A short quiz on computational stereo

Adrian F. Clark

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

   • 30%
   • 1%

   • 20%

   • 10%

   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.

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

   • We add the fractional errors

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

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

3. 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.

4. How does disparity vary with distance?

   • disparity is inversely proportional to the square of distance

   • disparity is inversely proportional to distance

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

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

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

   • 20%

   • 30%

   • 1%
   • 10%

   The percentage error in the measurement is 100 x (0.2 / 2.0) = 10%. As the volume is given by 4/3 pi r^3 = pi d^3/6 (where d is the diameter), we are calculating the product of three quantities with errors. Hence, their fractional (percentage) errors add, so we have 3 x 10 = 30% error in the volume.

6. What is disparity?

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

   • 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

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

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

   • the cameras are identical

   • the object is stationary

   • the images are captured by both cameras simultaneously
   • the optical axes of the cameras are parallel

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

8. In order to use computational stereo, we must find:

   • the location of different features in the left and right images
   • different pixels in the left and right images
   • the same pixel in the left and right images

   • the location of the same feature in the left and right images

   We must find the same feature in the left and right images in order to estimate the distance to it.

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

   • $Z = fB / D$

   • $Z = fD / B$
   • $Z = B / fD$
   • $Z = D / fB$

   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!

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

    • the lens
    • the optical axis

    • the back focal plane

    • the front focal plane

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