Automatic Annotation of Retinal Layers in Optical Coherence Tomography Images

OCT imaging [17] has become one of the best tools for diagnosis of retinal diseases [21]. Time-Domain OCT (TD-OCT) is one of the first modalities used in retinal diagnosis, however due to it’s shortcomings the Spectral-Domain OCT (SD-OCT) [11, 49] was introduced to handle these limitations. Since its introduction various protocols and modalities based on TD-OCT, SD-OCT, FD-OCT and different machines such as Stratus, Spectralis, Cirrus, Optovue etc and their various versions provides variety of information regarding retinal layer anatomy. The segmentation of various retinal layers from OCT is vital for tracking progress of medication and diagnosing various ocular diseases, in particular for Diabetic Retinopathy, Glaucoma and Age Related Macula Degeneration (AMD). This is especially intriguing as they are not noticed early enough by the patient, and usually cause irreversible impairment. Manual OCT segmentation is tedious, time-consuming, and suffers from inter- and intra-rater variability. Automated segmentation, on the other hand, holds the potential to reduce the time and effort required to delineate the retinal layers and also to provide repeatable, quantitative results. Additionally, considering the large number and variety of images which exist, it is not sustainable commercially to develop a new algorithm for each application [48].

In OCT images, two main kinds of noise exists i.e the speckle noise during acquisition and the shadows of blood vessels. Speckle noise in OCT images causes difficulty in the precise identification of the boundaries of layers or other structural features in the image either through direct observation or use of segmentation algorithms [1, 28]. The noise that corrupts OCT images is non-Gaussian, multiplicative and neighborhood correlated. Thus, it is not easily suppressed by standard software denoising methods [27]. Since OCT images are highly corrupted by speckle noise, some pre-processing steps are usually performed to reduce the effect of noise. In most cases, even though the segmentation algorithms are designed to handle uncertainties and noise, the pre-processing is used as a first step to handling the noise, irrespective of whether the analysis to be performed is in 2D [4, 21, 42] or 3D [43, 45, 46], in order to remove the speckle noises and enhance the contrast between layers. Usually the de-noising is achieved by using the 3D anisotropic diffusion method, 3D median filter, 3D Gaussian filter or 3D wavelet transform [47]. Previous attempts including spatial and frequency compounding techniques have been used to address the problem of speckle noise in OCT [18, 30] . However, the tolerance or adaptability of these techniques are limited, which then complicates the analysis stage. They are also quite sensitive to the choice and fine tuning of various parameters [36, 37].

On the other hand, a number of digital filters have been used for speckle suppression on OCT images, such as median filtering, wavelet-based filtering that employs nonlinear thresholds, anisotropic diffusion filtering [12] , and nonlinear anisotropic filtering [15]. While most of these methods are effective in reducing speckle noise, some of them tend to blur the structural boundaries in the OCT image. As a matter of fact, most of these algorithms use a defined filter window to estimate the local noise variance of a speckle image and perform the individual unique filtering process. The result is generally a reduced speckle level in areas that are homogeneous. But the image is either blurred or over smoothed due to losses in detail in non-homogeneous areas like edges or lines. Also, the conventional algorithms in OCT segmentation do not consider the intensity inhomogeneity in the image which can lead to inaccurate segments and inability to detect all layers. Clearly, the primary goal of noise reduction is to remove the noise without losing much detail contained in an image [36]. We propose a method, that preserves the edge information, and improve the visibility by hyperbolizing the image. This improves homogeneity of pixel values in every layer, which consequently improves performance of the segmentation method, and makes our method applicable, for diagnosis and tracking medication progress of ocular diseases.

The segmentation of retinal layers has been an area of active research and has drawn a large number of researches since the introduction of OCT. Various methods have been proposed, some with focus on the number of layers to be segmented, others on the computational efficiency. Segmentation of retinal images is challenging and requires automated analysis methods. In this regard a multi-step approach was developed by [2]. However the results obtained were highly dependent on the quality of images and the alterations induced by retinal pathologies. A 1-D edge detection algorithm using the Markov Boundary Model [23], which was later extended by [3] to obtain the optic nerve head and RNFL. Seven layers were obtained by [4] using a peak search interactive boundary detection algorithm based on local coherence information of the retinal structure. Statistical methods such as Expectation maximisatin and probabilistic modelling were reported in [19, 20]. The Level Set method was used by [29, 42, 44, 46] which were computationally expensive compared to other optimization methods. Graph based methods in [14, 16, 21, 31‐35] have reported successful segmentation results, with varying success rates. Recently, a method using the Fuzzy Histogram Hyperbolization (FHH) is proposed to improve the image quality, and then to be embedded into the continuous max-flow to simultaneously segment four retinal layers [9].

