Biomedical Engineering Reference
In-Depth Information
one-half the spatial sampling frequency can be
sampled and reconstructed without aliasing
[18]
.
Aliasing is evident when the reconstructed
image shows incorrect spatial frequencies that
are lower than the true image. If the spatial sam-
pling frequency in a given direction in the image
is
F
s
, and the true spatial frequency in the same
direction of some pattern in an image is
f
o
, then
if
f
o
>
F
s
/
2
, and the aliased frequency will be
capture images of the snow fence and transmit
the images back to a monitoring station. The
webcam uses a 1.3-megapixel CCD rectangular
sensor array (
1280H
×
720 V
pixels), and the
physical size of the CCD array inside the camera
is 19.2 mm horizontally by 10.8 mm vertically.
1
The aspect ratio of each image frame taken with
this camera is 16:9, and the aspect ratio of each
individual photodetector (pixel) in the CCD
array is 1:1 (i.e., square), such that the center-to-
center pixel spacing is the same in the
x
direction
and the
y
direction. The webcam uses a built-in
22.5 mm focal length lens that is permanently
fixed at a distance from the CCD array such that
it will always focus on objects that are relatively
far away (i.e., optical infinity). The snow fence is
made up of very dark-colored slats that are 2.44 m
(about 8 f) high and 200 mm wide, with 200 mm
of open space between adjacent slats. In the
expected snowy conditions, the contrast of the
dark slats against the light-colored background
should allow a good high-contrast daytime image
of the snow fence, within the limits of spatial
sampling requirements. No night-time images
are needed.
See
Figure 1.2
for a simple illustration of what
the snow fence might look like, not necessarily
drawn to scale nor at the actual viewing dis-
tance, with snow at the base obscuring some
unknown part of the slat height. Assume the
fence extends to the right and left of the figure
a considerable distance beyond what the simple
figure shows. You would like to view as wide a
section of the experimental snow fence as pos-
sible, so you want to place the camera as far
away from the fence as possible. Thus, you need
to calculate the maximum distance you can
place the webcam from the fence and yet still be
able to easily make out individual slats in the
image, assuming the limiting factor is the spatial
sampling frequency of the image. Assume the
F
s
/2
−
(
f
o
−
F
s
/2)
=
F
s
−
f
o
.
(1.3)
Aliasing in an image is most noticeable to
humans with regard to periodic patterns, such
as the stripes of a person's tie or shirt, which
when aliased tend to look broader and distorted
[18]
. Note that most real-world images are not
strictly band-limited, so some amount of alias-
ing is usually inevitable.
Fourier theory tells us that even a complex
image can be modeled as an infinite weighted
sum of spatially sinusoidal frequencies
[18, 19]
.
Knowledge of how these spatial frequencies are
sampled can help predict how well a vision sen-
sor may perform. Equation
(1.2)
allows us to
map transverse distances between the object
plane and the image plane and understand how
the spatial sampling interval compares to the
various transverse distances in the image.
Example Problem
:
As a real-world example
that highlights the use of these relationships, sup-
pose you need to remotely monitor the condition
of a small experimental snow fence at a certain
point along a northern-route interstate highway,
using a digital camera. The individual slats of the
snow fence are made of a new environmentally
green recycled material that may or may not hold
up under the wind pressures expected during the
winter; that is the purpose of the monitoring. The
imaging only needs to detect if a slat breaks and
thus appears to be missing. The camera will be
an inexpensive webcam that will periodically
1
It is traditional for manufacturers of cameras, monitors, televisions, etc. to provide size specifications as (horizon-
tal, vertical) and aspect ratios as H:V, so this is how the information is provided here. However, this is the
opposite
of most image-processing and linear algebra topics, where dimensions are usually speciied as (row, column).
