Apparent Motion Laboratory



This laboratory explores the phenomenon of apparent motion. When still frames are rapidly alternated, people often spontaneously perceive motion. By studying apparent motion phenomena, we can learn about how people subjectively structure the external world , the assumptions that people make about stimuli when perceiving, top-down effects in vision, and the specific mechanisms that people use to see motion. Apparent motion is also an indispensible to the motion picture industry because movies are nothing more than a series of still frames that are rapidly displayed.

The computer program for apparent motion does two things. First, it allows you to create and display apparent motion phenomena. You can design an apparent motion display, and then present it to yourself and determine the motion that you spontaneously see. Second, it provides a computational model of how people see apparent motion, based on models by Dawson (1993) and Ullman (1979), and serving as the basis for our work on a computational model of the perceptual processes underlying scientific discovery (Lara-Dammer, Hofstadter, & Goldstone, 2017, 2019, submitted). Typically, you will use this program by presenting the same apparent motion display to yourself and to the computational model, and observing whether the computer "sees" the same kind of motion that you do.

The program allows you to draw two static frames, and then alternates them in a manner specified by experimenter-controlled parameters. The program does not collect any data from the subject; there are too many possible data that might be collected. In many cases, the effects are so strong and immediately obvious that experimenters can use their own impressions as data, and can be fairly confident that other people will see the displays in the same way. This lab is designed to have quite a bit of flexibility. The experimenter can create their own displays with different geometric shapes, each with its own color and size.


The "Motion Correspondence Problem"

When people see motion between two successively presented frames, their minds unconsciousnly determine which parts from the first frame correspond to which parts from the second frame. When people see two parts as corresponding to each other, this means that they interpret the two parts as coming from the same object. If the two parts are separated from each other, then people will see a single object moving over time. Determining what parts correspond to each other tells us what parts come from the same object at different times. However, this task is intrinsically ambiguous. One part in one frame could correspond to many different parts in the other frame. Simple experiments will show that people sometimes see two parts as showing the same object moving over time even if the parts do not have the same color, size, location, or even shape! Your mind spontaneously figures out what parts correspond to each other, but underlying this seemingly effortless feat are sophisticated computations. Your mind uses several constraints in order to try to determine what parts correspond to each other. Constraints are valuable, not restrictive things to be avoided, because without constraints the world is too ambiguous. Constraints allow us to restrict our perceptions to the most plausible possibilities.


Assumptions That Solve the "Motion Correspondence Problem"

Imagine that there are two frames, each with three circles. Each object from one frame might correspond to any of the three objects from the other frame. Your mind makes assumptions about what objects are likely to belong together: All of these constraints act together to determine the motion that you will in a display. None of these constraints is hard and fast. Your mind can often times overrule these constraints, but they are biases that generally lead people to see motion in a reasonable manner. Impressively, all correspondences between all objects are determined at the same time, and the correspondences mutually influence each. The last two assumptions above make this clear. Whether or not an object corresponds to another object depends on all of the other objects and THEIR emerging correspondences.

Experimental Explorations of Apparent Motion

Notice here that you will most likely either see two dots sliding up and down, or two dots sliding left and right. It is probably very hard for you to see one dot in Frame 1 splitting to form two dots in Frame 2, while the other dot in Frame 1 just blinks on and off. This suggests that you have a strong constraint for every object in one frame to have a correspondence in the other frame. You can see either horizontal or vertical motion by selectively hiding pairs of dots and gradually introducing the other pair of dots.


This is called the "Ternus Display." The grid is displayed to show you the precise locations of dots. If there is a short blank period between these frames, people typically report seeing three dots moving up and down. This is suprising because some of the dots have EXACTLY the same location in the two frames, and yet people don't see them as stationary. People DO see them as stationary if there is no blank period between frames. What do you think is going on here (HINT: remember the motion similarity constraint)?


This display can be created although it will require a bit of ingenuity and painting large blue squares. It combines two illusions: illusory contours (seeing a complete blue square even though there are only red "pac-man" shapes) and illusory motion. What do you see when these displays are alternated? What does your perception imply about whether your mind creates illusory contours BEFORE or AFTER it creates apparent motion?


When you flip between these two frames, do you see the red dot in Frame 1 correspond to the blue or green dot in Frame 2? If you see it moving down to turn into the blue dot, that indicates an impressive ability of your motion perception system to work out globally consistent correspondences. To see what's going on here, let's add pale ghost images of each object showing where they would appear if they were in the other frame.


We see now that the red dot is equally distant from the blue and green dot. However, in the original frames, as the correspondences work themselves out from the unambiguous ends to the ambiguous middle section, the best way to assign close and consistent (no 2-to-1 mappings) correspondences is for the red dot to correspond to the blue dot. That way every dot gets one and only partner.

