The Research Experience for Teachers Program
http://www.cs.appstate.edu/ret
Activity Title: “Conducting Measurements in Images using ImageJ”
Introduction/Motivation: Some angles and lengths are difficult to measure in real life examples. For
example, it is challenging to measure how high Michael Jordan jumped to dunk during the NBA Dunk
competition in 1988 (Figure 1). It is also challenging to measure the height of the Manistee Lighthouse in
Michigan (Figure 2). Have you ever wondered who actually measured those distances? Have you ever
wondered how they did it? During this lab, you will use ImageJ tools to find out the answers.
Procedure
Background: By studying a simple photograph, we can find the lengths and angles of unknown
measures as long as a reference item is available within the image.
Preparation: Download the mjdunk.jpg and lighthouse.jpg files.
Figure 1 – Michael Jordan’s Dunk in 1988
Figure 2 – The Manistee Lighthouse in Michigan
Lab Activity:
Part 1:
Use the image of Michael Jordan’s dunk in 1988 (Figure 1) to answer questions #1-7.
1. Estimate how high Michael Jordan’s feet are off the ground.
2. Explain one method of determining the how high Michael Jordan’s feet are off the ground.
3. Download Figure 1 on your computer and open it in ImageJ. ImageJ can help you measure the exact
distance from the ground to the bottom of Michael Jordan’s foot. In order to do this, you will need a
reference item. Think of something in the image that you know the length of. For instance, a standard
basketball rim is 10 feet from the ground. Use the line tool to draw a line from the floor to the
basketball rim. Go to Analyze > Measure. Record the length measurement you found in ImageJ.
4. ImageJ uses pixels to calculate length until specified otherwise. You need to set the scale in ImageJ to
convert the current measurement to 10 feet. Go to Analyze > Set Scale to change unit. Now, use the line
tool to measure from the floor to the bottom of Michael Jordan’s foot.
5. Record how high (in feet) Michael Jordan’s feet are off the ground.
6. Does your answer to question 6 seem reasonable? Why or why not?
7. What other object or length in the image could you have used to set the scale (other than the
distance from the floor to the basketball rim)?
Part 2:
Use the image of The Manistee Lighthouse in Michigan (Figure 2) to answer questions #8-17.
8. Estimate the angle of elevation from the head of the individual closest to the lighthouse to the top of
the lighthouse.
9. Explain one method of determining the exact answer for the angle of elevation.
10. Download Figure 2 on your computer and open it in ImageJ. ImageJ can help you measure the exact
angle of elevation. Use the angle tool to draw an angle that represents the angle of elevation from the
head of individual closest to the lighthouse to the top of the lighthouse (Figure 3). Go to Analyze >
Measure. Record the angle measurement.
Figure 3 - The Angle of Elevation
11. Based on your answer to question 10, determine the angle of depression from the top of the
lighthouse to the head of the individual standing closest to the lighthouse (Figure 4). Use ImageJ to
confirm your answer.
Figure 4 – Angle of Depression
12. Assume individual standing closest to the lighthouse is 6 feet 4 inches tall, how tall is the lighthouse
(in feet)? You can do this by using the line tool, setting the scale, and Analyze > Measure like in Part 1 of
this lab.
13. Does your answer to question 12 seem reasonable? Why or why not?
14. The actual Manistee Lighthouse in Manistee, Michigan is 47 feet tall. Find the percent error of your
calculation based on the actual height.
Hint: % error = (Absolute value of{Actual height – your estimate}/Actual height)*100.
15. Draw a right triangle picture illustrating the lighthouse scenario and label all parts of the triangle
with your ImageJ measurements, including the height of the individual (6 feet 4 inches).
16. Use your diagram to set up an equation to determine how far away the individual is standing from
the lighthouse and then solve the equation to find the distance. Record your answer.
17. Use ImageJ to confirm your answer. Record the distance you found using ImageJ
Assessment:
Results/Conclusions:
Each student should turn in a completed “Measuring Images Student Handout.”
Reference(s):
http://www.notyouraveragefitnesstips.com/wp-content/uploads/2010/07/michael-jordan-dunk.jpg
http://upload.wikimedia.org/wikipedia/commons/9/96/Manistee_Lighthouse.jpg