Download A Photo-based Approach to Variable Plot Sampling

A Camera as an Angle-Gauge
Brock Stewart
Chris J. Cieszewski
Michal Zasada
The University of Georgia
Camera
Focal Point: where all rays converge
Focal Length: distance from focal point to
center of film
Inverted image
formed on film
Camera
Focal Point: where all rays converge
Focal Length: distance from focal point to
center of film
Inverted image
formed on film
Angle-Gauge
Angle-Gauges project angles.
Used to project the Critical Angle in AngleCount Sampling.
Angle-Count Sampling:
Project constant angle, the Critical Angle
toward trees
Count trees that appear wider than angle
BA/acre = (# counted)*BAF
Angle-Gauge
How is a camera used as an
angle-gauge?
Take pictures
at sample
points
Focal Point is
over the
Sample Point
Horizontal Field
of View
represents a
partial sweep
How is a camera used as an
angle-gauge?
Take pictures
at sample
points
Focal Point is
over the
Sample Point
Horizontal Field
of View
represents a
partial sweep
Trees
counted
in office
on
pictures
How are trees counted on
pictures?
By comparing their DBH on pictures against a
width that represents the Critical Angle.
How are trees counted on
pictures?
The width used to represent the Critical Angle
on pictures is called the Critical Width.
How are trees counted on
pictures?
The size of the Critical Width depends on how
far it is from the center of the picture.
How are trees counted on
pictures?
CW’s if 4x6 in. picture, BAF=10, f =50mm
How are trees counted on
pictures?
The Critical Width changes across a
picture, but not by much.
(Critical Width)*3
What is the Critical Width?
Borderline Tree directly in front
of camera
We know that when a
tree is borderline,
this means that the
arms of the Critical
Angle are tangent to
the tree’s crosssection
Critical
Angle
Borderline Tree directly in front
of camera
•Similarly, the angle
between light rays reflecting
off either edge of the tree
and traveling through the
Focal Point to the film is the
size of the Critical Angle
•Same angle on both
sides of the Focal
Point
Critical
Angle
Critical
Angle
Borderline Tree directly in front
of camera
•Distance between the two
points on the film where the
arms of the Critical Angle
meet the film is the Critical
Width on the film.
Critical
Angle
Critical
Angle
Borderline Tree directly in front
of camera
Image of the tree
on the film is
borderline
4 ½ Feet
Why does the critical width
change?
1
Critical
Angle
2
Critical
Angle
Critical
Angle
Critical
Angle
CW tree 2
CW tree 1
3-D geometry
(x2,y)
(x1,y)
f
3-D geometry
CW = |x2| - |x1|
(x2,y)
(x1,y)
|x2|
f
|x1|
Formula for Critical Width on
Pictures
CW 
 

 
f  y tan arctan 




 
2
2

 

    tan arctan 


f 2  y 2  2 


x
  
  

2
2 
2

f y 


x
f = Focal Length
α = Critical Angle
x, y = picture coordinates scaled down to film
coordinates
(x,y) = point where Critical Angle is projected
Formula for Critical Width on
Pictures
CW 
 

 
f  y tan arctan 




 
2
2

 

    tan arctan 


f 2  y 2  2 


x
  
  

2
2 
2

f y 


x
•This gives Critical Width as a width on film
•The result is scaled up to picture units
3-D geometry
TA =θ2 – θ1
(x2,y)
(x1,y)
θ2
TA
θ1
f
Formula for Tangent Angle of
trees on Pictures




x2
x1
  arctan 

TA  arctan 
2
2
2
2
 y f 
 y f 




f = focal length
x, y = picture coordinates scaled down to film
coordinates
x2 is farthest from y-axis
x1 is nearest to y-axis
Data
Data
Stand Point
1
1
2
3
1
2
2
3
1
3
2
3
1
4
2
3
4
3
5
# Trees "In"
Field
Picture
21
21
23
28
19
17
22
22
24
21
25
28
13
11
15
15
13
9
10
10
15
16
15
14
No Difference
Field < Pics
Field > Pics
Diff.
0
5
-2
0
-3
3
-2
0
-4
0
1
-1
% Diff.
0.0
21.7
-10.5
0.0
-12.5
12.0
-15.4
0.0
-30.8
0.0
6.7
-6.7
Average: -2.95%
Std. Dev.: 13.66%
Why use a Camera as an anglegauge?
“Oh, that’s what that stand looked like”,
plus, can make meaningful measurements
on the pictures.
Historical records, repeated measurements,
Borderline trees evaluated in office
Summary
Take pictures at sample point
Use the changing “Critical Width” to count
trees
Measure Tangent Angle of borderline trees
Need to know:
Camera’s focal length
Film Dimensions
Simple software can be used to count trees
with a changing width, also check
borderline trees