Geog 104 - Photogrammetry Exercise

104 Folks, I know this one is a bit rough but it will work. Let me know how to make it better as you work through it. Thanks. -Matt

Objectives: Consider image geometry and scale and the ability to measure things in aerial imagery via: scaling; radial relief displacement; and shadow length calculations.

Useful Equations:

RF = (focal length) / (flying height)   

RF = (map distance) / (ground distance)

(object height) = ((displacement)/(radial distance)) * (flying height)

tan(sun elevation angle) = object height / shadow length

tan(a) = Opposite side / Adjacent side

and the ever useful Pythagorean theorm:  a^2 + b^2 = c^2

Data: For this exercise use R0012846.JPG, one of the images taken from Chuck's ill-fated hexcopter on at 13:44:18 on 13 March 2013 (assuming that the camera's clock was right). This image is 3,648 by 2,736 pixels and records red, green and blue intensities for each pixel. The camera's focal length was 6 mm. The sensor is a 10 mp Sony ICX685CQZ. It measures 9.31mm diagonally and has a 4:3 aspect ratio.

Software: any image viewing program that will give you coordinates of pixels. Paint, GIMP, Photoshop, etc. would do.

On the image, you can see the steps on the west side of Hawaii Hall, several (nearly) vertical light poles, columns, and palm trees, (most) of the class, the concrete sidewalk and lawn. Some astute students noted that the people problably are looking at the helicopter, and that the helicopter cast a shadow on the sidewalk in the upper left of the image.

NB: This is not the standard 23cm x 23cm aerial survey camera imagery that is traditionally used to teach photogrammetry, but a bit of an experiment using consumer-grad digital cameras on a wobbly platform for less costly remote sensing. Our image is missing fiducial marks, has no indication of flying altitude or time printed on it, and we have no record of lens calibration. Still, one hopes it will be useful.

To help establish the scale of the image, some of the imaged ojects have been measured for you:

You can find the ground-size of the image pixels by finding how many pixels are represented by each of those measurements and dividing to get meters per pixel.

Vocabulary: Principal Point (axis of camera; center of relief displacement). Nadir (directly under camera). Isocenter (mid-point between PP and nadir; objects 'above' it displaced toward it, 'below' it displaced away from it). Vertical photos (< 3 degrees tilt).


  1. What are the ground dimensions of a pixel in this image? (i.e. average estimates from several measured lengths)
  2. How wide is the staircase? (scaling)
  3. What are the row and column coordinates of the principal point suggested by the relief displacement?
  4. What are the row and column coordinates of the principal point, assuming that the axis of the camera falls on the center of the image frame?
  5. What was the flying height of the hexcopter? (we have scale and focal length)
  6. How nearly "vertical" is the photo? ( arctan(distance between nadir and PP / flying height) )
  7. How tall is the lamp post at the right side of the image? (shadow length)
  8. How tall is the equipment cart in the lower right side of the image? (relief displacement)
  9. How tall is the person walking on the walk? (try shadow length and relief displacement and maybe average them)
  10. Find yourself (or another person) and try the same thing.
  11. Finally, suggest another question that might have been good to ask here.