Theoretical Treatment of Limitations Inherent in Simple 3D Stimuli: Triangles and the P3P Problem

Understanding the visual stimulus in a psychophysical experiment, theoretically, is critical for controlling the experiment, for interpreting the empirical results of the experiment, and for discussing the mechanisms the visual system used to get these results. This fact encourages visual scientists to use "simple" visual stimuli in their experiments. A triangle is one of the simplest stimuli that has been used by psychophysicists to study 3D perception. It has also been used to compose the polygonal meshes that represent complex 3D surfaces in computer graphics. The relationship between the shape, orientation, and retinal image of a triangle has also been studied as the Perspective-3-Point problem (P3P). In this study, the statistical properties of this relationship between the 2D retinal image of a triangle and its recovered 3D orientation were tested in a simulation experiment whose results showed that a triangle is qualitatively different from more complex shapes that have been used to recover 3D information from their retinal images. This raises an important question, namely, how many, if any, inferences about our visual system can be generalized to our perceptions in everyday life when they are based on psychophysical experiments that used very simple visual stimuli such as triangles.