Laboratory for Depth/Distance and Size Perception

Purpose: This laboratory will allow you to explore a number of different cues to distance perception, as well as a number of illusions related to distance and size perception.

 

Before beginning this laboratory, please study the map of Nootrac Island for approximately two minutes. Study the characters that you may have seen in various cartoons and try to keep in mind where each of the characters appears on the map. (That is, try to generate a mental image of the entire map!) Do not look back at the map as you proceed through the laboratory exercise! Click on the link to Nootrac Island.

 


 

1. Pictorial Depth Cues [Monocular Cues]

An artist who wants to create an effective two-dimensional representation of three-dimensional space faces challenges that are similar to those faced by our visual system. That is, the visual system must also work to achieve a three-dimensional representation based on input to the retinas, which only encode two dimensions. Artists developed a number of pictorial depth cues, and one can presume that the visual system makes use of many of these same cues. By definition, of course, pictorial depth cues are monocular. That is, they are effective cues to depth/distance when viewed with only one eye. Let's explore the use of such cues to create two-dimensional representations of three-dimensional space.

Here are the pictorial cues mentioned in your textbook: interposition (occlusion or overlap), (known) size, texture gradient, linear perspective, atmospheric perspective, shading (e.g., attached and cast shadows), and height (relative to horizon line).

a. First, go to the National Gallery of Art and take a look at Cuyp's Lady and Gentleman on Horseback (c. 1655) [it's the second Cuyp painting on the site]. You will achieve the most vivid sense of depth if you view the painting monocularly and through a reduction screen (formed by your hand) to eliminate cues that attest to the actual flatness of the screen. List as many different pictorial depth cues as you can, indicating where they appear in the painting. (Note: Some cues will appear many times in the painting.) What time of day might be depicted? How did you determine the time of day and how did that information inform your sense of depth? Imagine that you are looking at an actual scene. How far away, in feet or meters, are you (the viewer) from the Lady and Gentleman? What cues informed your judgment of that distance?

b. When a three-dimensional world is portrayed on a two-dimensional surface, you can gain a fairly realistic sense of that world. However, it is also possible to create a two-dimensional rendition of a world that cannot exist. First, examine the work of William Hogarth, which is very interesting, in part because of its age (ca. 1754). (Though, of course, there are older impossible drawings, such as The Madonna and Child from ~1025.) Look carefully at Hogarth's False Perspectiveand write down a number of "problems" in the picture. Can you see how Hogarth was able to use the two-dimensional surface to make the "problems" less obvious?

Tour these examples of artists that create impossible worlds, even though you may not immediately notice the impossibility of the created world. (You should have fun looking at the impossible images at the PlanetPerplex site.) Here are some artists of the impossible:

M. C. Escher

Oscar Reutersvärd1, Oscar Reutersvärd2

Jos de Mey

 


2. Depth from Shading (with Organization Using Gestalt Principles) [Monocular Cue]

Attached and cast shadows are important pictorial cues to depth. Note how, in the absence of other cues to depth, shadows can lead to a sense of depth.

a. Describe your perceptual experience of the illustration below--especially regarding depth. What cue or cues lead you to that perception? What assumption about lighting must your visual system be making to yield this perception?

 

b. Now look at the illustration below. How does your experience differ from that of the illustration above? What's different?

c. Carefully describe your sense of what you're seeing here. How might your perception of depth differ from that experienced in the illustration above? And, using this final illustration, you should reflect on the interaction between depth cues and the organizing principles that were illustrated in the laboratory on shape perception.

d. At the Sandlot Science site, look at the Distortions (on left, under optical illusions), especially Ball & Shadow. Check out the impact of the shadow on the perceived path of the ball. How does the path of the ball change? How do the different shadows alter your perception of the path of the ball?


3. Shape/Depth from Motion [Monocular Cue]

a. To accompany his Visual Intelligence book, Donald Hoffman has created a number of compelling interactive demonstrations of apparent shape/depth from motion. First, examine his sphere. Note how the shape/depth collapses when you stop the motion. Then play with the various parameters (controlled by buttons) to see what yields the greatest sense of apparent depth. You may also want to play with another version, where the luminance differences between the stimuli and the background can be varied.

b. Now try the same manipulations with Hoffman's cylinder.

c. Here's another example of depth from motion (the Kinetic Depth Effect).

Based on these demonstrations, to what extent do you think that motion is an important determinant of depth. What cues to depth does the motion of an object seem to highlight?


4. Binocular Cues to Depth and SIRDS

Depth can be perceived with only monocular cues, as you've seen in this laboratory and in class. Nonetheless, it is also true that binocular cues give rise to depth. Stereopsis, in fact, is a powerful cue to depth. The slightly different images formed on the two retinas give rise to a sense of depth for relatively nearby objects. (At greater distances, binocular cues are not particularly effective.)

I'm sure that you've all seen the Magic Eye demonstrations of apparent depth. These interesting stimuli have their roots in the old stereoscopes, wherein a different image was presented to each eye to give rise to a sense of depth. Maybe you've even used a ViewMaster to see such images.You can access a large number of sites devoted to stereoscopic viewing. You may even want to build your own stereoscope!

