A recently developed nonlinear mathematical model for spatial pattern discrimination, which is formally analogous to line element models in color vision, was applied to a variety of hyperacuity tasks. The computed results are in reasonable agreement with data on vernier acuity as a function of line length and separation, chevron acuity, periodic vernier acuity using sinusoidal lines, three line bisection acuity, vernier acuity using cosine gratings, and spatial interference with vernier acuity. In agreement with model predictions, data are presented showing that vernier acuity improves as a power function of contrast. It is concluded that the nonlinear, contrast dependent responses of visual mechanisms tuned for size and orientation can explain a wide range of hyperacuity and other spatial pattern discrimination tasks.