Automatic artery and vein classification is also planned for inclusion, adding valuable information to retinal microcirculation analysis in any diagnostic process. Images with perpendicular or radial sections will also be tested with the aiming of reducing the limitation of the method in its application in the same direction, in all cases. In addition, further validations will be made in the other areas of the retina, to confirm the accuracy of the proposal with bigger and cleaner vessels. Despite the difficulties, we will also inspect new methods to extract the vascular structure directly in the OCT sections, using only these images for the whole 3D reconstruction process and thereby avoiding the multimodality dependence of near-infrared reflectance retinography. The identification of the three-dimensional structure or the retinal vasculature could serve as input in posterior clinical studies that may involve the calculation and analysis of different measurements, as tortuosity or the arterio-venular-ratio. These measurements were typically calculated in two dimensions, mainly in the analysis of classical retinographies. Extension to three dimensions could be achieved using the real layout of the vasculature that may lead to more precise analysis and diagnosis.