From: Peter Bergstrom <peter@isy.liu.se>
<BR>
 To: aahumada@mail.arc.nasa.gov <aahumada@mail.arc.nasa.gov>
<BR>
 Date: Wednesday, December 02, 1998 4:21 AM
<BR>
Hi
<BR>
...
<BR>
I don't understand how you get the factor 2^0.75, in section 2.2.
<P>
You wrote,
"If fx equals fy, the components are orthogonal, and detection can be
predicted
either by probability summation, or more simply, by summing the fourth
powers of
the amplitudes and taking the fourth root. The latter leads to the
threshold
being increased by factor 2^0.75=1.68."
<P>
Regards, ...
<BR>
Peter Bergström 
<BR>
Image Coding Group 
<BR>
Dept. of EE
<BR>
Linköpings University 
<BR>
S-581 83 Linköping
<BR>
Sweden
<BR>
          Phone +46-13-282570
       Fax   +46-13-284422
<BR>
<P>
From al@vision.arc.nasa.gov Mon Jan 11 15:27:54 1999
<BR>
From: Al Ahumada <al@vision.arc.nasa.gov>
<BR>
To: peter@isy.liu.se
<BR>
...
<BR>
This paper by Quick shows the relation between probability
summation and vector summation.
<P>
R. F. Quick (1974)
A vector magnitude model of contrast detection,
Kybernetik, vol. 16, pp. 65-67.
<P>
The basic result is that if detection is based on the detection of
several independent features, with contrast thresholds T(i),
the combination threshold T will satisfy
<PRE>
   1              1
 ----- = Sum [ -------- ],
  beta    i        beta
 T             T(i)
</PRE>
where the summation exponent beta is related to the slope of
the psychometric function.
For contrast detection, this parameter beta is near 4.
<P>
Each of the two components has half the amplitude of a
single component, and thus twice the contrast threshold.
The threshold for the combination of these two half
amplitude components will be
<BR>
1/(2 (1/2^4))^(1/4) = 1/(2^(1-4))^(1/4) = 1/2^(-3/4) = 2^(3/4).