A method for detecting curve segments in a digital image is described. The method takes as input a set of edges, and produces as output the number of and parameters for the segments. The method is robust, requiring no thresholds. In place of thresholds, a model class must be provided. Using the information-theoretic minimum description length (MDL) principle, it evaluates each model in the model class, computing the optimal parameters for that model, and selects the best model as the one that gives the shortest encoding of the data and the model. Typical of such methods, the search space is extremely large. It is shown how the Hough transform (HT) may be used to reduce this search space greatly, yielding an efficient (although suboptimal) search. The result is an algorithm in which MDL overcomes standard problems with the HT, while the HT overcomes problems with MDL, and which produces a pleasing set of line segments.