Roberto Casati, January 19, 2000
1. Old and new facts
Consider a very well-known phenomenon (already discussed by Leonardo da Vinci). Take a small object and have it cast a shadow on a white sheet of paper. Now draw a black line matching the profile of the shadow. Something striking happens under your eyes, namely:
The area where the shadow is located does not look any more like a white area darkened by a shadow, it appears grey. The grey of the area appears solid, as if it were overlaid on the sheet.
A minor side-effects of this phenomenon is that as the area is no longer interpreted as a shadow, it looks as if it is lit by an independent source of light. It is somewhat brilliant. (As the area does not seem to be in the shade, we can hypothesise that the visual system is not very fussy about knowledge about and consistency of light sources.)
Hewald Hering offered an explanation of this phenomenon: the outline destroys the penumbra, which is the phenomenological mark of the shadow character. If the penumbra goes, so does the umbra.
Carl Bühler disagreed. He pointed out that if you draw a line within the shadow, thereby leaving the penumbra intact, the shadowy character disappears as well. Thus the penumbra seems to be irrelevant. But then, what is so important about the line?
Actually, the line is not very important by itself. In the context of the study of pictorial representation, J.M. Kennedy observed that line drawing of shadows in pictures can still convey the impression of shadows, unless the area corresponding to the shadow is filled in with textures of various sorts - in which case the shadow character is destroyed.
Let me summarise the facts so far:
(1) Outlines (lines matching shadow boundaries) are sufficient in order to destroy the shadow character (figure inspired by Hering).
(2) Lines matching shadow boundaries are not necessary in order to destroy the shadow character (figure inspired by Bühler).
(3) In pictorial representation, outlines can convey the shadow character.
(4) In pictorial representation, internal texture can destroy the shadow character.
I decided to try some new operations on the shadow area so as to add some elements to the discussion. First, consider some relatively trivial modifications related to the figure-ground articulation: the shadow may appear to interrupt a line on the sheet, or the shadow can contain lines that appear to interrupted at its border. In both circumstances, the boundaries of the shadow are enhanced and the shadowy character disappears. Here again lines, although virtual (amodal) ones, may appear to play a shadow-disrupting role.
It turns out that lines are not necessary. I found that one can fill in the shadow area with small circles or crosses or dots that do not interfere with the boundary of the area but still destroy the shadow character.
(5) Virtual (amodal) lines can destroy the shadow character (figure with external lines, figure with internal lines, leopard texture).
(6) Filling in the shadow (crosses, circles, dashes) can destroy the shadow character.
I am after a hypothesis that explains (1) and (6).
2. Shadow perception: the phenomenological label
Let me add some background facts.
(9) Shadows are extremely salient in the very early stages of perceptual processing. The light gradient at the border between a shaded area and the neighbouring areas is very steep, and in many cases it overrides any other gradient in the image (most importantly, it overrides the gradient between the areas where physical object are located and the background of physical objects, which is particularly disturbing if a shadow is cast across both the object and the object's background). In spite of this lightness saliency,
(7) We seldom notice shadows (Baxandall). For instance we do not make any conscious or unconscious effort to avoid them as we walk around. On the other hand,
(8) Shadows are exploited at some level in perception to retrieve information about objects' shapes (Waltz) and locations and movements relative to a surface (Kersten et al.). A shadowless world is inhabited by relatively free-floating, shape-indeterminate entities.
We know that shadows are transitory. The shaded areas do not correspond to non-transitory properties of objects. Quite to the contrary: the object onto which a shadow is cast is likely to be uniformly coloured (or if not uniformly coloured, to coloured in such a way that does not correspond with the boundary of the shadow). It is to be expected that visual cognition is in a position to deliver the distinction between transitory and non-transitory discontinuities in the scene. To so do, the visual system must counterbalance the lightness saliency of shadows. Indeed, the whole phenomenon of colour constancy is devoted to this very task. Picture it as the following (figurative) sequence of subtasks. (A) The dark area corresponding to the shadow is cancelled out. (B) The very same area is filled in with the colour of the object. (C) The shadow is added back, and is now usable as a parameter to retrieve some of the characteristics of shape and position of the object. Observe that only at this stage, when constancy is already acquired, the shadow is usable; if treated as a colour patch, the shadow cannot inform about the shape and position of the object. (D) After use, the shadow is preserved but receives a peculiar phenomenological label: "Please dismiss me", or "I do not matter" - so as to be considered as a transitory detail. The distracting label is interesting per se, and it would be worthwhile to study its nature.
