Detecting blood vessels in retinal images with the presence of bright and dark lesions is a challenging unsolved problem. In this paper, a novel multiconcavity modeling approach is proposed to handle both healthy and unhealthy retinas simultaneously. The differentiable concavity measure is proposed to handle bright lesions in a perceptive space. The line-shape concavity measure is proposed to remove dark lesions which have an intensity structure different from the line-shaped vessels in a retina. The locally normalized concavity measure is designed to deal with unevenly distributed noise due to the spherical intensity variation in a retinal image. These concavity measures are combined together according to their statistical distributions to detect vessels in general retinal images. Very encouraging experimental results demonstrate that the proposed method consistently yields the best performance over existing state-of-the-art methods on the abnormal retinas and its accuracy outperforms the human observer, which has not been achieved by any of the state-of-the-art benchmark methods. Most importantly, unlike existing methods, the proposed method shows very attractive performances not only on healthy retinas but also on a mixture of healthy and pathological retinas.