Continuous optical transformations do not elicit unique perceptual descriptions

The ceiling of the Church of St Ignatius and the perception of concave surfaces

This research describes two hitherto unobserved phenomena in the frescoes of the seventeenth century architect and painter, Andrea Pozzo, painted on the vaulted ceiling of the central nave of the Church of St Ignatius in Rome. The present research also reports the results of two experimental studies on the problem of the perception of shapes projected on concave surfaces. A quantitative evaluation of the phenomena perceived from various points of observation is made by means of stimuli projected at various angles on a semicylindrical surface. The validity of the assumption of invariance, and in particular of the projective invariant called the cross-ratio, is discussed within the framework of ecological theories on perception.

Why anamorphoses look as they do: an experimental study

The aim of this research was to understand why anamorphic images break up until they are unrecognizable when the observer's eye moves away from the regularization point. An experimental device was set up allowing the anamorphic deformation of images, consisting of a rotating screen on which figures were projected. The point from which subjects observed the screen was far from the projecting point. The projected figures lengthened equally when the screen rotated either clockwise or counterclockwise. On the other hand, the perceptual result was the opposite: in the former case, a rigid figure was seen rotating around its own vertical axis; in the latter case, the same figure was seen elongating or shortening in a non-rigid manner, without rotating. Since we were in a projective condition, the invariance of the cross-ratio was maintained. Therefore, we were in a situation of non-rigidity, in spite of the invariance of the cross-ratio. Three stimuli, white on a black background, were used in experiment 1. They were a segment, three aligned points, and four aligned points. Subjects had to rotate the screen at will and stop it at the point when they saw the transformation of movement from rigid rotation to non-rigid elongation. The results showed that: (i) in spite of being a projective invariant, the cross-ratio is not always a perceptual invariant too; (ii) the threshold screen position between the two motions was located at the position where the modifications of the solid angle subtended to the stimulus assumed a different trend from that of a sinusoid. Two stimuli were used in experiment 2: a continuous segment and one intersected by four vertical lines. The aim was the same as for experiment 1, but subjects had to repeat it from five different points of observation. The results showed that: (1) there was no significant difference depending on type of stimulus, indicating that the computability of the cross-ratio is not a necessary condition for the execution of the task; (2) the more the observer moved away from the projection axis, the more evident the distortion of the stimulus appeared, in accordance with what happens when observing an anamorphosis; (3) when the metamorphosis from rigid motion to elastic motion was seen the visual angle subtended to the stimulus was constant for all distances from the projection axis, in accordance with the hypothesis of rigidity.