In this paper, an algorithmic scheme is proposed to estimate different local characteristics of image structures using discrete geometry tools. The arithmetic properties of Digital Straight Lines and their link with the Farey sequences allow the introduction of a new directional filter. In an incremental process, it provides local geometric information at each point in an image, such as the length, orientation and thickness of the longest Digital Straight Segment passing through that point. Experiments on binary and grayscale images are proposed and show the interest of this tool. Comparisons to a well-known morphological filter for grayscale images are also presented.