The next stage in the evolution of portraying depth was to remove the monocular cues to depth that were present in stereoscopic images. Bela Julesz developed random dot stereograms, which allowed people to see depth when a different arrangement of "random" dots was presented to each eye. Christopher Tyler was instrumental in the next step, which was to present in a single image all the information necessary for both eyes. And thus were born Single Image Random Dot Stereograms (SIRDS) or, as they are also called, autostereograms.

OK, so now can you figure out how they work? You can use a search engine (such as Google) to locate sites that provide you with information on autostereograms or SIRDS to help you understand the principles.


5. Depth/Size Illusions

a. A classic illusion of depth/size is the Ponzo illusion, illustrated below:

Ponzo illusion

In this illusion the upper horizontal line should appear to be longer than the lower horizontal line. A good explanation of the illusion relies on the notion of visual angle coupled with the notion that the oblique lines provide our visual system with a cue to depth/distance. That is, the upper horizontal line appears to be farther away than the lower horizontal line. So, why should it appear to be longer as well as farther away? For that explanation, you'll need to understand the concept of visual angle.

Visual Angle

 

If two objects were the same distance from the viewer, the longer object would have the larger visual angle. However, as illustrated above, two objects (circles A and B) at different distances (70 and 35 cm) can have identical visual angles (and identical images on the retina) if they are different in size (i.e., A larger than B).

In the Ponzo illusion, both horizontal lines are the same length, so what is the size of their respective visual angles? OK, then if two objects have identical visual angles, but one is farther away, what must be true about the length of the more distant object? How might you alter the figure if you wanted to enhance the disparity in apparent length of the two horizontal lines?

b. Probably the most studied of these illusions is the Müller-Lyer illusion. First, try out the illusion at the SandlotScience site. Choose the Müller-Lyer illusion from the menu on the left under Distortions. Follow the instructions, moving the line on the left to try to get the two lines to be equal in length. What principles underlie this illusion?

c. Do you think that apparent depth plays a role? If so, how would you explain the barbell variant of this illusion (seen below)?

Barbell

While you're at the SandlotScience site, check out a number of the distortion illusions they have on their menu. As they say at the site, Way Cool!

d. Try to experience either the Banana Card Illusion or the Banana & the Pepper Illusion without reading the explanation proferred at the Sandlot Science Site. How would you explain the illusion?

e. How would you explain the Breathing Objects (Square) Illusion? What happens when you make the red squares very large?

f. How would you explain the Pyramid Illusion? What other illusion(s) of distance is(are) similar?

g. You are familiar with the Necker Cube, which illustrates a multistable illusion of depth. On Mark Newbold's site, note how the use of moving objects helps to disambiguate the depth of the cube.


6. Memory for Distance

a. How far is it from the college center to the library? How far is it from the field house to the Department of Psychology? Answering such questions relies on your ability to generate a mental image of the campus. Presumably, you use a similar strategy when attempting to answer the question, "How many windows are there in your house?"

b. Read the story below and when you are finished reading the story, move on to part c. Try to keep the image of the scene in your mind as you proceed through the next exercise.

You are at the Jefferson Plaza Hotel, where you have just taken the escalator from the first to the second floor. You will be meeting someone for dinner in a few minutes. You now stand next to the top of the escalator, where you have a view of the first floor as well as the second floor. You first look directly to your left, where you see a shimmering indoor fountain about 10 yards beyond a carpeted walkway. Though you cannot see below the low stone wall that surrounds it, you suppose that its bottom is littered with nickels and pennies that hotel guests have tossed in. The view down onto the first floor allows you to see that directly below you is a darkened, candle-lit tavern. It looks very plush, and every table you see seems to be filled with well-dressed patrons. Looking directly behind you, you see through the window of the hotel's barbershop. You can see an older gentleman, whose chest is covered by a white sheet, being shaved by a much younger man. You next look straight ahead of you, where you see a quaint little giftshop just on the other side of the escalator. You've a sucker for little ceramic statues, and you squint you eyes to try to read the hours of operation posted on the store's entrance. Hanging from the high ceiling directly above you, you see a giant banner welcoming the Elks convention to the hotel. It is made from white lettering sewn onto a blue background, and it looks to you to be about 25 feet long. (From Matlin 1994, based on Tversky, 1991)

c. OK, now it's time to return to Nootrac Island in your mind. (Don't peek back at the map, you need to complete this task without referring to the original image. Answer the questions on your worksheet now.

Memory for Cartoon Characters on the Map

On your lab worksheet, indicate which of the following characters were actually on the map of Nootrac you saw at the beginning of lab.

Number Character Number Character
1
13
2
14
3
15
4
16
5
17
6
18
7
19
8
20
9
21
10
22
11
23
12
24

When you are done, check your answers when you are finished by clicking here.

 

 

 

Judging Relative Distance

On your lab worksheet, indicate which of the two pairs below were closer together on the map.

Number Pair 1 Pair 2
1
2
3
4

 

 

Judging Absolute Distances

For each of the following pairs of characters, just how far apart they were on the map (using inches or centimeters).

Number Pair
1
2
3
4

 

 

 

 

 

 

 

b. Finally, on your lab sheet answer the questions about the Jefferson Plaza Hotel.

 

Here are the cartoon characters you actually saw: 2, 3, 6, 8, 9, 12, 14, 17, 19, 21, 22, 23. Back to next part.