3. The hypothesis: how shadows are destroyed by an evaluation of the (un)likeliness of spatial coincidences
I daresay that it is somewhat curious and not quite optimal that shadows are not completely filtered out after use. But so it is, and we have to deal with them in the visual scene. Clearly shadows have phenomenological features of their own. Rudolf Arnheim tried out a description that is not completely satisfactory: he said that shadows are like a half-transparent film. They are not. Surely they do not appear to belong to the surface of the object. But they do not have a precise location in three-dimensional space: are they over the surface and touching it, or in the surface? Their location seems to be indeterminate. Besides, they do not have a colour of their own. Consider the question: what colour is the shadow over there? (Kardos 1934) It may sound to you as meaningless, or you may want to answer something about the colour of the object. These are then the main visual features of a shadowy appearance: indeterminate colour and location. (They are visual labels, as opposed to the non-visual label "Please dismiss me".)
These features are destroyed, and the shaded area acquires a determinate colour and location, when one performs on the area operations such as outlining or texturing.
I propose the following hypothesis as an explanation for the disruption of the shadow character. The added marks, be they outlines or textures, speak in favour of the non-transitory character of the discontinuity intervening at the shaded zone. The visual system has two pieces of information: a discontinuity related to a light gradient, and a discontinuity related to the distribution of the marks. The system decides that this reinforcement is unlikely to be a coincidence, and interprets the shaded area as a dark patch. It is unlikely that a textured or outlined area just happens to be perfectly fit the shape of a shadow passing by.
It is unclear at which stage this evaluation is made. Still it is interesting that so little is required to let the visual system discard the shadow character and prefer the patch character.
As a matter of fact, there is no need to intervene directly on the shaded area. One can modify the neighbouring area (for instance by filling it with small crosses); the visual system still interprets the shaded area as a dark patch. This prediction seems to be confirmed:
(10) External textures (crosses) destroy the shadow character.
Let it be noted that the non-shadow character is very robust in spite of some obvious conscious judgements about the overriding evidence that the area under exam is in the shade and is not an independently coloured dark patch. We may have plenty of reasons (geometric, contextual, etc.) to consider that area as a shadow, but we cannot help see it as a patch. This in turn suggests that visual processing does not include a geometric computer that may intervene at some stage and overrun the patch effect, say after assessing the geometric plausibility of the shadow. As a matter of fact, if you put side to side two objects and outline the shadow of one of the two only, the outlined shadow does appear as a patch, whereas the other is left intact (figure). Shadow perception is local in the extreme.
Bibliography
Arnheim, R., 1974, Art and Visual Perception (The New Edition), Berkeley and Los Angeles: University of California Press.
Baxandall, M., 1995, Shadows and Enlightenment New Haven: Yale University Press.
Bühler, C., as quoted by Katz, D. 1935, The World of Colour. London: Kegan Paul, Trench, Trubner.
Hering, E., 1964, Outlines of a Theory of Light Sense, Cambridge, Mass.: Harvard University Press (originally1878, Zur Lehre vom Lichtsinne, Wien: Gerold.).
Horn, B. "Obtaining Shape from Shading Information", in P.H. Winston, ed., The Psychology of Computer Vision, New York: McGraw Hill, 1975, 115-155.
Kardos, L. Ding und Schatten, Leipzig: Barth, 1934.
Kennedy, J.M., A Psychology of Picture Perception, San Francisco: Jossey-Bass Publishers, 1974.
Kersten, D., Knill, D.C., Mamassian, P., Bülthoff, I., "Illusory motion from shadows", Nature, 379, 1996, p. 31.
Waltz,, D., "Understanding Line Drawings of Scenes with Shadows", in P.H. Winston, ed., The Psychology of Computer Vision, New York: McGraw Hill, 1975, pp. 19-91.
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