The present study describes the structure of monocular depth perception using an experimental basis. It regards the traditional theory of perspective, which is a subset of descriptive geometry, only as a construction guide for flat, albeit depth eliciting, visual stimuli. The investigation starts with a definition of structure as a set with an automorphism on it. In the present context the projection of the physical stimuli onto the retina provide a suitable ground set. After suitable confinement of the stimuli to a horizontal plane, the effects of eye and head movements of the subject can be represented as projective mappings of the retinal image onto itself. The present approach represents these as visual automorphisms. They are each characterized by a special visual invariance. The automorphisms form a group which comprises the affine, the affine unimodular and the orthogonal groups (in this order) as subgroups. Experimental studies of the different invariants of these subgroups as well as the consideration of other empirical observations lead to the conclusion that the structure of monocular space perception is characterized by the affine unimodular subgroup of the projective group. There are indications that the phenomena of size constancy can be represented by affine unimodular maps instead of orthogonal (metric) maps as sometimes has been conjectured.