This paper compares the ability of human observers to detect target image curves with that of an ideal observer. The target curves are sampled from a generative model which specifies (probabilistically) the geometry and local intensity properties of the curve. The ideal observer performs Bayesian inference on the generative model using MAP estimation. Varying the probability model for the curve geometry enables us investigate whether human performance is best for target curves that obey specific shape statistics, in particular those observed on natural shapes. Experiments are performed with data on both rectangular and hexagonal lattices. Our results show that human observers' performance approaches that of the ideal observer and are, in general, closest to the ideal for conditions where the target curve tends to be straight or similar to natural statistics on curves. This suggests a bias of human observers towards straight curves and natural statistics.