Two experiments are reported in which we examined the ability of observers to identify landmarks on surfaces from different vantage points. In Experiment 1, observers were asked to mark the local maxima and minima of surface depth, whereas in Experiment 2, they were asked to mark the ridges and valleys on a surface. In both experiments, the marked locations were consistent across different observers and remained reliably stable over different viewing directions. These findings indicate that randomly generated smooth surface patches contain perceptually salient landmarks that have a high degree of viewpoint invariance. Implications of these findings are considered for the recognition of smooth surface patches and for the depiction of such surfaces in line drawings.