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Why does a person with only one working eye have zero depth perception? (Part 2)
Category: Physics
Published: July 28, 2023
5. Relative Size
If two objects in your field of view are the same type of object, then your brain assumes that their true physical sizes must be the same. Therefore, your brain assumes that the difference in their perceived sizes must be solely caused by perspective effects. Your brain can therefore extract depth information based on how much the perceived sizes of the two objects differ. For instance, if two single-story houses are in view, then the house that appears to be five times taller than the other house must be about five times closer to you. The figure below demonstrates the "relative size" depth cue.
For the image on the right, your brain notices that each of the four objects has the same shape and therefore assumes that they all have the same true size. Therefore, your brain perceives that the smaller objects must be farther away. In contrast, the objects in the image on the left all have the same size and therefore appear to be at the same distance. I have intentionally chosen here an object with an unfamiliar size and shape so that only the depth cue present is the relative size depth cue.
6. Familiar Size
If a certain object has a known size, then its perceived size corresponds to how far away it is, even if there are no other objects in the field of view to compare it to. Your brain can therefore extract depth information from the perceived size of the object. For instance, an apple is usually a few inches tall. An apple that appears to be much smaller than this must therefore be far away. The figure below demonstrates the "familiar size" depth cue.
The image on left includes two non-specific, unfamiliar objects so that no depth cues are present. As a result the two objects in the left image appear to be the same distance away. In contrast, the image on the right includes two familiar objects. Because you are familiar with baseballs and soccer balls, and you know that the true size of a baseball is smaller than the true size of a soccer ball, your brain perceives that the soccer ball must be farther away. In order to get this effect to work well while looking at this figure, try to visualize the balls as real objects in a real scene.
7. Estimated Size
Amazingly, even if you see an object that has nothing to compare it to and has an unfamiliar shape and size, your brain can still extract depth information from its perceived size by estimating its true size. In other words, your brain estimates the most probable true size of the object and then uses this as if it were a familiar size depth cue. The estimated size depth cue is not particularly effective because the estimated size will typically not be very accurate. The figure below demonstrates the "estimated size" depth cue.
Although the objects in the image on the right are unfamiliar, your brain may assume that cylindrical objects in everyday life (like soup cans) tend to have a small true size while conical objects in everyday life (like Christmas trees) tend to have a large true size. Therefore, your brain may assume that the conical object in the right image is much bigger in true size and therefore must be farther away from you than the cylindrical object because it does not look that much bigger. If you have a hard time seeing depth in the placement of the two objects in the right image, don't worry because this depth cue is not particularly effective.
8. Uniform Size
For a single, extended object that is known to be roughly constant in size along its length, the parts of the object that appear to be smaller must be farther away because of perspective effects. For instance, a baseball bat is roughly constant in width along its length. Therefore, the end of the baseball bat that appears to be much smaller than the other end must be much farther away. In art, this effect is called "foreshortening". The figure below demonstrates the "uniform size" depth cue.
A cylindrical rod in the real world has a uniform size along its length. Therefore, when one end of the rod appears larger than the other end, your brain correctly sees the larger end (the red end in this case) as the closer end. When looking at the image on the right, notice how the red end of the rod seems to be sticking out of the screen. In contrast, the image on the left shows the same rod but without the "uniform size" depth cue present.
9. Parallel Lines
This cue can be thought of as a general case of the uniform size depth cue. This is because when two lines are parallel to each other in the real world, this is equivalent to a single overall object having a uniform size along its length. For instance, a straight road extending away from you has a uniform size along its length, but can be thought of as two parallel lines (i.e. the two sides of the road).
Two lines that are parallel to each other in the real world will be perceived as converging toward each other as they stretch farther away from you. If your brain knows that the two lines are parallel in the real world then it can extract depth information based on how close the lines appear to be. The places where the lines appear closer to each other must be farther away from you. The figure below demonstrates the "parallel lines" depth cue.
The image on the right shows a scene involving two roads on a flat ground plane with this depth cue at work. Therefore, these roads appear to be stretching away from you into the distance. In contrast, the image on the left shows the same scene but without this depth cue, leading it to look flat.
For a set of parallel lines that all extend exactly away from you, they will all appear to meet at one vanishing point at the center of your field of view, as shown in the figure above. In contrast, if a set of parallel lines extends away from you at an oblique angle, then these lines will all appear to meet at one vanishing point that is not at the center of your field of view. This effect is shown in the figure below.
