In previous research, we have shown that detection thresholds for Gaussian shapes increase with a power of 1.3 of spatial width. In the present three experiments, we generalized this finding to more complex shapes and to discrimination tasks. In Experiment 1, we found that the slope of the psychometric function for detection (i.e., distinguishing curved from flat surfaces) was independent of surface shape. In Experiment 3, we found the same result for discrimination of two different curved shapes. In Experiment 2, we found that detection and discrimination functions had the same dependence on spatial width, except that discrimination thresholds were two to four times larger. Possible neural mechanisms underlying these results are discussed.