The problem of detecting straight lines arises frequently in image processing and computer vision. Here we consider the problem of extracting lines from range images and more generally from sets of three-dimensional (3D) points. The problem is stated as follows. Given a set Γ of points in 3D space and a non-negative constant , determine the line that is at a distance at most ε from the maximal number of points of . The extraction of multiple lines is achieved iteratively by performing this best line detection and removing at each iteration the points that are close to the line found. We consider two approaches to solve the problem. The first is a simple approach that selects the best line among a randomly chosen subset of lines each defined by a pair of edge points. The second approach, based on tabu search, explores a larger set of candidate lines thus obtaining a better fit of the lines to the points. We present experimental results on different types of three-dimensional data (i) range images of polyhedral objects (ii) secondary structures (helices and strands) of large molecules.