![]() The shapes of the triangle ( ω A, ω B, ω C) and the retinal image ( θ BC, θ CA, θ AB) were randomly generated in each trial by randomly sampling ω A, ω B, θ BC, θ CA, and θ AB from uniform distributions. We tested the frequencies of the number of possible 3D interpretations of the triangle ABC for the retinal image in two Monte-Carlo simulation experiments by using an algorithm developed by Fischler & Bolles for solving the P3P problem. So, an understanding of the geometrical properties of the stimuli employed is necessary if one wants to understand the difference observed between veridical and non-veridical 3D perception (see References for a discussion about the importance of Theories in Science). ![]() Theoretically, both the constraints and the cues require visual stimuli that have at least some geometrical complexity. ![]() The visual system uses a priori constraints and depth cues to establish veridical 3D perception. This difference in the veridicality of the 3D perception can be attributed to the geometrical properties of the stimuli employed. It has been shown that the 3D perception of these triangles, and dots, as well as some other very simple visual stimuli is not veridical while the perception of 3D scenes and objects “out there” is veridical in our everyday life (see References for discussions). Note that these triangles and dots are two of the simplest stimuli that have been used to study 3D perception. Triangles are commonly used to compose the polygonal mesh because a triangle is the simplest polygon that can enclose a surface that is always planar. These polygons are used to compose a polygonal mesh that represents, approximately, any complex surface of a scene and of an object. Often, there is even more reduction of the visual stimuli employed in computer vision and in computer graphics where 3D scenes and 3D objects are often represented as compositions made up of points, or of polygons. 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. 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. The relationship between the shape, orientation, and retinal image of a triangle has also been studied as the Perspective-3-Point problem (P3P). It has also been used to compose the polygonal meshes that represent complex 3D surfaces in computer graphics. A triangle is one of the simplest stimuli that has been used by psychophysicists to study 3D perception. This fact encourages visual scientists to use “simple” visual stimuli in their experiments. 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.
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