Define Monocular Depth Cues Assignment

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Activity 6.1 Monocular Depth Cues

Introduction

When you look at the photograph at left (of the Hawthorne Bridge crossing the Willamette River in Portland, Oregon), you get a compelling sense of depth—a sense that the various objects in the picture are at different distances from you—despite the fact that you’re really just looking at an array of light specks on your computer monitor, all of which are exactly the same distance from your eyes.

We infer object distances in photos using pictorial depth cues. Like the Gestalt principles we learned about in Chapter 4, no single depth cue is always available or always reliable, but by combining multiple pictorial cues, we are usually able to parse depth relations pretty well. We’ll cover seven pictorial cues in this activity: occlusion, relative size, familiar size, relative height, texture gradients, linear perspective, and aerial perspective.

The pictorial depth cues are a subset of our collection of monocular depth cues: cues that we need only one eye to use. The other two monocular cues we’ll cover in this activity are motion parallax and accommodation/convergence.

The other major depth cue, stereopsis, is binocular (you need both eyes to use it). Binocular vision and stereopsis will be the subject of the other three activities in this chapter.

Instructions

Click on the image links within the text of each page to see all images. The first time you do this activity, you should probably go through the parts in order from top to bottom.

Occlusion

Occlusion is probably the most pervasive and most reliable of all the depth cues. It is also perhaps the simplest: If part of object A is covering part of object B, A is almost certainly closer to you than B. In Image 1, we perceive the bicycle to be in front of the railing because the bicycle’s parts cover the railing’s metal tubes.

Image 2 shows another example in a more complex scene, a cityscape from Boston, Massachusetts. Here we perceive two clusters of tall buildings in the distance, one on the left and one on the right. In each cluster, one building is clearly perceived to be behind the rest because of occlusion: The John Hancock building on the left and the Prudential building on the right. Image 3 highlights the occlusion relations, and makes it clear that we also perceive the trees as being closer to us than the skyscrapers because they occlude the buildings.

Image 4 shows the Portland street scene again. Can you identify the places in the scene where occlusion allows us to disambiguate the depth relations? Image 5 highlights some of them.

Relative Size and Familiar Size

Remember the distance-to-object size to retinal-size relationship discussed back in the Chapter 3 activity on Visual Angle? We learned that visual angle is proportional to object size divided by distance from the observer. Thus, after doing a little reshuffling of the formula, we can determine that the distance from an object to our eyeball is proportional to the object’s size divided by its retinal size (Image 1).

One consequence of this relationship is that the farther away an object is, the smaller it appears on the retina. Furthermore, if there are two of the same type of object present in the scene you’re looking at, the object whose retinal image size is smallest must be farthest away (and vice-versa: the object with the largest retinal image must be closest). Thus, in Image 2, the disembodied eyeball knows that the red flower is farther away than the purple flower because the red flower projects a smaller retinal image.

This monocular depth cue, called relative size, is quite effective because it turns out that in many real-world visual scenes, we see multiple objects that can be assumed to be about the same size. For example, in Image 3, one of the ways we know that the statue in the center of the photo is closer than the three statues on the left because the central statue’s retinal image is much larger.

As its name implies, the relative size cue tells us how far away different objects are relative to each other, but it can’t, on its own, tell us exactly how far away any of the objects are. However, if we know how big an object really is, our brains can solve the distance-equals-object-size-divided-by-relative-size relationship to determine absolute distances. In this case we are using the familiar size depth cue.

Thus, adding people to the statues in Image 4 improves the sense of depth compared to Image 3 because now you can use your knowledge about how tall people are to mentally calculate how far away they are. And since the people are standing next to the central statue, you can use them to judge the exact height of this statue (this is an alternative use of the relative height cue).

Returning to our Portland street scene again (Image 5), can you identify some sets of objects whose relative or absolute distances can be inferred from the size cues? Image 6 highlights two such sets of objects: The cars circled in green must be at different distances since their retinal sizes are different, whereas the traffic lights must all be at about the same distance since their retinal sizes are all identical.

Relative Height

In Image 1, how far away is the boy in the center of the photo (call him Bob) relative to the other boys? Bob is not occluding any of the boys, and since we can’t say for sure how old any of them are, the size cues don’t help us either. Nevertheless, it should be quite clear that Bob is the closest of the boys.

