Introduction
In your textbook, you read about the ability of the visual system to achieve color constancy—discounting the effects of lighting conditions to determine the true color of objects in the world. This activity demonstrates a similar phenomenon—lightness constancy. Here, the goal is to determine the actual reflectance of surfaces in the world—the proportion of light (of any color) that is reflected off each surface, despite variations in lighting. A white piece of paper has high reflectance (most of the light that hits it bounces right back), while the reflectance of a chocolate bar is low (most of the light that hits it is absorbed, and little is reflected). The white paper seen under dim lighting conditions may in fact reflect fewer photons than the chocolate bar under bright light, but you still see the paper as a light surface and the chocolate bar as a dark surface. Therefore, your visual system must be taking into account the lighting conditions of the scene to figure out what the surface properties of the piece of paper or chocolate bar really are.
As with color constancy, the visual system achieves lightness constancy by applying assumptions about the way light sources and surfaces interact in the world. This activity presents three illusions that reveal some of these assumptions.
Activity Description
Each part of the activity contains multiple images. The user can click on the images to toggle between them (image numbers referred to in the explanations appear above the image).
The Folded Card Illusion
The first image shown appears to be a card folded horizontally into three sections. There is a dark gray column going vertically up the center of the card. The top and bottom folded sections appear to be facing upwards towards the light source while the middle section appears to be facing towards the observer and in a shadow. There are two dots on the card to indicate two squares that will be discussed. The blue dot is in the middle of the top row and appears to be in a square section that is dark gray. The green dot is in the right square of the middle row and appears to be in a section that is light, but has a dark cast to it because it is covered by a shadow.
Which of the square regions in Image 1 appears darker, the one with the blue dot or the one with the green dot? The one marked with the blue dot in the top row seems darker. In fact, however, the two are identical, which becomes obvious in Image 2 (the user can click on the image to toggle between Images 1 and 2). In image 2, the central square (which was originally dark gray) is changed to appear bright white. The consequence is that the middle row no longer appears to be in a shadow, and instead the surface appears to be facing the other way! Whereas the center row of the card appears to be in a shadow in image 1, it appears instead to be facing towards the light source in image 2, having no shadow any longer.
Folded Card Illusion Explained
The visual system has a strong inclination to perceive Image 1 as a folded card. As one scans the image from left to right, the changes in brightness from the leftmost to the central to the rightmost squares appear to be caused by moving from a lighter portion of the card to a darker portion and then back to a lighter portion. That is, the visual system makes the assumption that there is a dark vertical stripe printed on the card, and that changes in luminance from left to right in the image are due to changes in the surface reflectance of the card.
On the other hand, if one scans the image from top to bottom, the visual system assumes that the changes in luminance are due to lighting shifts caused by the folds in the card, not to changes in surface reflectance. The middle section of the card appears to be in a shadow, which means that the light source is above the card. This is a reasonable assumption to make: the card clearly seems to be folded, and it is unlikely that the folds occur exactly at points where the surface reflectance changes abruptly on its own. Also, most surfaces in the world are lit from above, due to the sun, making the assumption of an overhead light source very natural (more on this in the “Bumps and Dimples Illusion” next). Based on these assumptions, the square with the blue dot is seen as part of the dark stripe in the light, while the one with the green dot is seen as a lighter surface in the shadow. Even though the areas are equally bright, your visual system cannot discount the perceived difference in lightness, so the two squares do not look identical.
In Image 2, the central square is changed to white, eliminating the perception of the dark central stripe, and thus the interpretation of the middle section as being covered by a shadow. Now, the entire surface seems to be illuminated equally. The visual system has no choice but to assume that all the luminance changes in the image are due to changes in surface reflectance rather than changes in lighting. Therefore, the squares with the blue and green dots are perceived as having equal reflectance and are seen as equally bright, eliminating the illusion in Image 1.
