Name_________________________________
Problem Set #2
BOT/GEOG 4111/5111
Fall 2015
The problems are open book, open note. Please work on them individually and not in
groups or with another student. Use your own paper if necessary. Show your work! If
you have questions I’m happy to help you but don’t ask me to confirm all of your
answers! The problems are due on Thursday, November 5 in class.
1. You find 10 locations for ground control points (GCPs) in an image that you are
rectifying, and you are able to extract UTM coordinates for the same GCPs using
a topographic map of the same area. You are uncertain about whether you
should use a 1st, 2nd, or 3rd order transformation to “warp” the image to fit the
GCPs, so you graph them:
UTM Coordinates
B
A
Image Coordinates
a. Based on the graph, which type of transformation would be most
appropriate? Draw it on the graph. What types of areas are appropriate
for using this transformation type? (4 pts.)
b. The GCPs labeled A and B are anomalous. What might be causing this?
How might you deal with them? (4 pts.)
c. Why do GCPs rarely fit the transformation equation perfectly? (2 pts.)
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2. The blue band from an 8-bit Landsat 5 image has the following histogram, with
pixel values ranging from a minimum of 60 to a maximum of 130.
a. In the same graph above, draw the histogram that would result from
doing dark pixel subtraction (4 pts.)
b. What is the minimum pixel value (DN) after you complete dark pixel
subtraction? (2 pts.)
c. If a pixel somewhere in the uncorrected image has a DN of 125, what will
its DN be in the corrected image? (2 pts.)
d. What part of the radiance equation are you correcting for when you use
dark pixel subtraction? (2 pts.)
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3. You collect training data for three tree-dominated types (Oak, Maple, Spruce)
in your study area and then use the training data to determine the range of
values of red and NIR DNs for each type as follows:
Oak: Red DNs range from 40 to 80; NIR from 220 to 250
Maple: Red DNs from 60 – 90; NIR from 200 to 240
Spruce: Red DNs from 80 – 100; NIR from 80 to 140
a. Draw a feature space graph on the grid (next page) using Red as the xaxis and NIR as the y-axis and draw each tree type from the table above
as it would occupy the feature space using a parallelepiped classifier (8
pts.)
b. Given the following three unknown pixels and their DNs in each of the
same 2 satellite bands used in part (a) above (red and NIR), which of the
three tree types (if any) would each be classified as using the
parallelepiped limits you drew. If your answer is “unknown” or
“uncertain,” explain why in the comment column (7 pts.).
Unknown
Pixel
A
Red DN
NIR DN
50
230
B
150
150
C
70
230
Tree Type?
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Comment (if needed)
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(Use grid above for question #3)
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4. You are mapping (supervised) the same tree types (maple, oak, spruce) as in
question 3 above, and have characterized the training data as summarized in the
following table:
Tree Type
Maple
Oak
Spruce
Red avg. DN
50
50
25
Red Std. Dev.
20
50
10
NIR avg. DN
100
150
50
NIR Std. Dev.
20
50
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a. Graph the centroid of the training data for each tree type below with NIR as the
y-axis and Red as the x-axis (4 pts).
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b. To which tree type would a pixel with Red DN = 50 and NIR DN = 120 be assigned
using a minimum distance classifier and why? (8 pts.)
c. Which tree type would the same pixel be classified as using a maximum
likelihood classifier and why? (8 pts.)
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5. You are working at a local recycling center and must group items to be
transported to regional recycling centers for reprocessing.
a. Create a hierarchical classification scheme for the following items (8 pts):
metal
clear glass
brown glass
plastic #3
glass
aluminum soda cans
plastic
newspaper
plastic #7
aluminum
paper
green glass
steel cans
office paper – white
aluminum foil
office paper – colored
plastic bags
steel
magazines
cardboard
b. Does this hierarchy have the same number of levels throughout? (2 pts.)
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DN or Reflectance
6. The graph below shows the spectral reflectance curves for 2 materials (A and B)
that occur in an area that you are studying, in terms of satellite bands
(numbered on the x-axis from 1 - 11). Answer the questions that follow.
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2
3
4
5
6
7
8
9
10
11
a. Write the equation of an algebraic index using 2 bands that will
distinguish materials A and B. (6 pts.)
b. Will the image resulting from calculation of your index appear as black
and white or color if you display it on your computer? Why? (5 pts.)
c. What would material A look like on your screen? (2 pts.) What would
material B look like? (2 pts.)
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7. In the space below, draw a graph showing how NDVI (y-axis) changes with
increasing Leaf Area Index (LAI) (x-axis) (8 pts.), and answer the question that
follows.
a. Is the response of NDVI to increasing LAI linear or non-linear? (2 pts.)
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8. Draw and label the first and second principal component axes (PC1 and PC2)
through the data cloud outlined in the 2-band feature space below by applying
the rules we discussed in lecture for constructing these axes. (10 pts.)
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