Moreover, the use of gradient information derived from the retinal structures has in recent years been of interest to OCT segmentation researchers. It was utilised by [5] with the Graph-Cut method, where the retinal structure is employed to limit search space and reduced computational time with dynamic programming. This method was recently extended to 3D volumetric analysis by [38] in OCTRIMA 3D with edge map and convolution kernel in addition to hard constraints in calculating weights. They also exploited spatial dependency between adjacent frames to reduce processing time. Edge detection and polynomial fitting was yet another approach proposed to derive boundaries of the retinal layers from gradient information by [25], and machine learning by [24] with the use of random forest classifier. The utilization of gradient information on OCT images is largely based on the changes that occur at layer boundaries in the vertical direction, thereby attracting segmentation algorithms to exploit this advantage. The paths obtained by the default shortest path algorithms, have no optimal way of handling inconsistencies (such as the irregularity in OCT images), as thus it sometimes obtains the wrong paths, which we refer to as “wrong short-cuts”. To handle this issue, we reassign the weights to promote homogeneity between adjacent edges, such that transition at layer boundaries become clearer, and this contributes largely to the success of our graph-cut approach. Our method takes into account the retinal structure and gradient information, but more importantly, the re-assignment of weights in the adjacency matrix, because segmentation using graph cut methods, depends on assignment of appropriate weight.

Every image I, is represented by the following [13]: Where g_mn represents the intensity of the mn^th pixel and μ_mn its membership value, given m = 1,2,3…M and n = 1,2,3…N. In line with this, using the linear index of fuzziness, we calculated image fuzziness with [39] : where μ_I(g_ij) is the membership function of greylevel g_ij and \(\bar {\mu }_{I}(g_{ij})\) = 1 - μ_I(g_ij). This maps image greylevel intensities into a fuzzy plane using membership functions. The membership functions are modified for contrast enhancement, and the fuzzy plane is mapped back to image grey level intensities. The aim is to generate an image of higher contrast than the original image by giving larger values to the greylevels that are closer to the mean greylevel of the image than to those that are farther from the mean.

Using the concept of histogram and fuzzy histogram hyperbolization described in [40] and [41], we calculate membership value for each greylevel as: where the maximum and minimum intensity values are represented by \(g_{\max \limits }\) and \(g_{\min \limits }\) respectively. Then β as a fuzzifier and the desired grey level value L, are used to calculate the new grey values of image using the following transformation [41] : Fuzzy histogram hyperbolization is simple and straight forward, yet effective to a range of image and signal processing applications [26]. The value of β determines a number of operations that could be performed with membership modification [40]. As the value of β approaches 0, the results are similar to that of histogram equalization, whereas if β approaches values 5 and above, it tends to provide result similar to segmentation. We therefore take two issues into consideration: 1) Most image de-noising processes are sensitive to the choice of various parameters [36]. 2) The fuzzifier β modifies the membership values additionally, and so, the gray level dynamics of the resulting image can be changed [40]. Consequently, the value of β from Eq. 4 is constrained to arbitrate within a specified window by the following conditions: where \(T_{\min \limits }\) and \(T_{\max \limits }\) are the minimum and maximum acceptable values of β. To achieve the above, we introduce constant C, called the stabilizer. The stabilizer keeps the value of β within the set threshold. This allows the method to set a suitable value for the image based on the membership information without the need for user input. Of course the threshold values can always be adjusted easily, for the method to adapt to a wider range of images and applications, however, we limit our study to the enhancement of retinal OCT images to suppress and handle speckle noise and blood vessel interference. After the transformation, the image is enhanced and this has positive effect in calculating the flow. Examples of image transformations with various values of β are shown in Fig. 2. For this image, β is set to 2.2 in our experiment and will vary depending on the image.

Unlike other preprocessing methods, which reduce image quality or leads to loss of data, this method preserves edge information and adapts to OCT inconsistencies as the value is computed based on each image. This allows the method to adapt to different OCT images.