We know this because of another depth cue, relative height. Physics tells us (or, at least, our brain’s implicit knowledge of physics tells us) that for objects standing on the ground, the higher an object is in the retinal image, the farther away it is.

Image 2 makes the relative heights of the boys explicit: Bob (“1”) is closest, followed by the boys whose shoes are labeled “2” and “3,” then “4,” and finally “5.”

In Image 3, you should see that relative height alone is enough to provide a fairly powerful sense of one object being closer to you than another. At first, the red cube should appear farther away than the blue cube. Click and drag the red cube to move it around the yellow frame, and you should easily be able to make the red cube appear to be closer. Note that the shadows are crucial to getting a sense of depth in this image; without them, you might perceive the cubes as floating in midair, and the brain (appropriately) does not apply the relative height cue when objects aren’t rooted to the ground.

Image 4 shows our Portland street scene again. Can you identify the objects whose relative heights allow us to order them in depth? Image 5 highlights some of these objects.

Texture Gradients and Linear Perspective

Our next two depth cues are really just special (but common and effective) combinations of relative size and relative height. In Image 1, it is readily apparent that the cup on the right is closer than the cup on the left. In part, this is due to the relative sizes and heights of the cups themselves. But the strong sense of depth in this picture is conveyed even more by the other objects in the image—the bricks.

For the most part, our brains consciously ignores the bricks because they are part of the background of the scene, and we’re usually more interested in objects in the foreground. Unconsciously, though, our brains notice that some bricks are considerably smaller and higher in the visual field than others (Image 2). Therefore, the bricks form a texture gradient. The distance to any object sitting on the texture can be accurately judged by comparing it to the part of the texture (i.e., the bricks) the object happens to be sitting on.

In Image 3, depth is conveyed by a similar cue, linear perspective. If we assume that the two sides of the road are parallel to each other, we know that the actual three-dimensional distance across the road is the same everywhere in the image. Therefore, the fact that the retinal distance across the road shrinks as the road goes on (Image 4) tells us that the road must be winding away from us into the distance. By extension, we can judge the relative distances of the motorcycles driving on the road.

You will never find texture gradients or linear perspective in a scene without also encountering the relative size and relative height cues, since, as we saw above, relative size and relative height effectively define texture gradients and linear perspective. However, when a scene includes a texture gradient and/or linear perspective, the sense of depth increases dramatically. For example, Image 5 shows our two cubes from the Relative Height part of this activity, with some background elements that provide a texture gradient and linear perspective. In this image, you should get a much more powerful sense that the cubes are at different distances.

There are two more interesting things to note in this image. First, you may perceive the red cube to be larger than the blue one. Click and drag the red cube so that it is next to the blue one, though, and you can confirm that the size of the two cubes is the same. When the cubes were in their original position, you perceived the red one to be farther away than the blue one, so your brain solved the distance–object size–relative size equation, calculated the actual object size of the red cube and determined that it must be bigger than the blue cube. The retinal sizes of the two cubes are equal, but the red cube’s distance is greater; therefore, the red cube’s object size must also be greater.

Second, if you start with the red cube back in its original position and drag it off to the right side of the window, you will probably perceive it as floating in midair right above the blue cube. Here, in the absence of a texture gradient cue, your brain sees that the retinal sizes of the two cubes are the same, assumes that the actual object sizes are the same, and therefore concludes that the distance to the two objects must be the same. This would mean that the red cube floating in the air must be at the same distance as the blue cube, which is a reasonable interpretation since there isn’t a shadow cue to indicate that the red cube is anchored to the wall.

Aerial Perspective

The atmosphere is mostly empty, but every molecule in the air scatters a little bit of sunlight, and over a long distance this scattering adds up to make distant objects appear hazier and less distinct than closer objects. This provides our last pictorial depth cue: aerial perspective, illustrated in Image 1. Look closely and you will see that the buildings in the lower-right portion of the photo are sharpest, the buildings across the river on the left are fainter, and the buildings above the trees in the center-right of the photo are hazier still (Image 2 shows close-ups of these three areas). Thus the distances of the three sets of buildings must be ordered accordingly (closest, medium distance, farthest).

Image 3 shows our Portland street scene one more time. The object whose distance is determinable via aerial perspective should be obvious here: Mt. Hood (Image 4), which is located some 60 miles to the east of the point where this picture was taken.

