In this paper we propose a new method for detecting straight line segments in digital images. It improves upon existing methods by giving precise results while controlling the number of false detections and can be applied to any digital image without parameter setting. The method is a nontrivial extension of the approach presented by Desolneux etal. in [1]. At the core of the method is an algorithm to cut a binary sequences into what we call a multisegment: a set of collinear and disjoint segments. We shall define a functional that measures the so called meaningfulness of a multisegment. This functional allows us to validate detections against an a contrario background model and to select the best ones. The result is a global interpretation, line by line, of the image in terms of straight segments which gives back accurately its geometry. Comparisons with state of the art methods will be performed (more examples are available on line).