## 1 Introduction  
The fovea is a small depression (about 1 mm in diameter) located in the center of the macula area of the retina [1]. Fovea detection is necessary because the grade of diabetic retinopathy depends on their distance to the fovea. Early detection and diagnosis of retinopathies decrease the risk of retinal lesion and effectively control the illness. However, due to problems of retinal image quality, such as poor contrast and physicians' subjective observation, the diagnoses can be unstable and uncertain. Computer analysis systems for retinal images can offer an efficient and stable assistance for diagnosis. The performance of the computer analysis system is generally influenced by retinal anatomy detection. The fovea is difficult to observe, but it usually is where the diabetic retinopathy occurs. The consequence of this obvious visual structure in retinal images is that fovea localization becomes very difficult. Although a great deal of research has studied this issue, there are still many restrictions to their methods. The fovea region is always darker than the surrounding retinal tissue. Previous studies searched for it directly on retinal images. [PERSON] _et al._[2] located dark pigment regions to identify the potential fovea. [PERSON] and [PERSON] [3] defined the fovea as the area with the lowest intensity. The foveae were identified by using matching correlation together with characteristics typical of a fovea, e.g., the darkest area near the optic disc, by [PERSON] _et al._[4]. However, these methods face problems when the region is covered by lesions or hemorrhages. [PERSON] _et al._[5] located the fovea as the region of minimum vessel density within a search region which is defined by the anatomical priors. This method does not require parameter adjustments for different image resolution, but it relies on the quality of vessel segmentation. In the meantime, some studies utilized the location of the optic disc (OD) and vasculature features to detect the fovea. [PERSON] and [PERSON] [6] depicted the major routes of the retinal vessels with 30 extracted landmark points, using them to fit a parabola for the fovea localization. [PERSON] _et al._[7] proposed a method for fovea localization based on the geometrical directional pattern of the retinal vascular system, which can be geometrically modeled as two parabolas with the same vertex. [PERSON] _et al._[8] also applied this model to find the horizontal raphe of the retina, which is a line passing approximately through the OD and the fovea. [PERSON] _et al._[9] described a method whereby an elliptic form of the major retinal blood vessels is used to obtain approximate locations, which are refined by the circular edge of the optic disc and the local darkness at the fovea. [PERSON] _et al._[10] used the local vessel geometry alongside the intensity information to detect the fovea. Geometrical models are usually applied for locating fovea. However, most studies based on a parabolic model often took the center of the OD as the vertex of the parabola-like vasculature. According to observation, the ideal vertex is the entry point of the main blood vessels (_i.e._, vessel origin (VO)), which is beside the OD center. Therefore, a VO-based parabolic model for fovea localization is proposed in this paper. This model takes the VO as the vertex of the parabola-like-vasculature and finds the fittest parabola with the Hough transform. The fovea is located on the symmetry axis of the parabola with a certain distance from the VO. Some studies concerning VO detection have been presented. In order to detect vessels within OD, [PERSON], _et al_. [11] roughly estimated VO by selecting the darkest 20% of pixels of the OD and taking the mean of these pixels as the VO. This paper modifies the algorithm presented in [12] and presents a novel algorithm of VO detection. This can be used to improve the detection of blood vessels in OD and the localization of fovea.