Motion Parallax

The last two depth cues we will discuss in this activity are not available in static pictures. We will illustrate the first of these monocular-but-non-pictorial cues with the situation diagrammed in Image 1. You are on a train (top) traveling through the countryside, looking out the window (bottom) at a flower, a cow, and a tree. A pictorial depth cue (which one?relative height) already tells us that the flower is closest, the cow is in the middle, and the tree is farthest away. But when we set the train in motion (Image 2), the motion parallax depth cue kicks into effect, and the depth relations jump out in a much more compelling way.

Motion parallax is based on the idea that objects that are closer to you move more quickly across your field of view than objects that are farther away. When your head moves, every object in the scene you’re looking at shifts position on your retina. The fact that objects that are closer to you shift position more than objects that are farther away is just a consequence of projective geometry. And once again, we find that your brain knows more about geometry than you probably realized, because it instantly compares the relative magnitudes of these position shifts to order the objects in depth.

You can also see motion parallax in action with the following demonstration: Hold your right index finger up about a foot in front of your face, then hold your left index finger up at arm’s length. Now close one eye and move your head back and forth from right to left (you have to actually move your head, not just shift your gaze). You will see your right finger move much farther across your field of vision than your left finger, and the depth relation between the two fingers will pop right out.

Accommodation/Convergence

Our final monocular depth cue, which, like motion parallax, is only available in the real world (not in pictures) is a byproduct of the process of focusing our eyes. When you are focused on a distant point (Image 1), your eyes are pointed at a certain angle toward each other and your lens is relatively thin.

As you shift your gaze to a nearer spot (Image 2), your eyes turn inward and your lens gets fatter. The eye-turning is called convergence and the lens fattening is called accommodation. If you reshift your gaze to the more distant spot (Image 3), your eyes diverge and your lens gets thinner again.

Thus, assuming your brain has access to the state of the muscles controlling your lens shape and gaze direction, the extent to which your eyes are converged and your lens is accommodated should provide cues to the distance of the object you are focused on. If your lens is fat, you must be looking at something near; if your lens is thin, the object must be farther away.

Note that accommodation and convergence almost always occur in concert. This is why they are listed as a single depth cue.

Your instructor may assign a quiz for this Activity. Activity quizzes are available here.

 

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© 2014 Sinauer Associates

For objective comparisons of size, see Orders of magnitude (length).

Depth perception is the visual ability to perceive the world in three dimensions (3D) and the distance of an object. Depth sensation is the corresponding term for animals, since although it is known that animals can sense the distance of an object (because of their ability to move accurately, or to respond consistently, according to that distance), it is not known whether they "perceive" it in the same subjective way that humans do.[1]

Depth perception arises from a variety of depth cues. These are typically classified into binocular cues that are based on the receipt of sensory information in three dimensions from both eyes and monocular cues that can be represented in just two dimensions and observed with just one eye.[2][3] Binocular cues include stereopsis, eye convergence, disparity, and yielding depth from binocular vision through exploitation of parallax. Monocular cues include size: distant objects subtend smaller visual angles than near objects, grain, size, and motion parallax.[4]

Monocular cues[edit]

Monocular cues provide depth information when viewing a scene with one eye.

