Retinal vessel segmentation by a divide-and-conquer funnel-structured classification framework
Introduction
Retinal vessel segmentation is an important part of computer-aided diagnosis of retinal diseases, like arteriosclerosis, vein occlusions, and diabetic retinopathy [1], [2], [3]. A reliable assessment for those diseases can be achieved by regularly performing accurate measurement of the vessel width, tortuosity and proliferation [4], [5]. If abnormal signs are detected at early stage, timely treatment can be advised to perform on patients. Manual segmentation of retinal vessel is a tedious task that requires experience experts to annotate a huge amount of retinal images by hand, thus not feasible for large-scale research study and clinical utility. Vessel segmentation based on computer vision and image processing provides an efficient and economic benefit tool for retinal image analysis.
Many algorithms for automatic retinal vessel segmentation have been reported that can be generally divided into two groups: unsupervised and supervised methods. Unsupervised methods mainly focus on the inherent characteristic of the retinal vessel without the need of prior information from the manual annotated training data. Vessel tracking [6], [7], morphological morphology [8], [9], active contour [10], [11], [12] and graph-based approaches [13], [14], are four popular unsupervised categories for retinal vessel segmentation. Supervised methods on the basis of pixel classification rules assign each pixel to be vessel or non-vessel. K-nearest neighbors algorithm (KNN) [15], Gaussian mixture model (GMM) [16], support vector machine (SVM) [17], [18], neural network (NN) [19], [20], random forest classifier(RFC) [21], [22], are five widely used decision models in retinal vessel segmentation system. Fraz et al. [23] utilized an ensemble classifier of boosted and bagged decision trees to distinguish vessel from background. Gu et al. [24] extracted the context distance features together with the structured features for vessel classification based on the boosted tree classifier. Classification results produced by fuzzy logic, artificial NN and SVM, were fused together by Barkana et al. [25]. In [26], a cascade classification network that enveloped a set of computationally efficient Mahalanobis distance classifiers was proposed to form a highly nonlinear decision boundary for retinal vessel classification.
Deep learning based methods demonstrate superior performance in image recognition, such as semantic segmentation [27], [28], and image classification [29]. Recently, they have also been successfully applied to retinal vessel segmentation [30], [31], [32], [33], [34], [35], [36], [37], [38], [39], [40]. Yan et al. [35] jointly adopted both the segment-level and the pixel-level losses to train the deep learning network. Oliveira et al. [36] combined the stationary wavelet transform with a multiscale fully convolutional neural network for vessel structure delineation. Hu et al. [37] applied a multiscale convolutional neural network with an improved cross-entropy loss for retinal vessel detection. Yan et al. [38] divided the vessel segmentation task into three sub-tasks, each of which was trained by a deep learning model using a unique pixel-wise loss. Yu et al. [39] used the segmentation result generated by deep neural network to hierarchically divide retinal vessel tree. Feng et al. [40] proposed a cross-connected convolutional neural network (CcNet) for the automatic retinal vessel segmentation.
Supervised methods usually perform better than the unsupervised ones on retinal vessel segmentation. Nevertheless, the decision boundary between vessel and non-vessel is sometimes hard to be determined. Fig. 1 shows intensity profile of cross section of three representative vessel samples. Intensity profile varies with the vessel scale, e.g. vessels with large scale tend to be darker than those with small scale. In addition, since vessels almost never have ideal step edges [41], intensity of vessels near the center differ from those located at edge. Previous methods treat all vessel pixels equally and train a global discriminative model for retinal vessel detection. The large geometrical structure difference among retinal vessels with different scale and position greatly limits the precision of the decision boundary of the global discriminative model.
Motivated by that it is extremely difficult to handle the large variation of vessel pixels by learning a single global discriminative model, we develop a novel divide-and-conquer funnel-structured classification framework for retinal vessel segmentation. Main contributions of our work include: first, we propose a multiplex vessel partition method to divide the retinal vessel pixels into well constrained subsets where vessel pixels with similar geometrical property are assigned together. This multiplex vessel partition method decomposes the complex vessel pixel pattern into a number of homogeneous patterns, making each of them easier to be classified from the non-vessel pixels. Thus, a set of homogeneous classifiers are trained in parallel to form discriminative model for each subset. Training a retinal vessel model in each subset leads to two benefits: one is that it reduces the computation cost like time and storage and the other is that it makes the vessel pixels more separable from the non-vessel pixels as vessel samples in the same subset have smaller variation. Second, we propose a funnel-structured vessel segmentation framework to reclassify the uncertain samples caused by imperfect data partition in the dividing phase. This further enhances the complexity and discriminative capability of the decision model. Our approach achieves high performance for retinal vessel segmentation consistently on all three diverse databases, better than the state-of-the-art methods. To the best of our knowledge, this is the first published work for retinal vessel segmentation under a funnel-structured segmentation framework with the divide-and-conquer strategy. In addition, the proposed framework can also be extended to other general image segmentation tasks.
Section snippets
Proposed method
In this section, we describe the details of our proposed hierarchical architecture for retinal vessel segmentation based on divide-and-conquer strategy. The proposed divide-and-conquer funnel-structured architecture is shown in Fig. 2. First, we propose a multiplex vessel partition (MVP) method to divide retinal image pixels into 6 subsets on the basis of their geometric property, i.e. three scales (small, medium, and large) and two positions (edge and center) for each scale. For each of the 6
Materials
To evaluate the performance of our proposed vessel segmentation framework, extensive experiments are performed on four standard publicly available databases:
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The DRIVE database [15] contains 40 color fundus images (565 × 584 pixels) captured by Canon CR5 nonmydriatic 3 charge-coupled-device cameras at 45∘ field of view. This database is divided into two sets: training set and test set, and both comprise 20 fundus images. Two manual segmentations for each image in test set are provided, and the
Conclusion
In this paper, we have proposed a new divide-and-conquer funnel-structured classification framework for retinal vessel segmentation. By dividing the retinal vessel pixels into well constrained subsets where samples with similar geometrical property are grouped together, the sample variation in each subset is largely reduced. This decomposes a complex classification problem into a number of relatively simpler ones. Training a set of homogeneous classifiers in parallel not only reduces the
Conflict of interest
None.
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