A short quiz on computational stereo

Adrian F. Clark

1. The disparity of a nearby object is:

   • indeterminate

   • greater than that of a distant object

   • the same as that of a distant object
   • less than that of a distant object

   Disparity increases as an object approaches the cameras. Disparity D and distance Z are related by Z = fB / D so as Z increases then D must decrease.

2. Which of the following is usually the most important source of error in computational stereo?

   • failing to align the optical axes to be parallel

   • measuring the baseline inaccurately
   • having dissimilar cameras
   • locating the centre of the image

   The only item listed which is measured, which means its error can be estimated and accommodated in calculations of distance, is the baseline.

3. As the baseline, the distance between the cameras, increases, what happens to the disparity?

   • the disparity decreases
   • the disparity stays the same

   • the disparity increases

   • the product of disparity and focal length stays the same

   The disparity must increase as the baseline increases. You can easily show this by pointing at something and moving your head from side to side.

4. How does disparity vary with distance?

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

   • disparity is inversely proportional to distance

   • disparity is inversely proportional to the square of distance

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

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

   • $Z = fD / B$

   • $Z = fB / D$

   • $Z = D / fB$
   • $Z = B / fD$

   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!

6. 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.

7. Why is a pin-hole camera rarely used in practice?

   • Exposure times are long

   • Only nearby objects are in focus
   • The pin-hole is always too large for an image to be made
   • Only distant objects are in focus

   A pin-hole lets very little light into the camera, so exposure times are long.

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

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

   • the object is stationary

   • 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!

9. A particular measurement of the height of a building is repeated many times. The mean and standard deviation of the measurements are calculated and found to be (50.0 +/- 0.5) m. Assuming the uncertainties are Gaussian-distributed, which of the following statements is true?

   • With 95% confidence, you can say that the height of the building is in the range 49.5--50.5 m
   • With 95% confidence, you can say that the height of the building is in the range 49.75--50.25 m

   • With 95% confidence, you can say that the height of the building is in the range 49.0--51.0 m

   • With 95% confidence, you can say that the height of the building is in the range 48.5--51.5 m

   We obtain 95% confidence with 2 standard deviations (SDs) from the mean. As the SD is 0.5 m, 2 x SD = 1 m, and that corresponds to 49--51 m.

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

    • 1%
    • 10%

    • 30%

    • 20%

    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.