A group model of form recognition under plane similarity transformations

A structure of the normal subgroups of the plane similarity group was constructed. In this group model, the plane similarity contains two normal subgroups: the direct similarity group and the dihedral group. While the latter preserves the size of a form, the former preserves its sense. Both subgroups contain a cyclic group as their normal subgroup. An experiment in form recognition using reaction time as the behavioral index was designed and conducted to test the theory of the group structure. The experimental results agree with the group theoretical model. The images generated by a normal subgroup that preserves the sense of a form require less time to identify than those induced by a normal subgroup that preserves its size. The reversal of the sense of a form creates more instability in an image and provides less information than change of size of the form. The normal subgroup that preserves the sense and the uprightness of a form maximizes symmetries and supplies the most information. Therefore, it provides the best condition for recognition of the image of a form.