page 494
17.11 PRACTICE PROBLEMS
1. Consider a circle and an ellipse that might be viewed by a vision system. The circle has a 4” radius, whereas the ellipse has a minor and major radius of 2” and 4”. Compare the two definitions using form factors (compactness and thickness) and show how they differ.
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ans.
circle |
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circle |
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R = 4 |
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R1 = 2 |
R2 = 4 |
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Dmin |
= 8 |
Dmax = 8 |
Dmin |
= 4 |
Dmax |
= 8 |
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A = π R2 = 50.3 |
A = π |
R1R2 = 25.1 |
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P = π ( 2R) |
= 25.1 |
P ≈2π |
R12 + R22 |
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19.9 |
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2 |
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Compactness values differ |
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C = |
P2 |
= 12.5 |
C = |
P2 |
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----- |
----- = 15.8 |
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A |
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A |
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the min/max values are the same for the circle |
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Dmin |
T |
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Dmin |
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0.16 |
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Tmin |
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Tmax |
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= ----------- = 0.16 |
min |
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A |
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Dmax |
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Tmax |
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0.32 |
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A |
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2. Describe image resolution in vision systems.
ans. Resolution of a video image describes the number of rows and columns of pixels in a video image. A higher resolution means that there are more rows of pixels in the images, and therefore we can distinguish smaller details.
3. An image has been captured from a video camera, and stored in the matrix below.
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64 |
87 |
54 |
64 |
12 |
35 |
22 |
36 |
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36 |
57 |
76 |
24 |
84 |
26 |
63 |
74 |
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84 |
187 |
201 |
234 |
195 |
222 |
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25 |
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54 |
78 |
197 |
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34 |
75 |
218 |
74 |
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25 |
9 |
84 |
202 |
194 |
213 |
192 |
79 |
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37 |
25 |
57 |
98 |
93 |
95 |
91 |
89 |
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a) Use a threshold of 100 to filter the image.
ANS. |
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b) Perform an edge detection on the thresholded image.
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c) Segment the image into distinct regions.
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d) Calculate the compactness and thickness for the region above the threshold.
ANS. |
( 22) |
2 |
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6 |
C = |
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T = -----OR----- |
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e) Calculate form factors including perimeter, area, centroid, compactness and minimum and
maximum thickness.
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4. We have four part shapes (as listed below) that will be arriving on a conveyor. We want to develop a decision tree for the vision system to tell them apart. We also need to find their centroids relative to the top left of the image so that a robot may pick them up.
Isosceles triangle 6” per side
Rectangle 2” by 8”
Triangle with side lengths 8”, 5” and 4”
Circle 5” Radius
ans.
First, calculate the form factors
Form |
Area |
Perim |
Com- |
Tmin |
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eter |
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pact |
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isosceles tri- |
15.5 |
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0.333 |
angle |
9 |
18 |
20.78 |
3 |
rectangle |
16 |
20 |
25 |
0.125 |
A > 40
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circle |
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A < 40 |
Tmin < 0.18 |
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rectangle |
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Tmin > 0.18 |
C > 28 |
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odd triangle |
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C < 28 |
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isosceles triangle |
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