Size Constancy Lab II

Background:

1. Purpose and Goals
   1. To determine the depth cues that provide the best size constancy.
   2. The develop an understanding of the difference between quantitative and qualitative predictions
   3. To compare data to hypothesis when the hypothesis is mathematically precise
   4. To learn more about designing your own experiment
2. Size Constancy - Briefly, will discuss more in class next week of classes
   1. Recall from class
   2. This week we will add a Monocular Cue
3. Quantitative Predictions
   1. A qualitative prediction deals with trends.
      1. An example would be from the retinal acuity lab
      2. acuity gets worse farther out in the periphery. 
      3. This statement does not predict how worse.  Thus, it is qualitative.
   2. A quantitative prediction deals with both trends, but the size of the trends.
      1. To apply this to the last lab it might say, for each degree of visual angle out from the fovea acuity gets worse by 10%.
      2. This type of statement allows a much finer test of the idea.
      3. This type of statement can also be written as an equation

         Acuity = (distance from Fovea * .10*acuity at fovea)+

                          acuity at fovea.

         This is simply a translation of the statement at 3.b.i into a mathematical expression.

   3. Quantitative Elements of this situation.
      1. Size Constancy

         S_r α 1/d_p
         S_p =  k

         S_{r is the size of the retinal image}

         S_{p is the perceived size of the object}

         d_{p is the perceived distance of the object (since in our case the distances will all be virtually created)}

         α means proportional to.

         k is a constant.

         To translate all this into English: The retinal image size decrease as distance increases such that they are proportional.  That means as distances doubles, the height of the image in the eye is cut in half.  However, the perceive size stays the same regardless of the change in image distance.

      2. Perceived Distance

         Distance from Screen = Viewing dist(mm) * disp(mm)
                                                  Interpup dist (mm)

         Perceived Dist = Viewing Dist - Dist from Screen

      3. These will be brought together when the experiment is explained

The Experiment:

1. Equipment
   1. Here is the link to the lab experiment: ISLE 7.4 (b.2) Size Constancy Experiment
2. Design:
   1. Arrangement of Stimuli:
      
             Standard               Comparison
   2. IV1 is amount of depth (in this case, amount of binocular disparity).
   3. IV2 is the depth cue being tested:
      1. Today we are adding texture gradient
      2. Next week we add relative height
   4. DV is size of comparison circle relative to the Standard (left) circle
3. Method:
   1. Viewing Distance is 75 centimeters (be precise and convert to millimeters for the calculations below).
   2. Open the lab webpage.
   3. Stimulus Settings:
      1. Select texture gradient and disparity
      2. Chose the depth setting for your monocular cue.
      • Chose the same number of levels for depth as week 1 for steropsis but fill the possible range
      • Make sure the relative settings for the two depth cues are the same
      • Note that they use different number ranges
      • Fill the range of texture gradient.
      • Measure how the screen looks for all of your settings
      • These number values are mostly convenient to the program and nothing real
      3. Make sure all other depth cues are unchecked this week, except disparity
         • So when setting each condition yiou will set two depth settings: A disparity setting from last lab and a matching texture gradient setting
      4. Next week we will add relative height.
   4. Method Settings: Method of Adjustment
      1. We are Measuring a Point of Subject Equality (PSE). What is this?
      2. Choose Number of Trials: Should do several (USE THE SAME AS LAST WEEK FOR THE METHOD)
         1. Set the parameters for the method as you think will give you sufficient data and clean results
         2. Again, try some of the settings out
         3. Messy results may be easy to collect but no fun to interpret
      3. Leave range of variation and maximum and minimum values unchanged
4. Procedure:
   1. On each trial respond as directed on the screen.
5. Generating Predictions:
   1. First, make sure all measurements are in the same units, i.e., millimeters, or your answers will be incorrect
   1. The two measurements you need off of the screen are the size of the standard (left) circle and the disparity
   2. These measures are illustrated below
      
   3. To measure the standard size, measure the diameter of the left hand circle
   4. To measure disparity, measure, for each disparity setting, the distance from the edge of one color to the edge of the white where the two colors overlap
   5. If you use the same setting for crossed, positive, and uncrossed, negative, disparities, you only need to measure the disparity once. Use either the crossed or the uncrosse disparity
   6. Keep the sign on your disparity. If you are measuring a crossed disparity, keep your measurement positive. If you are measuring an uncrossed disparity, put a negative sign in front of your measurement
   2. Measure Perceived Distance for each disparity condition: e.g., viewing distance = 750 mm, disparity = 3.4 mm, interpupillary distance = 63 mm
      1. Distance from Screen = (750mm * 3.4mm)/63mm = 40.5 mm
      2. Perceived Distance = 750mm-40.5mm = 709.5mm
   3. According to Size Constancy: when two objects appear the same size the retinal image sizes are inversely proportional to the two distance.
      1. in English, an object that is twice as far away has to be half as tall on the retina to appear the same size. To do this for this lab, divide the distance from the screen by the perceived distance since the depth is virtual, we are dealing with Emmert's Law
      2. So, the predicted relative size is 750mm/709.5mm = 1.06 (note, no units as the two mm cancel each other out)
6. Write-up: (Full report)
   1. Week 3: Do a graph of your predictions for the stereopsis condition to hand in so I can inspect them
   1. Type of graph is an x-y (scatter), using Excel's term
   2. The x-axis should be your disparity, in the millimeters you have measured off of the screen, not the settings from ISLE
   3. The y-axis is your predicted relative size (no units)
   2. At end of lab, do all sections of the lab report specified in the lab report format. This will be due two weeks after lab.
      1. This lab report has a particularly complicated stimulus section you need to measure the following elements:
         • The disparity in mm: from edge or color (red or cyan) to edge of white on same side
         • The size of the standard in mm
         • Will talk more measurements later