Motion parallax 
When an observer moves, the apparent relative motion of several stationary objects against a background gives hints about their relative distance. If information about the direction and velocity of movement is known, motion parallax can provide absolute depth information.[5] This effect can be seen clearly when driving in a car. Nearby things pass quickly, while far off objects appear stationary. Some animals that lack binocular vision due to their eyes having little common field-of-view employ motion parallax more explicitly than humans for depth cueing (e.g., some types of birds, which bob their heads to achieve motion parallax, and squirrels, which move in lines orthogonal to an object of interest to do the same [6]).[note 1]
Depth from motion 
When an object moves toward the observer, the retinal projection of an object expands over a period of time, which leads to the perception of movement in a line toward the observer. Another name for this phenomenon is depth from optical expansion.[7] The dynamic stimulus change enables the observer not only to see the object as moving, but to perceive the distance of the moving object. Thus, in this context, the changing size serves as a distance cue.[8] A related phenomenon is the visual system’s capacity to calculate time-to-contact (TTC) of an approaching object from the rate of optical expansion – a useful ability in contexts ranging from driving a car to playing a ball game. However, calculation of TTC is, strictly speaking, perception of velocity rather than depth.
Kinetic depth effect 
If a stationary rigid figure (for example, a wire cube) is placed in front of a point source of light so that its shadow falls on a translucent screen, an observer on the other side of the screen will see a two-dimensional pattern of lines. But if the cube rotates, the visual system will extract the necessary information for perception of the third dimension from the movements of the lines, and a cube is seen. This is an example of the kinetic depth effect.[9] The effect also occurs when the rotating object is solid (rather than an outline figure), provided that the projected shadow consists of lines which have definite corners or end points, and that these lines change in both length and orientation during the rotation.[10]
Perspective 
The property of parallel lines converging in the distance, at infinity, allows us to reconstruct the relative distance of two parts of an object, or of landscape features. An example would be standing on a straight road, looking down the road, and noticing the road narrows as it goes off in the distance.
Relative size 
If two objects are known to be the same size (e.g., two trees) but their absolute size is unknown, relative size cues can provide information about the relative depth of the two objects. If one subtends a larger visual angle on the retina than the other, the object which subtends the larger visual angle appears closer.
Familiar size 
Since the visual angle of an object projected onto the retina decreases with distance, this information can be combined with previous knowledge of the object's size to determine the absolute depth of the object. For example, people are generally familiar with the size of an average automobile. This prior knowledge can be combined with information about the angle it subtends on the retina to determine the absolute depth of an automobile in a scene.
Absolute size 
Even if the actual size of the object is unknown and there is only one object visible, a smaller object seems further away than a large object that is presented at the same location [11]
Aerial perspective 
Due to light scattering by the atmosphere, objects that are a great distance away have lower luminance contrast and lower color saturation. Due to this, images seem hazy the farther they are away from a person's point of view. In computer graphics, this is often called "distance fog". The foreground has high contrast; the background has low contrast. Objects differing only in their contrast with a background appear to be at different depths.[12] The color of distant objects are also shifted toward the blue end of the spectrum (e.g., distant mountains). Some painters, notably Cézanne, employ "warm" pigments (red, yellow and orange) to bring features forward towards the viewer, and "cool" ones (blue, violet, and blue-green) to indicate the part of a form that curves away from the picture plane.
Accommodation 
This is an oculomotor cue for depth perception. When we try to focus on far away objects, the ciliary muscles stretch the eye lens, making it thinner, and hence changing the focal length. The kinesthetic sensations of the contracting and relaxing ciliary muscles (intraocular muscles) is sent to the visual cortex where it is used for interpreting distance/depth. Accommodation is only effective for distances less than 2 meters.
Occultation 
Occultation (also referred to as interposition) happens when near surfaces overlap far surfaces.[13] If one object partially blocks the view of another object, humans perceive it as closer. However, this information only allows the observer to create a "ranking" of relative nearness. The presence of monocular ambient occlusions consist of the object's texture and geometry. These phenomena are able to reduce the depth perception latency both in natural and artificial stimuli.[14][15]
Curvilinear perspective 
At the outer extremes of the visual field, parallel lines become curved, as in a photo taken through a fisheye lens. This effect, although it is usually eliminated from both art and photos by the cropping or framing of a picture, greatly enhances the viewer's sense of being positioned within a real, three-dimensional space. (Classical perspective has no use for this so-called "distortion," although in fact the "distortions" strictly obey optical laws and provide perfectly valid visual information, just as classical perspective does for the part of the field of vision that falls within its frame.)
Texture gradient 
Fine details on nearby objects can be seen clearly, whereas such details are not visible on faraway objects. Texture gradients are grains of an item. For example, on a long gravel road, the gravel near the observer can be clearly seen of shape, size and colour. In the distance, the road's texture cannot be clearly differentiated.
Lighting and shading 
The way that light falls on an object and reflects off its surfaces, and the shadows that are cast by objects provide an effective cue for the brain to determine the shape of objects and their position in space.[16]
Defocus blur 
Selective image blurring is very commonly used in photographic and video for establishing the impression of depth. This can act as a monocular cue even when all other cues are removed. It may contribute to the depth perception in natural retinal images, because the depth of focus of the human eye is limited. In addition, there are several depth estimation algorithms based on defocus and blurring.[17] Some jumping spiders are known to use image defocus to judge depth.[18]
Elevation 
When an object is visible relative to the horizon, we tend to perceive objects which are closer to the horizon as being farther away from us, and objects which are farther from the horizon as being closer to us.[19] In addition, if an object moves from a position close the horizon to a position higher or lower than the horizon, it will appear to move closer to the viewer.

