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Re: [WM]: What is spatial frequency
The word "degree" in the phrase cycles per degree refers to
the angle, in degrees, subtended. Consider a cone, the center of
which is the axis along which you are looking. Let this cone have
an angle of theta.
(this
picture is in a font with fixed width (currier new)
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...------- D ----- H = PN
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Theta is the whole angle, and theta/2 is from the axis line
up.
theta/2 = arctan( H/(2D) )
theta = 2*arctan( H/(2D)
)
where H is the picture height, which is a function of the dot
pitch of the display. If the image is displayed on a monitor with
a dot pitch of P and if the picture is N pixels high, then H = PN.
D is the distance to the display plane. Notice that unless the
display is curved, D will not be constant. As long as D is large
enough compared to the image height, we can approximate D as a
constant.
To convert frequency in cycles / pixel to
frequency in cycles / degree set N=1. In other words, consider the
case where H = P, the distance between adjacent pixels. Assume
that there is a frequency on the display and that X cycles fit in this
H. So, the frequency is X/1 cycles/pixel. From the
perspective of angle, the same X cycles fit in theta. So the
frequency is X/theta cycles per degree. Dividing, this gives
1/theta pixels/degree.
rho (cycles/degree) = f (cycles/pixel) *
1/( 2*arctan( P / 2D ) )
For example, my
Sun monitor has a dot pitch of 0.31mm. If display an image on the
monitor and view it at 40cm, then the conversion becomes: (have to
make sure that P and D are in the same units)
rho = f *
140.752
- Jeffrey
At 04:09 AM 8/19/2002 -0700, Parthipan Siva wrote:
Hi all,
What is spatial frequency in
cycles per degree?
I am trying to find an algorithm for
comparing the
original image with the watermarked image. Most
papers
I read accounts for the HVS using this spatial
frequency. I am unfamiliar with this term.
Can someone
tell me how from an N x N gray scale image
I can get the spatial
frequency in cycles per degree.
Thank you,
Parthipan
Siva ---
Dr. Jeffrey A Bloom,
Video and Web Informatics
Sarnoff Corporation, 201 Washington Road,
CN 3500, Princeton, NJ 08543-5300
Email:
jbloom@sarnoff.com
http://www.geocities.com/Jeffrey_Bloom
Phone: (609)
734-3287 &nbs
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Fax: (609) 734-2662
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