The card sometimes appears to switch orientations when the middle square is turned light, and this is a form of an aftereffect, similar to the afterimages discussed in Activity 5.4. In Image 1, the visual system assumed that the surface was oriented towards the right, and the neurons representing that interpretation became fatigued over time. When Image 2 appears, the other possible interpretation of the image—that the surface is facing towards the left—asserts itself more strongly because none of the neurons representing this interpretation are fatigued. The image is equally consistent with the surface facing either right or left, but if one perceived a shadow, then the interpretation that the surface is facing right was initially more probable.
Bumps and Dimples Illusion
The image in this section consists of a three by three grid of nine circles. Five of the circles are lighter on top and darker on the bottom and four of the circles are dark on the top and light on the bottom. The circles that are light on top appear to be “bumps” that are sticking out towards the observer. The circles that are dark on top appear to be “dents” that are recessed into the image. If the user clicks the image twice, the perception of the image will change. (Each time the user clicks the image, the pattern in the circles changes orientation by 90 degrees. Two clicks leads to the circles that used to be bumps appearing as dents and vice versa. The shading in every circle has changed by 180° such that the circles that used to be light on top and dark on the bottom are now dark on top and light on the bottom.)
Why does one see five bumps and four dimples in Image 1 but five dimples and four bumps in Image 3?
Bumps and Dimples Illusion Explained
These images reveal two more assumptions that the visual system makes in order to interpret changes in illumination across an image. First, we know that a portion of a surface that faces toward a light source will be brighter than a portion of the surface facing away from the light. Second, all else being equal, we assume that lighting in a scene comes from above.
In Image 1, the lightest parts of the circles in the X pattern are on top, while the darkest parts are at the bottoms of the circles. If the lighting was coming from above, these circles would have to be bumps, since this configuration would make the lighter portions of the circles face towards the light. Conversely, the other circles would have to be dimples because their bottoms are lighter than their tops.
In Image 3, the scene has been rotated 180° and therefore the situation is reversed. Still assuming the lighting is coming from above, the circles forming the X must be dimples and the other circles must be bumps.
Image 2 and Image 4 are more ambiguous. One may fail to see any of the circles in these images as either bumps or dimples. Note, however, that if one does see them as bumps or dimples, they will also see the lighting as coming from either the left or the right accordingly.
The Checkerboard Shadow Illusion
Image 1 shows a cylindrical block sitting on a checkerboard, with a light source above and to the right of the cylinder, causing it to cast a shadow over part of the checkerboard. Two of the squares on the checkerboard are marked with a dot – one in the shadow of the cylinder and one outside of the shadow. The marked square in the cylinder’s shadow appears to be a white square and the marked square outside of the shadow appears to be a black square. Would you believe that the two checkerboard squares with black dots are exactly the same brightness? Image 2 isolates the two checkers and proves that they really are identical. (If the user clicks to reveal Image 2, everything in the image except for the two squares is deleted, and the two squares are indeed the same shade of gray even though they looked to be different shades in Image 1.)
The Checkerboard Shadow Illusion Explained
As with the folded card illusion, this illusion happens because the visual system cannot disregard its interpretation of the light sources and shadows in scenes when making judgments about the brightness of surfaces. The marked square near the center of the image falls in the shadow of the cylinder. Since the visual system assumes that shadows make surfaces less bright, it boosts the estimate of the reflectance of this square accordingly. The visual system also assumes that the checkerboard pattern is regular, so that the lighter squares in the pattern are all the same lightness and the darker squares are all the same darkness. These assumptions lead it to strongly believe that the more central marked square in the shadow is lighter than the marked square on the edge of the board, so one is tricked into thinking that the former is brighter than the latter, too.
As the creator of this image, Edward Adelson at MIT says, “The visual system is not very good at being a physical light meter, but that is not its purpose.” The assumptions used by the visual system are designed to help one determine the qualities of surfaces in the world, not the light reflecting off the surfaces. It is the surfaces themselves that one wants to know about, not the particulars of how they happen to be illuminated.