Sixty subjects were tested to assign orientation to 10 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 two ways of estimation of the orientation were used. It was demonstrated that the assignment of orientation to the patterns did not depend on their position in the visual field, as well as on the method of estimation used. A quantitative measure for the elongation of a dot pattern has been proposed, which correlates with the degree of unambiguity in the estimation of the orientation of the pattern: the greater the elongation the smaller the standard deviation of the estimates given by the subjects. The same holds true for the dependence of the standard deviation on the dot number for dot patterns with equal elongations. The data obtained support the hypothesis that the assignment of orientation to dot patterns results from a process of optimization that takes place in the visual system.