This paper introduces a feature based method for the fast generation of sparse 3D point clouds from multiple images with known pose. We extract sub-pixel edge elements (2D position plus associated orientation) and use a space sweeping scheme to compute the accurate 3D location of these edge features. Our approach relies mainly on the geometric properties of the extracted primitives and incorporates a robust uncertainty estimation to detect outliers. Epipolar constraints between views are used to narrow down the search space of potential candidates in the images. In order to improve the efficiency of spatial queries, for detecting edgels lying close to an epipolar line, we utilise a pairwise stereo rectification scheme. The detection and verification of tentative hypotheses is carried out in 3D-space, thus allowing to perform an event driven search mode. An uncertainty measure that models the location inaccuracies in the feature extraction process and errors introduced in the camera pose estimation stage allows to assign a likelihood value to each hypothesis. Optionally an image-based similarity measure can be used to verify the 3D hypotheses and to identify false positives. We perform experiments on a synthetic data set and on several real datasets. The results indicate that the proposed method yields accurate measurements on depth discontinuities and thus represents a complementary technique to standard dense matching approaches.