The tortuosity changes of curvilinear anatomical organs such as nerve fibers or vessels have a close relationship with a number of diseases. Therefore, the automatic estimation and representation of the tortuosity is desired in medical image for such organs. In this paper, an automated framework for tortuosity estimation is proposed for corneal nerve and retinal vessel images. First, the weighted local phase tensor-based enhancement method is employed and the curvilinear structure is extracted from raw image. For each curvilinear structure with a different position and orientation, the curvature is measured by the exponential curvature estimation in the 3D space. Then, the tortuosity of an image is calculated as the weighted average of all the curvilinear structures. Our proposed framework has been evaluated on two corneal nerve fiber datasets and one retinal vessel dataset. Experiments on three curvilinear organ datasets demonstrate that our proposed tortuosity estimation method achieves a promising performance compared with other state-of-the-art methods in terms of accuracy and generality. In our nerve fiber dataset, the method achieved overall accuray of 0.820, and 0.734, 0.881 for sensitivity and specificity, respectively. The proposed method also achieved Spearman correlation scores 0.945 and 0.868 correlated with tortuosity grading ground truth for arteries and veins in the retinal vessel dataset. Furthermore, the manual labeled 403 corneal nerve fiber images with different levels of tortuosity, and all of them are also released for public access for further research.