Binocular cues[edit]

Binocular cues provide depth information when viewing a scene with both eyes.

Stereopsis, or retinal (binocular) disparity, or binocular parallax 
Animals that have their eyes placed frontally can also use information derived from the different projection of objects onto each retina to judge depth. By using two images of the same scene obtained from slightly different angles, it is possible to triangulate the distance to an object with a high degree of accuracy. Each eye views a slightly different angle of an object seen by the left and right eyes. This happens because of the horizontal separation parallax of the eyes. If an object is far away, the disparity of that image falling on both retinas will be small. If the object is close or near, the disparity will be large. It is stereopsis that tricks people into thinking they perceive depth when viewing Magic Eyes, Autostereograms, 3-D movies, and stereoscopic photos.
Convergence 
This is a binocular oculomotor cue for distance/depth perception. Because of stereopsis the two eyeballs focus on the same object. In doing so they converge. The convergence will stretch the extraocular muscles. As happens with the monocular accommodation cue, kinesthetic sensations from these extraocular muscles also help in depth/distance perception. The angle of convergence is smaller when the eye is fixating on far away objects. Convergence is effective for distances less than 10 meters.[20]
Shadow Stereopsis 
A. Medina Puerta demonstrated that retinal images with no parallax disparity but with different shadows are fused stereoscopically, imparting depth perception to the imaged scene. He named the phenomenon "shadow stereopsis". Shadows are therefore an important, stereoscopic cue for depth perception.[21]

Of these various cues, only convergence, accommodation and familiar size provide absolute distance information. All other cues are relative (i.e., they can only be used to tell which objects are closer relative to others). Stereopsis is merely relative because a greater or lesser disparity for nearby objects could either mean that those objects differ more or less substantially in relative depth or that the foveated object is nearer or further away (the further away a scene is, the smaller is the retinal disparity indicating the same depth difference.)

Theories of evolution[edit]

Most open-plains herbivores, especially hoofed grazers, lack binocular vision because they have their eyes on the sides of the head, providing a panoramic, almost 360°, view of the horizon - enabling them to notice the approach of predators from almost any direction. However, most predators have both eyes looking forwards, allowing binocular depth perception and helping them to judge distances when they pounce or swoop down onto their prey. Animals that spend a lot of time in trees take advantage of binocular vision in order to accurately judge distances when rapidly moving from branch to branch.

Matt Cartmill, a physical anthropologist & anatomist at Boston University, has criticized this theory, citing other arboreal species which lack binocular vision, such as squirrels and certain birds. Instead, he proposes a "Visual Predation Hypothesis," which argues that ancestral primates were insectivorous predators resembling tarsiers, subject to the same selection pressure for frontal vision as other predatory species. He also uses this hypothesis to account for the specialization of primate hands, which he suggests became adapted for grasping prey, somewhat like the way raptors employ their talons.

In art[edit]

Photographs capturing perspective are two-dimensional images that often illustrate the illusion of depth. (This differs from a painting, which may use the physical matter of the paint to create a real presence of convex forms and spatial depth.) Stereoscopes and Viewmasters, as well as 3D films, employ binocular vision by forcing the viewer to see two images created from slightly different positions (points of view). Charles Wheatstone was the first to discuss depth perception being a cue of binocular disparity. He invented the stereoscope, which is an instrument with two eyepieces that displays two photographs of the same location/scene taken at relatively different angles. When observed, separately by each eye, the pairs of images induced a clear sense of depth.[22] By contrast, a telephoto lens—used in televised sports, for example, to zero in on members of a stadium audience—has the opposite effect. The viewer sees the size and detail of the scene as if it were close enough to touch, but the camera's perspective is still derived from its actual position a hundred meters away, so background faces and objects appear about the same size as those in the foreground.

Trained artists are keenly aware of the various methods for indicating spatial depth (color shading, distance fog, perspective and relative size), and take advantage of them to make their works appear "real". The viewer feels it would be possible to reach in and grab the nose of a Rembrandt portrait or an apple in a Cézanne still life—or step inside a landscape and walk around among its trees and rocks.

