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Shape from Shading

Figure 1.
Shaded spheres: Some are lighter above and therefore seem convex (domed, or pushed out). The others are lighter below, making them seem concave (dented, pushed in).

Figure 2: The Sacrifice of Isaac
Italian: Sacrificio d'Isacco
Sacrifice of Isaac-Caravaggio (Uffizi)
Artist	Caravaggio
Year	c. 1598

Shape from shading is the name given to a monocular (can be perceived with one eye only) depth cue, which imparts the ability to visually perceive an object’s shape from its shading alone, in the absence of any other information.

Many species of animal, including humans, are able to perceive the three-dimensional shape of an object from the intensity of light on its surface – its shading information. For example, the image to the right (Figure 1) contains six two-dimensional circles. Some of the circles are light at the top and dark at the bottom, and appear convex (pushed out). The others are dark at the top and light at the bottom, and appear concave (pushed in). In 1786, Rittenhouse suggested that most people would perceive the spheres in this way because they assume that the light source comes from above the objects. This perception reflects what is usually seen in the natural environment: light (e.g. from the sun or electric lights) usually falls upon the uppermost surfaces of convex objects, causing the greatest intensity of light to be at the top. In concave objects, the uppermost edge of the object obscures light that comes from above, allowing only the lower edge to catch the light.

Representing shape using shading is a common technique in art. For example, Leonardo Da Vinci is famous for his exquisite explorations of shape and shading via a technique known as sfumato, in which graduations in tone and brightness produce a soft and natural perception of depth. Similarly, paintings using the chiaroscuro technique (e.g. those by artists such as Caravaggio), exploit extremes of light and dark to create a stronger sense of depth in the images.

Scientific experiments have demonstrated that non-human animals, such as birds and primates, can perceive an object's shape from its shading, and it is assumed that most mammals experience this depth cue because of the prevalence of countershading (a type of camouflage) in nature. In countershading, light-coloured skin or fur appears on the underside of the animal, and dark at the top – this is the opposite of the expected pattern of light and enables animals to hide from predators by producing a flatter appearance.

Figure 3: A simplified example of countershading: first, the expected pattern of light intensity on an animal is shown; then, the depth of colour on the animal's skin or fur; and finally, the flatter effect this creates to help conceal the animal.

How it works

The Light Field

Visual System
Figure 4. The visual system includes the eyes, the optical nerves, and parts of the brain.
Anatomical terminology

See also: light field

Light particles (photons) are emitted from “primary radiators”, such as the sun or electric light bulbs, and travel in straight lines. When photons contact an object they are reflected and scattered, and the object becomes known as a secondary radiator. When light enters the eye, and therefore the visual system, the process of seeing begins.

The Visual System

See also: Visual system

When light reflects off objects in the visual field, the light waves travel through the cornea and lens of the eye. The cornea and lens project an image of the object upside-down onto the back of the retina.

Rod cells on the retina are stimulated by light, and contribute to the perception of brightness, size, and shape of objects. Rod cells convert photons into electrical and chemical signals, which travel down the optic nerve and into the brain. Humans have around 130 million rod cells in each eye.

Figure 5: The human eye.
The image projected onto the retina is inverted due to the cornea and lens.

In shape from shading, the pattern of light reflected off an object in the visual field stimulates the rod cells of the retina at different intensities. This means that rod cells become very active when many photons come into contact with them (areas of brighter light reflect more photons); conversely, rod cells stimulated by fewer photons are less active. In this way, the pattern of light reflected off objects is reproduced. The cells on the retina transmit this information into the brain, where the process of visual perception begins.

Visual Perception

See also: Visual Perception

Visual perception relies upon the ability to reconstruct an image of the world based on the information available to the eye. This information is two-dimensional, so to perceive depth the brain must estimate the three-dimensional shape of the image.

Figure 6:
Photon vectors (light particles traveling from light source) reflecting off an object and entering the eye. The upper portion of the object is located closer to the light source and prevents the lower half from receiving the same intensity of light, casting it into shadow.

Shape from shading is an inverse problem; this means that the conditions that produce a particular outcome must be guessed from the outcome itself. So, in this context, light at different intensities (e.g. the shading information) is projected onto the retina, and from that end result the visual system has to determine what shape created that pattern of light.

The inverse problem can be demonstrated using the crater illusion: a phenomenon in which an image of a crater on the surface of the moon appears concave (dented) when viewed at the correct angle; however, when the image is inverted it looks like a volcano because the light hits the top and makes it appear convex (domed). This illusion is caused by an implicit assumption that the light source in the picture is placed above the crater.

Assumed Light Source

The perception of shape from shading depends upon the assumption that a light source is present, because without light there can be no shading. Early experiments argued that in stimuli with no obvious light source (e.g. the shaded spheres in Figure 1), the light is assumed to come from above. Using reaction time data, experiments that investigated the perception of shape from shading found that people were faster to identify shapes that were lighter at the top as convex.

However, the light-from-above assumption seems to have been an oversimplification; evidence suggests that humans assume the light is placed slightly to the left of, instead of directly above, the observer. To find out where the average person's assumed light source is, Sun and Perona asked people to press a button when they saw a convex sphere among concave spheres. The participants were faster to identify convex spheres when the lightest point was approximately 30 degrees to the left of the highest point of the sphere. The possible causes of this left bias are currently being investigated. 

Learned

In this explanation, researchers acknowledge the influence of experience. Since the sun and most electric light sources are placed overhead, placing the lower half of convex objects further from the light source and into shadow, we have learned to expect objects to be lighter at the top.

The slight shift to the left could also be learned: because most people are right handed, perhaps they arrange their environment so that their dominant hand does not cast a shadow over their work - a compelling explanation, but one that later researchers have been unable to replicate. Providing further evidence that this bias might be altered by experience, people who read from right-to-left (such as readers of Hebrew or Arabic) have a leftward bias that is smaller than left-to-right readers - this could be because their attention is usually oriented to the right side of space before the left when reading or writing.

Innate

There is evidence that an assumed light source bias is present at birth. Hershberger used laboratory-raised chickens to test this question. He raised the chickens in an environment where the light came perpetually from below and trained them to peck at pictures of concave or convex spheres. In the photographs, the spheres were lit from both the left and right sides simultaneously. The chickens were then exposed to shaded spheres that were lit from above or below (as in figure 1). The chickens that had been trained to peck at convex spheres pecked at those that were lighter at the top, and those that were trained to peck at concave spheres pecked at those that were lighter at the bottom. Therefore, the chickens reacted to photographs of shaded spheres as though light comes from above, even though they had never experienced light coming from above.

There is evidence that a visual bias to the left side of space is biologically based, rather than learned through experience; for example, when neurologically normal people are asked to mark the centre of a horizontal line (in what is called a line bisection task), their mark is usually placed slightly to the left of the true centre. This is called pseudoneglect, and the degree of error in the line bisection test (e.g. how far away from the true centre the mark is placed) is correlated with the degree of the assumed light source bias. Even right-to-left readers, who make smaller errors in this task, still show a bias to the left side of space. The assumed light source bias might, therefore, reflect brain lateralisation, in which one hemisphere dominates the other in certain tasks. In this theory, a bias to the left side of space would indicate that the right hemisphere is dominant in orienting visual attention.

External links

• Human eye
• Optical illusion
• Perception
• Retina
• Senses
• Visual perception