Virtual and drawing structures for the Müller-Lyer illusions.

This research assessed the relative contribution of 3-D virtual structure that generated the stimulus drawings (scene-based and picture-based theories) and 2-D structure of the drawings (object-based theories). Virtual structures were right-angle convex and concave corners in front of and behind the picture plane, respectively. Virtual corner size was manipulated directly (Experiment 1) and indirectly by manipulating drawing station point distance (Experiments 2 and 3), corner depth (Experiment 4), and corner distance from the picture plane (Experiments 5 and 6). Experiments 2 and 4 held the size of the projected corner edge (interior target line) constant, causing virtual corner size to vary, whereas Experiments 3, 4, 5, and 6 held size of the virtual corners constant, causing size of the projected corner edge or interior target line to vary. Subjects reproduced the length of the projected corner edge (interior target line). The illusions (difference between reproduced size of the projected corner edge and T-junction control) were generally well fit by the weighted sum of virtual corner size and size of the projected corner edge, but the projected distance between boundary line terminations (intertip distance) appeared as an additional contributing factor in Experiments 5 and 6. The implications of this methodological approach are discussed for theories of the illusions.