Many different relaxation schemes have been proposed for image analysis tasks. We have developed a general matching procedure for comparing semantic network descriptions of images, and we have implemented a variety of relaxation techniques. An automatic segmentation and description system is used to produce the image representations so that the matching procedures must cope with variations in feature values, missing objects, and possible multiple matches. This environment is used to test different relaxation matching schemes under a variety of conditions. The best performance (of those we compared), in terms of the number of iterations and the number of errors, is for the gradient-based optimization approach of Faugeras and Price. The related optimization approach of Hummel and Zucker performed almost as well, with differences primarily in difficult matches (i.e., where much of the evidence is against the match, for instance, poor segmentations). The product combination rule proposed by Peleg was extremely fast, indeed, too fast to work when global context is needed. The classical Rosenfeld, Hummel, and Zucker method is included for historical comparisons and performed only adequately, producing fewer correct matches and taking more iterations.