A short quiz on computational stereo

Adrian F. Clark

1. What is disparity?

   • The foreshortening of an object with distance
   • The distance to an object in an image
   • The relative size of the same object when it is nearby and far away

   • The discrepancy in the apparent position of an object in the left and right images

   Disparity, which is essentially the same as parallax, is the `shift' in appearance between the left and right eyes' views.

2. If the length of the sides of a brick is (20.00 +/- 0.02) cm, the length of two bricks placed side by side is

   • The result is (40.00 +/- 0.02) cm

   • The result is (40.00 +/- 0.04) cm

   • The result is (40.02 +/- 0.04) cm
   • The result is (40.04 +/- 0.02) cm

   When we add quantities, we must add their errors.

3. Which of the following statements is generally true regarding uncertainties?

   • About 67% of measurements should lie within three standard deviations
   • About 67% of measurements should lie within two standard deviations
   • Uncertainties cannot be thought of as following a Gaussian distribution

   • About 67% of measurements should lie within one standard deviation

   About 67% of values lie within $+/- 1$ standard deviation of the mean of a Gaussian distribution, which is the distribution that most experimental uncertainties follow.

4. Which of the following equations determines the distance to an object $Z$ given its disparity $D$, baseline $B$ and focal length $f$?

   • $Z = D / fB$
   • $Z = fD / B$

   • $Z = fB / D$

   • $Z = B / fD$

   This is an equation that you need to be very familiar with; if you got this wrong, make sure you learn the equation and are able to derive it!

5. Which of the following is not an assumption we have made in considering computational stereo?

   • the optical axes of the cameras are parallel

   • the object is stationary

   • the cameras are identical
   • the images are captured by both cameras simultaneously

   The one thing we haven't assumed is that the object is stationary: this would make motion capture practically impossible!

6. When dividing two quantities that have associated errors, which of the following procedures is correct?

   • We subtract the absolute errors
   • We add the absolute errors
   • We subtract the fractional errors

   • We add the fractional errors

   When we multiply or divide quantities, we must add their fractional errors.

7. How does disparity vary with distance?

   • disparity is inversely proportional to the square of distance
   • disparity is proportional to distance

   • disparity is inversely proportional to distance

   • disparity is proportional to the square of distance

   Disparity D and distance Z are related by Z = fB / D so Z is inversely proportional to D.

8. In a camera, the incoming light is focussed onto:

   • the optical axis

   • the back focal plane

   • the front focal plane
   • the lens

   The place where a camera forms its image is known as the back focal plane.

9. If the diameter of a circle is measured as (2.0 +/- 0.2) m, what is the percentage error in the circle's circumference?

   • 1%
   • 30%

   • 10%

   • 20%

   The percentage error in the measurement is 100 x (0.2 / 2.0) = 10%. As the circumference is given by 2 pi r = pi d (where d is the diameter), the percentage error in the circumference is also 10%. Although pi is an irrational number and hence has an infinite number of decimal places, it is known to >10^9 decimal places which is well beyond the accuracy of any measurement we are likely to make.

10. If the diameter of a circle is measured as (2.0 +/- 0.2) m, what is the percentage error in the circle's area?

    • 1%
    • 30%
    • 10%

    • 20%

    The percentage error in the measurement is 100 x (0.2 / 2.0) = 10%. As the area is given by pi r^2 = pi d^2/4 (where d is the diameter), we are calculating the product of two quantities with errors. In this case, the fractional (percentage) errors add, so we have 10 + 10 = 20% error in the area.