Identification of ambiguous geometric forms by human subjects with brief experience or pre-knowledge of the stimulus may call upon Bayesian specialised mechanisms. Subjects were presented with a 2-alternative forced choice between a pair of incomplete geometric figures in conditions with common and varying components. Stimuli of 1, 3, 5, and 6 pixel acuity grades were displayed in iterative order in randomised blocks at 100, 200, 260, and 360 ms exposure times, rotated or upright, under local or global viewing. Analysis of probability of correct identification against stimulus intensity, acuity demand, and stimulus duration revealed: (i) sigmoid or dipper-shaped nonmonotonic psychometric functions; (ii) Poisson-like skewed binomial distributions of errors; and (iii) category-based dependence on the stimulus and its ambiguity. This is attributable to the high uncertainty constraints imposed on tasks sharing and also varying in their stimulus parameters and dimensions. Nonlinearities shown reflect category-based strategies and attention allocation, interactions as a drive for performance stability manifested in equalisation across sub-categories and invariances of errors, with acuity demand accounted for perhaps by mechanisms of differential attention allocation. Two sources of error are apparent: (i) possibly ‘bottleneck of attention’-related and individually varying ‘blink of attention’, with small falls distributed across stimulus intensities, and (ii) ‘lapse of attention’ with large falls on easier tasks, and rightward-skewed deviations from normal Poisson-like binomial distributions ( p<0.001), the high correlation to performance effort suggesting an active process of pay-off.