Precise characterization and analysis of corneal nerve fiber tortuosity are of great importance in facilitating examination and diagnosis of many eye-related diseases. In this paper we propose a fully automated method for image-level tortuosity estimation, comprising image enhancement, exponential curvature estimation, and tortuosity level classification. The image enhancement component is based on an extended Retinex model, which not only corrects imbalanced illumination and improves image contrast in an image, but also models noise explicitly to aid removal of imaging noise. Afterwards, we take advantage of exponential curvature estimation in the 3D space of positions and orientations to directly measure curvature based on the enhanced images, rather than relying on the explicit segmentation and skeletonization steps in a conventional pipeline usually with accumulated pre-processing errors. The proposed method has been applied over two corneal nerve microscopy datasets for the estimation of a tortuosity level for each image. The experimental results show that it performs better than several selected state-of-the-art methods. Furthermore, we have performed manual gradings at tortuosity level of four hundred and three corneal nerve microscopic images, and this dataset has been released for public access to facilitate other researchers in the community in carrying out further research on the same and related topics.