| fitting mixed gaussians [message #44140] |
Tue, 17 May 2005 11:22 |
btt
Messages: 345
Registered: December 2000
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Senior Member |
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Hello,
I would like to employ a "mixed gaussian" fitting routine that fits not
just one peak in a distribution but rather fits any number of peaks.
According to my old Gonzales and Woods Image Processing book this
technique is used in Bayesian classifier - in the two class problem the
saddle of the two fitted curves is used as the point around which the
classes are separated. I just to segment simple grayscale images with it
usiing the histogram as the data to model.
Using GAUSSFIT or MPFIT it's very easy to fit one (the tallest) peak
shown in the example (see code example below.) But how the heck to fit
the second peak? I have scoured the internet and find much written
about it - but it is all in Greek. Really. Yikes.
Is it possible to make the curve fitting routines I have on hand to fit
two gaussian models?
Thanks,
Ben
******START HERE
PRO example_mixedgaussfit
n = 256.
x = Findgen(n)/(n-1)*(n-1)
y = 0.4*RANDOMN(seed, n)
; the coefficients are amplitude, center and width
a = [0.3, n/4., n/20. ]
b = [0.05, n-n/4., n/10.]
z1 = (x - a[1])/a[2]
z2 = (x - b[1])/b[2]
; start with random noise.
y = 0.02*RANDOMN(seed, n) > 0.0
;now add in the 'model' peaks
;the first gaussian the second gaussian
y = y + a[0]*exp(-z1^2/2) + b[0]*exp(-z2^2/2)
;rescale to 0-1 as if probability
y = y/MAX(y)
;use the built in gaussfit
;note that the highest peak is fit
r = gaussfit(x,y, c, nTERMS = 3)
plot, x, y, title = 'Mixed Gaussians'
oplot, x,r, thick = 3
XYOUTS, x[a[1]], y[a[1]]/4 , 'peak a', align = 0.5
XYOUTS, x[b[1]], y[b[1]]/4 , 'peak b', align = 0.5
END
******END HERE
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