Cubism was based on the idea of incorporating multiple points of view in a painted image, as if to simulate the visual experience of being physically in the presence of the subject, and seeing it from different angles. The radical experiments of Georges Braque, Pablo Picasso, Jean Metzinger's Nu à la cheminée,[23]Albert Gleizes's La Femme aux Phlox,[24][25] or Robert Delaunay's views of the Eiffel Tower,[26][27] employ the explosive angularity of Cubism to exaggerate the traditional illusion of three-dimensional space. The subtle use of multiple points of view can be found in the pioneering late work of Cézanne, which both anticipated and inspired the first actual Cubists. Cézanne's landscapes and still lives powerfully suggest the artist's own highly developed depth perception. At the same time, like the other Post-Impressionists, Cézanne had learned from Japanese art the significance of respecting the flat (two-dimensional) rectangle of the picture itself; Hokusai and Hiroshige ignored or even reversed linear perspective and thereby remind the viewer that a picture can only be "true" when it acknowledges the truth of its own flat surface. By contrast, European "academic" painting was devoted to a sort of Big Lie that the surface of the canvas is only an enchanted doorway to a "real" scene unfolding beyond, and that the artist's main task is to distract the viewer from any disenchanting awareness of the presence of the painted canvas. Cubism, and indeed most of modern art is an attempt to confront, if not resolve, the paradox of suggesting spatial depth on a flat surface, and explore that inherent contradiction through innovative ways of seeing, as well as new methods of drawing and painting.

Disorders affecting depth perception[edit]

  • Ocular conditions such as amblyopia, optic nerve hypoplasia, and strabismus may reduce the perception of depth.
  • Since (by definition), binocular depth perception requires two functioning eyes, a person with only one functioning eye has no binocular depth perception.
  • Depth perception must be learned using an unconscious inference, which is much less likely to happen after a few years of age

See also[edit]

References[edit]

