Statistical mechanics and invariant perception

We consider the problem of discrimination among ensembles of images generated by distortions of a prototype and the addition of noise. As the noise level is increased the discrimination task becomes qualitatively more difficult in that optimal discrimination requires the computation of increasingly longer-ranged correlations or the solution of increasingly difficult optimization problems. These results suggest the use of such image ensembles in probing the computational abilities of the human visual system, and possible theoretical implications of such experiments are discussed.