Visual processing of contour curvature was investigated by measuring increment thresholds for curvatures from 0.31 to 25.4 deg-1. Curvature discrimination was assessed for three classes of stimuli: simple curved contours, high-frequency bandpass-filtered contours, and low-pass-filtered contours. High-frequency bandpass filtering had no effect on discrimination at low curvatures and only a modest effect at high curvatures. In contrast, low-pass filtering caused substantial threshold elevations at all curvatures. Thus the data lead to the surprising conclusion that high-spatial-frequency, orientation-selective mechanisms dominate curvature processing over the entire range of curvatures tested, a conclusion at odds with previous suggestions that large, low-spatial-frequency filters are involved in analyzing low curvatures. The data are explained accurately by a two-process model for curvature extraction: at high curvatures the local-processing model proposed by Wilson [J. Opt. Soc. Am. A. 2, 1191 (1985)] fits the data well, whereas at low curvatures orientations are compared at points displaced a fixed distance along the tangent to the curve.