Tortuosity is among the first alterations in the retinal vessel network to appear in many retinopathies, such as those due to hypertension. An automatic evaluation of retinal vessel tortuosity would help the early detection of such retinopathies. Quite a few techniques for tortuosity measurement and classification have been proposed, but they do not always match the clinical concept of tortuosity. This justifies the need for a new definition, able to express in mathematical terms the tortuosity as perceived by ophthalmologists. We propose here a new algorithm for the evaluation of tortuosity in vessels recognized in digital fundus images. It is based on partitioning each vessel in segments of constant-sign curvature and then combining together each evaluation of such segments and their number. The algorithm has been compared with other available tortuosity measures on a set of 30 arteries and one of 30 veins from 60 different images. These vessels had been preliminarily ordered by a retina specialist by increasing perceived tortuosity. The proposed algorithm proved to be the best one in matching the clinically perceived vessel tortuosity.