But if we move the lowest-leftmost purple dot in Frame 2 to the hollow purple dot position as shown to the left, then the best globally consistent mapping now places the red and green dots into correspondence. In this way, the correspondences on the ends have ripples of influence that extend all the way to the middle of the frames!


Computational Modeling of Apparent Motion

The computer simulation is a simple neural network that has been designed to implement the assumptions/constraints previously described. In this network, one unit (also called 'node' sometimes) is created for every potential correspondence between two objects. If two frames each have 3 objects in them, 9 correspondence units will be created because each of three objects in one frame can correspond to three objects from the other frame. Each unit has an activation, and the more active the unit is, the more strongly the computer "feels" that the two objects connected by the unit should be placed in correspondence. In the simulation, the activity of a correspondence unit is shown by the amount of green in the connection between objects.
In the network here, Unit hypothesizes that the top red circle in Frame 1 corresponds to the top red circle in Frame 2. It receives excitation from color, shape, and size similarity constraints because the two circles have exactly the same values along all three factors. There are negative connections between units that are inconsistent with each other - if they lead to two objects in one frame corresponding to a single object in the other frame. For example, Unit Q puts the red circle from Frame 1 into correspondence with the blue circle in middle of Frame 2, and R put the red circle from Frame 2 into correspondence with blue circle in the middle of Frame 1. Unit A is inconsistent with Units Q and R because if the red circle in Frame 1 corresponds to the red circle in Frame 2 then these red circles shouldn't also correspond to any other circle. So, as Unit A become more active, it will tend to deactivate Q and R, and vice versa.

Other correspondences are consistent with each other because they do not entail 2-to-1 mappings. For example, Units A, B, and C are consistent with each other, and will mutually excite one another, particularly if the object motions that are implicated by them are similar to one another.


In accordance with the described constraints, the following principles govern the change in a unit's activity over time: The neural network begins with all correspondences' activations set 0. Then, the units gradually change their activations by the above principles, and as they do so, they will change other units' activations.

Using the Laboratory Software

When you run the program, you will see a screen that contains a description of Frame 1 and Frame 2. The first thing you will want to do is create the two frames that will make up the animation. To do this, you can select from six different shapes (square, circle, star, blob, horizontal line, and vertical line), three different sizes, and six different colors. To paint objects on the frames, select the paint mode and click on the spot in the frame where you want the object to appear. The appearance of the object will be determined by the color, shape, and size that you have selected. To remove an object, select the delete mode and click on the object that you wanted deleted. To move an object, select the drag mode, and then click on the object you want to move, and drag it to its new location. To copy an object from one frame to the other, select the copy mode and click on the object you want copied. Press clear if you want to erase all of the objects, 'play/pause animation' to turn on/off the animated alternation of the two frames, and grid if you want a grid to (dis) appear on the screen that can help you position objects. There are some pre-configured displays that you can explore by selecting one from the menu toward the upper-right portion of the screen. Press the "information" button to find out more information about how to use the program.

While the two frames are flipping, no button or slider can be altered. While the two frames are flipping, each will appear on the screen for a period of time that you determine by selecting a value on the slider called 'Frame Time'. There may also be a time period between each frame during which the screen is blank. You specify how long this time period is by selecting a value on the 'Blank time' slider.

In addition to the above buttons and sliders, there are other sliders that you will need to use if you are interested in exploring the computational model of human apparent motion perception. The sliders color, size, and shape determine how much the neural network bases its correspondences between the two frames on each of these properties. The consistency slider specifies how much the model tries to enforce the one-to-one mapping constraint. The motion similarity slider specifies how much the model tries to have objects move in similar directions. The match slider specifies how hard the model tries to find a partner for each object. For each of these parameters, as you move the slider value to the right, the parameter has a greater influence on how the neural network. The speed slider determines how quickly correspondences are determined, and the randomness slider specifies how much randomness is added to correspondence units' activity.

The computational model is hidden/revealed by pressing the 'Show/hide simulation' button. When the model is started by pressing the "Start Simulation" button, a set of correspondence units is created, one unit for each possible connection between objects across the two frames. Each correspondence unit starts with zero activity. On each time step, the activity of a correspondence unit changes, based on the parameters that you specify. The strength of a correspondence unit is indicated by its green hue. The computer predicts that objects connected by bright green lines will be perceived as coming from the same moving object.

The ghost button allows you to see where an object from one frame would appear if it were on the other frame. It will appear as a pale object on the other frame. If ghosting is turned on and the modeling is on, then rather than drawing correspondences between objects across frames, the computer will draw correspondence from the objects of one frame to the ghosts of the objects in the other frame.

References



Designed and programmed by Robert Goldstone (rgoldsto@indiana.edu). Visit our Percepts and Concepts Laboratory housed within the Cognitive Science Program and Department of Psychological and Brain Sciences at Indiana University
Previous versions of this software include a Pascal version created by Robert Goldstone in 1993 and a Java version created by Tom Busey and Ruth Eberle around 2000.