# Statistical Edge Detection and Circular Hough Transform for Optic Disk Localization
## 1 Introduction
### Optic Disk Detection Literature  
There have been many studies proposed in the literature related to the detection of the OD. These studies are mainly related to localization of the OD, which stands for detection of the location of the OD in the retinal image, and related to segmentation of the OD region, which is the extraction process of the actual region of the OD. OD detection is comprised by three categories, which are morphology-based methods, template-based methods, and deformable model-based methods. Morphology-based approaches benefit from brightness and shape properties of the OD. Therefore, boundaries of the OD can be detected by utilizing morphological operators. The shape of the OD, with some errors, was detected by morphological filtering techniques and the watershed transformation algorithm [8]. An adaptive morphological method was proposed to determine the OD and OD boundaries (rim) and was applied to the DRIVE and DIARETDB1 public datasets and compared with the success rates of other methods [9]. [PERSON] et al. [10] offered a new method for automatically segmenting the OD in fundus images based on variational models with multiple energies. Firstly, a sparse coding-based method was designed in which the initial boundary curve is estimated by the circular Hough transform to determine the OD center. Then, OD segmentation was considered as a problem of energy minimization, and a variational model combining the three energy terms to reach the limit of the OD curve was proposed. Within the second category, template-based approaches are generally interested in the shape of the OD, for example, the circular or elliptical shape. A template-matching algorithm was applied to OD segmentation in one study [11]. In another study carried out in 2004 [12], principal component analysis (PCA) and a modified active shape model (ASM) were used for model-based OD detection. The Sobel edge-detection algorithm and Hough transform were used to detect the OD and its center [13]. [PERSON] et al. [14] proposed a framework based on the density of the image and the parabolic placement of retinal blood vessels in order to obtain the OD position. In cases where the OD location cannot be detected by image density, OD localization is obtained with respect to the placement of retinal blood vessels. The approximate location of the OD is detected by finding the intersection of the thickest veins in the retinal fundus images [15]. [PERSON] et al. [16] proposed an isotropic diffusion-based method which uses an ant colony algorithm for OD localization. [PERSON] et al. [17] used a one-dimensional scanned density profile analysis for rapid and accurate localization of the OD and fovea. The proposed method effectively uses both time- and frequency-domain information for OD localization with high  
Figure 1: Anatomical structures on the retina. accuracy rates. [PERSON] et al. [18] proposed a methodology for localization of the OD center based on the staining of vessels around the OD. After detection of the center of the OD, an adaptive threshold-based region growing technique was applied to obtained points. Regarding the deformable model-based approaches, they exploit the specific characteristics of the OD. [PERSON] et al. [19] proposed a model based on the combination of probability models in order to detect the OD and its boundaries. Furthermore, they increased the accuracy of the method using axiomatic and Bayesian approximations. [PERSON] et al. [20] designed and trained a deep multiscale sequential convolutional neural network for simultaneous localization of the OD and fovea. In this deep learning method where public databases are used, the detection of the OD and fovea are done accurately and fast. [PERSON] et al. [21] focused on swarm intelligence techniques and also proposed a novel preprocessing approach called background subtraction-based optic disk detection (BSODD) for effective and fast OD localization.