Sixty subjects were tested to assign orientation to ten dot patterns differing in their overall form and the number of dots in the pattern. The patterns were presented in four different positions in the visual field and their orientation was estimated in two ways. It was demonstrated that the assignment of orientation did not depend on the position of the pattern in the visual field as well as on the method of estimation used. A quantitative measure for the elongation of a dot pattern is proposed which correlates with the degree of ambiguity in orientation estimation. The greater the elongation the smaller the standard deviation of the estimates given. The distributions of the estimates for the ten patterns were analyzed. It was shown that they can be presented as superpositions of two or more groups of normally distributed estimates determined by some salient characteristics of the stimuli. Data are discussed from the point of view that assignment of orientation to dot patterns reveals the existence of optimization mechanisms in human brain that extract perceptual invariants from external stimulation.