In this stage we obtain the vertical gradient of the image, normalize the gradient image to values in the range of 0 to 1, and then we obtain the inverse of the normalized image gradient as shown in Fig. 3. These two normalized gradient images are then used to obtain two separate undirected adjacency matrices, where Fig. 3a and b contains information for transitions from bright-dark and dark-bright respectively. The adjacency matrices are formulated with the following equation [5]: where w_ab, g_a, g_b and \(w_{\min \limits }\) are the weights assigned to the edge connecting any two adjacent nodes a and b, the vertical gradient of the image at node a, the vertical gradient of the image at node b, and the minimum weight added for system stabilization. To improve the continuity and homogeneity in the adjacency matrices they are hyperbolized, firstly by calculating the membership function with the fuzzy sets equation (3) [41] and then transformed with Eq. 8. where w_mn and w_mx represents the maximum and minimum values of the adjacency matrix respectively, the adjacency matrices are then transformed with the following equation: where \(w_{ab}^{\prime }\) is the membership value from Eq. 7, and β_w, the fuzzifier is a constant. Considering the number of edges in an adjacency matrix, we use a constant β_w instead of calculating the fuzziness. The main reason is to reduce computational time and memory usage. The resulting adjacency matrices are such that the weights are reassigned, and the edges with high weights get higher values while those with low values get lower edge weights. Our motive here is that, if continuity or discontinuity is re-emphasized the algorithm will perform better, where in this case we improve both. The edges connecting pixels of the same region get higher values close to each other, while those connecting pixels of the background and layer boundaries gets lower along the way. This is more realistic and applicable in this context (as the shortest path is greedy search approach), because at the boundary of each layer there is a transition from bright to dark or dark to bright, and therefore improving it aids the algorithm in finding correct optimal solutions that are very close to the actual features of interest.

The weight calculation is followed by several sequential steps of segmentation that are discussed in the next few subsections. We adopt layer initialization from [5], where two columns are added to either side of the image with minimum weights (\(w_{\min \limits }\)), to enable the cut move freely in those columns. This is based on the understanding that each layer extends from the first to last column of the image, i.e. dividing the image horizontally at each layer boundary, and that the Graph-Cut method prefers paths with minimum weights. We use Djikstra’s algorithm [6] in finding the minimum weighted path in the adjacency matrix (other optimization methods utilizing sparse adjacency matrices might be used in finding the minimum path). Graph-Cut methods are optimal at finding one boundary at a time, and therefore to segment multiple regions in most cases, requires an iterative search in limited space. Limiting the region of search is a complex task, it requires prior knowledge and is dependent on the structure of the features or regions of interest. Some additional information on automatic layer initialization and region limitation are discussed in [5, 7, 21].

It is commonly accepted that the NFL, IS-OS and RPE exhibits high reflectivity in an OCT image [5, 25, 38]. This is also evident from our previous work [9], where we segmented the four most reflective layers. Taking into account this reflectivity and the dark-bright transition we segment the ILM and IS-OS boundaries using Dijkstra’s algorithm [6]. The ILM (vitreous-NFL) boundary is segmented by searching for the highest change from dark-bright, this is because there is a sharp change in the transition, additionally it is amidst extraneous features, above it is the background region in addition to no interruption of the blood vessels, as can be seen in the gradient image. All of the above reasons make it easier to segment the ILM than other layers. We then limit the region below ILM and search for the next highest change from dark-bright in order to segment the IS-OS boundary. In most cases the ILM is segmented, but to account for uncertainties, i.e to differentiate or confirm which layer was segmented, we use the mean value of the vertical axis of the paths to determine the layer segmented, as the ILM is above the IS-OS (similar to [5].

As mentioned earlier, RPE is one of the most reflective layers. The RPE-Choroid boundary exhibits the highest bright-dark layer transition as can be seen in Fig. 3a. Additionally based on experimental results, it is better to search for the transition from bright to dark for the RPE, due to the interference of blood vessels and the disruption of hyper-reflective pixels in the choroid region. Therefore searching for the bright-dark transition is ideal for the RPE most especially to adapt to noisy images. To segment the NFL-GCL boundary,we limit the search space between ILM to IS-OS, and utilize the bright-dark adjacency matrix to find the minimum weighted path. The resulting path is the NFL-GCL boundary, as it is one of the most hyper-reflective layers. Additionally if we limit our search space to regions below the ILM and above the RPE, the resulting bright-dark and dark-bright minimum paths are the NFL-GCL and IS-OS respectively (i.e the NFL-GCL and IS-OS boundaries exhibits the second highest bright-dark and dark-bright transition respectively in an OCT image).

To segment the OS-RPE and three other boundaries (IPL-INL, INL-OPL, and OPL-ONL) from IPL to ONL, we use the prior segmented layers as benchmarks for search space limitation. We obtain the OS-RPE region by searching for the dark-bright shortest path between IS-OS and the RPE-Choroid. For the remaining boundaries, first we segment the INL-OPL, because it exhibits a different transition among the three. This is done by searching for the shortest path between NFL-GCL and IS-OS on the dark-bright adjacency matrix. Consequently the IPL-INL and OPL-ONL boundaries are obtained by limiting the region of path search between INL-OPL and NFL-GCL, and INL-OPL and IS-OS regions respectively, on the bright-dark adjacency matrix.