The image on the right shows two sets of parallel lines on the ground that each has its own non-central vanishing point. The image on the left shows the same scene but without any depth cues. In general, every set of parallel lines has its own vanishing point. Therefore, there could be an infinite number of independent vanishing points in an image. Interestingly, if all the sets of parallel lines in a scene are all parallel to the ground plane, all of their vanishing points will lie on the horizon line (which is where the sky appears to meet the ground). This may seem like a rare case, but humans love to build things with surfaces parallel to the ground, so it is actually quite common. It is so common, in fact, that some people mistakenly think that vanishing points must always lie on the horizon.
In every day life, humans tend to build objects that are a box shape or a collection of box shapes, such as buildings, desks, shelves, cabinets, books, tables, beds, and so forth. The edges of a box form three sets of parallel lines. Therefore, a collection of boxy objects that have their faces aligned will have only three vanishing points. First instance, a row of houses has most of its edges appear as lines converging at one of the three vanishing points. For such cases, artists speak of drawing in "three-point perspective".
Sometimes in art, the vertical vanishing point is ignored (so that all lines that are vertical in real life are drawn as vertical on the paper). For a collection of aligned boxy objects, this reduces the situation down to two vanishing points, which artists call "two-point perspective". If there is a collection of aligned boxy objects and two of the dimensions are drawn without perspective, then there is only one vanishing point, which artists call "one-point perspective". These concepts are shown in the figure above.
Note that the parallel lines depth cue is not a special case of the horizon effect depth cue. The perception of depth established by parallel lines arises from the lines converging at a vanishing point and not from objects being close to the horizon. In fact, the parallel lines depth cue works even if there is no horizon at all. The figure below shows a situation where there is no horizon.
In the image on the right, all of the lines that are running along the length of the tunnel meet at the central vanishing point. In contrast, the image on the left shows the same tunnel without the parallel lines depth cue present, insofar as that is possible. Note that if there is not a horizon but there are vanishing points, the horizon effect still occurs in the sense that the closer an object appears to be to a vanishing point, the farther away it seems to be. However, the vanishing point horizon effect still has nothing to do with parallel lines directly.
10. Texture Gradient
Similar to how objects that are closer to you appear larger, parts of the pattern in a texture that are closer to you will appear larger. Your brain can therefore extract depth information from how the different parts of a texture compare to each other in perceived size. Additionally, the texture of a surface can indicate the tilt of the surface, which can help portray the three-dimensional shape of objects. The figure below demonstrates the texture gradient depth cue.
In the image on the left, all of the spots of the textured surface are perceived as being the same size, the same shape, and at about the same spacing, making this image appear flat. In contrast, the image on the right shows that the dots near the top of the image are smaller, closer together, and more distorted than the other dots, giving the impression that they are farther away. Note that the left image and the right image in the figure above show the exact same textured surface with the dots in the same places.
The texture gradient effect works not only on flat ground planes. It can also portray the three-dimensional shape of complicated objects and scenes. For instance, the figure below is the same as the figure above, except that a canyon has been cut in the ground.
The three-dimensional shape of the canyon is made apparent in the image on the right by the texture gradient depth cue. Note that there are no other depth cues present in this image (except for a small amount of recess shading). The image on the left shows the same texture and the same canyon but without the texture gradient depth cue. Another example of the texture gradient depth cue is shown in the figure below.
As this figure demonstrates, a texture gradient does not have to consist of a pattern that has been painted on a flat surface. It can also consist of a large collection of three-dimensional objects that are situated so that they approximately form a flat surface. An additional example of the texture gradient depth cue is shown in the figure below.
As this figure demonstrates, a texture gradient does not have to consist solely of independent features or objects. Rather, it can consist of an interconnected pattern. The image on the right includes the texture gradient effect. As a result, the top of the image appears to be farther away from you than the bottom of the image. In contrast, the image on the left shows a texture but without the texture gradient effect, making it look flat.
11. Horizon Effect
For an object sitting on the ground, the physics dictates that the closer the object's center appears to be to the horizon, the farther away the object is from you. Your brain can therefore estimate how far away an object is from how close its center appears to be to the horizon line. The figure below demonstrates the "horizon effect" depth cue.
In the image on the left, all three objects are at the same height in the image. In contrast, the image on the right shows the same three objects but at different perceived heights. Your brain sees the blue cone as visually closer to the horizon and therefore perceives that it is farther away from you than the other objects.
Interestingly, the horizon can also take the form of a vanishing point. For instance, for objects sitting in a tunnel, the closer that an object appears to be to the tunnel's vanishing point, the farther away it seems to be. The figure below demonstrates the "horizon effect" depth cue when there is a vanishing point instead of a horizon line.
In the image on the right, the blue cone appears to be closer to the vanishing point and therefore is perceived to be farther away from you. The image on the left shows the same scene, insofar as it is possible, without the horizon effect depth cue or the parallel lines depth cue.