Nonlinear features in vernier acuity

Nonlinear contributions to pattern classification by humans are analyzed by using previously obtained data on discrimination between aligned lines and offset lines. We show that the optimal linear model (which had been identified by correlating the noise added to the presented patterns with the observerÕs response) can be rejected even when the parameters of the model are estimated individually for each observer. We use a new measure of agreement to reject the linear model and to test simple nonlinear operators. The first nonlinearity is position uncertainty. The linear kernels are shrunk to different extents and convolved with the input images. A Gaussian window weights the results of the convolutions and the maximum in that window is selected as the internal variable. The size of the window is chosen such as to maintain a constant total amount of spatial filtering, i.e. the smaller kernels have a larger position uncertainty. The results of two observers indicate that the best agreement is obtained at a moderate degree of position uncertainty, ~ plus-minus one min of arc. Finally, we analyze the effect of orientation uncertainty and show that agreement can be further improved in some cases.