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This work presents a curvelet-based algorithm for detection of optic disk (OD) and exudates on low contrast images. This algorithm which is composed of three main stages does not require user initialisation and is robust to the changes in the appearance of retinal fundus images. At first, bright candidate lesions in the image are extracted by employing DCUT and modification of curvelet coefficients of enhanced retinal image. For this purpose, the authors apply a new bright lesions enhancement on green plane of retinal image to obtain adequate illumination normalisation in the regions near the OD, and to increase brightness of lesions in dark areas such as fovea. Following this step, the authors introduce a new OD detection and boundary extraction method based on DCUT and level set method. Finally, bright lesions map (BLM) image is generated and to distinguish between exudates and OD (i.e. a false detection for the final exudates detection), the extracted candidate pixels in BLM that are not in OD regions (detected in previous step) are considered as actual bright lesions. The sensitivity and specificity of the authors exudates detection method are 98.4 and 90.1%, respectively, and the average accuracy of their OD boundary extraction method is 94.51%.