  1. ^Howard, Ian (2012). Perceiving in Depth. New York: Oxford University Press. ISBN 978-0-199-76414-3. 
  2. ^Sternberg, R. K. (2012).
  3. ^Goldstein E.B. (2014)Sensation and perception (9th ed.). Pacific Grove CA: Wadsworth.
  4. ^Burton HE (1945). "The optics of Euclid". Journal of the Optical Society of America. 35 (5): 357–372. doi:10.1364/JOSA.35.000357. 
  5. ^Ferris SH (1972). "Motion parallax and absolute distance. Journal of experimental psychology". 95 (2): 258–263. 
  6. ^Kral K. (2003). Behavioural-analytical studies of the role of head movements in depth perception in insects, birds and mammals. Behavioural Processes 64: 1-12.
  7. ^Swanston, M.C.; Gogel, W.C. (1986). "Perceived size and motion in depth from optical expansion". Perception & Psychophysics. 39 (5): 309–326. doi:10.3758/BF03202998. 
  8. ^Ittelson, W.H. (Apr 1951). "Size as a cue to distance: Radial motion". American Journal of Psychology. 64 (2): 188–202. doi:10.2307/1418666. JSTOR 1418666. 
  9. ^Wallach, H.; O'Connell, D.N. (1953). "The kinetic depth effect". Journal of Experimental Psychology. 45 (4): 205–217. doi:10.1037/h0056880. PMID 13052853. 
  10. ^Kaufman, Lloyd (1974). Sight and Mind. New York: Oxford University Press. pp. 139–141. 
  11. ^Sousa, R., Brenner, E., & Smeets, J. B. J. (2011). Judging an unfamiliar object's distance from its retinal image size. Journal of Vision, 11(9), 10, 1-6. Sousa, R., Smeets, J. B. J., & Brenner, E. (2012). Does size matter? Perception, 41(12), 1532-1534.
  12. ^O'Shea RP, Blackburn SG, Ono H (1994). "Contrast as a depth cue". Vision Research. 34 (12): 1595–1604. doi:10.1016/0042-6989(94)90116-3. PMID 7941367. 
  13. ^Johnston, Alan. "Depth Perception". UCL Division of Psychology and Language Sciences. Retrieved 22 September 2013. 
  14. ^Gillam B, Borsting E (1988). "The role of monocular regions in stereoscopic displays". Perception. 17 (5): 603–608. doi:10.1068/p170603. PMID 3249668. 
  15. ^Schacter, Daniel L.; Gilbert, Daniel T.; Wegner, Daniel M. (2011). "Sensation and Perception". Psychology (2nd ed.). New York: Worth, Inc. pp. 136–137. 
  16. ^Lipton, L. (1982). Foundations of the Stereoscopic Cinema - A Study in Depth. New York: Van Nostrand Reinhold. p. 56. 
  17. ^Mather G (22 February 1996). "Image Blur as a Pictorial Depth Cue". Proceedings: Biological Sciences. 263 (1367): 169–172. Bibcode:1996RSPSB.263..169M. doi:10.1098/rspb.1996.0027. 
  18. ^Takashi Nagata; Koyanagi, M; Tsukamoto, H; Saeki, S; Isono, K; Shichida, Y; Tokunaga, F; Kinoshita, M; Arikawa, K; et al. (27 January 2012). "Depth Perception from image defocus in a jumping spider". Science. 335 (6067): 469–471. Bibcode:2012Sci...335..469N. doi:10.1126/science.1211667. PMID 22282813. 
  19. ^Carlson, Neil R.; Miller Jr., Harold L.; Heth, Donald S.; Donahoe, John W.; Martin, G. Neil (2010). Psychology: The Science of Behavior (7th ed.). Pearson. p. 187. ISBN 978-0-205-76223-1. 
  20. ^Okoshi, Takanori. (2012). Three-dimensional imaging techniques. Elsevier. pp. 387–387. ASIN B01D3RGBGS. 
  21. ^Medina Puerta A (1989). "The power of shadows: shadow stereopsis". J. Opt. Soc. Am. A. 6 (2): 309–311. Bibcode:1989JOSAA...6..309M. doi:10.1364/JOSAA.6.000309. PMID 2926527. 
  22. ^Schacter, Daniel L. (2011). Psychology (2nd ed.). New York: Worth, In. p. 151. 
  23. ^Daniel Robbins, Jean Metzinger: At the Center of Cubism, 1985, Jean Metzinger in Retrospect, The University of Iowa Museum of Art, p. 22
  24. ^Albert Gleizes 1881–1953, a retrospective exhibition, Daniel Robbins. The Solomon R. Guggenheim Museum, New York, in collaboration with Musée national d'art moderne, Paris; Museum am Ostwall, Dortmund, published 1964
  25. ^Peter Brooke, Albert Gleizes, Chronology of his life, 1881-1953
  26. ^Robert Delaunay – Sonia Delaunay, 1999, ISBN 3-7701-5216-6
  27. ^Robert Delaunay, First Notebook, 1939, in The New Art of Color: The Writings of Robert and Sonia Delaunay, Viking Press, 1978

Notes[edit]

  1. ^The term 'parallax vision' is often used as a synonym for binocular vision, and should not be confused with motion parallax. The former allows far more accurate gauging of depth than the latter.

Bibliography[edit]

  • Howard, Ian P.; Rogers, Brian J. (2012). Perceiving in Depth. New York: Oxford University Press.  In three volumes
  • Palmer, S. E. (1999). Vision science: Photons to phenomenology. Cambridge, MA: Bradford Books/MIT Press. 
  • Pirazzoli, G.P. (2015). Le Corbusier, Picasso, Polyphemus and Other Monocular Giants / e altri giganti monòculi. Firenze, Italy: goWare. 
  • Pinker, Steven (1997). "The Mind's Eye". How the Mind Works. pp. 211–233. ISBN 0-393-31848-6. 
  • Sternberg RJ, Sternberg K, Sternberg K (2011). Cognitive Psychology (6th ed.). Wadsworth Pub Co. 
  • Purves D, Lotto B (2003). Why We See What We Do: An Empirical Theory of Vision. Sunderland, MA: Sinauer Associates. 
  • Steinman, Scott B.; Steinman, Barbara A.; Garzia, Ralph Philip (2000). Foundations of Binocular Vision: A Clinical Perspective. New York: McGraw-Hill Medical. ISBN 0-8385-2670-5. 
  • Okoshi, Takanori. (2012). Three-dimensional imaging techniques. Elsevier. pp. 387–387. ASIN B01D3RGBGS. 

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Perspective, relative size, occlusion and texture gradients all contribute to the three-dimensional appearance of this photo.

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