Contour smoothness is a fundamental constraint in the visual interpretation of images. We aimed to quantify the human visual system's intrinsic model for contour curvature and to test whether this model corresponds to that determined from measurements of natural images. We did this by measuring how well observers could estimate contours in visual noise as a function of contour curvature. Contours were generated by appending line segments that could turn 45 deg left, remain straight, or turn 45 deg right. Contour models were generated by assigning various turning probabilities. Thus, for example, one model might generate contours that tended to zigzag, and another model contours that tended to be straight. Images were generated by assigning intensity values, y, to pixels according to probability distributions p(y|on) or p(y|off) depending on whether the pixel was on or off a contour. Observers were asked to estimate the pixels belonging to the contour by tracing a path through a sample image. In a given session, the contour probability model was fixed and known to the subject. To assess subjects' use of the prior information we measured efficiency by comparing human to ideal performance for several models, i.e. several sets of contour turning probabilities. There are two plausible predictions for efficiency. If an observer uses his or her knowledge of the turning probabilities, we would expect no difference in efficiency across turning probabilities. On the other hand, if the observer uses a fixed prior model, we predict a peak in efficiency for turning probabilities matched to the observer's prior. We found: 1) efficiencies were peaked and high (50-77%), indicating use of a fixed intrinsic prior model; 2) the intrinsic prior favored straight contours; and 3) the computed turning probabilities from a set of natural image contours were also biased toward straight contours.