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Analyze .
Tools .
Number of restarts To ensure that the result is trustworthy (i.e., that it did that it did
not get “stuck” or find a local minimum), CurveFitter tries at least twice to find the
minimum, with different starting points. If the two results are not the same, Number
of restarts determines how often it may start two additional runs, until the best two
results agree within the error tolerance. There is no limit for the number of restarts,
apart from the maximum number of iterations.
4. Click Apply to create a 32–bit copy (see Image Types and Formats) of the current image
transformed with the chosen function.
CurveFitter’s built-in functions. A more detailed summary of the CurveFitter’s abilities is
available online. The complete documentation can be accessed through the ImageJ API. Most functions
use linear regression to determine the first two coefficients directly, which generally increases the quality
of the result [42]. As explained in Curve Fitting. . . , simplex fitting options can be adjusted by selecting the
Show settings checkbox. For polynomials, the proposed criteria are known to yield optimal convergence.
Function
Straight line
Formula
Comments
y = a + bx
cf. Pixel Inverter (Analyze . Calibrate. . . )
2nd –8th degree
polynomial
y = a + bx + cx2 + . . . + ix8
The range of x values should not be too far from 0,
especially for higher-order polynomials
4th : should fulfill |xMean | < 2 × (xMax − xMin )
5th : should fulfill |xMean | < (xMax − xMin )/2
7th & 8th : should fulfill |xMean | xMax − xMin
Power†
y = a × xb
†
Exponential†
y = a × ebx
Exponential
with offset
y = a × e−(bx) + c
Exponential
recovery
y = a × (1 − e(−bx) ) + c
Log
y = a × ln(bx)
y = a + b × ln(x − c)
Rodbard
y=
d+(a−d)
b
1+( x
c)
Rodbard
(NIH Image)
x=
d+(a−d)
1+( yc )b
Inverse
Rodbard
1/b
y = c × ( x−a
d−x )
Gaussian
y = a + (b − a) × e−
Gamma variate
y = b × (x − a)c × e−(
See also:
CurveFittingDemo,
Profile Plot Options. . .
Optionally, fit can be performed without linear
regression during minimization. Most curve-fitting
programs such as Microsoft® Excel® use
regression. Fitting without regression assumes
equal weight for all data points and is insensitive to
zero or negative data
cf. FRAP_Profiler plugin
[42], see DeLean A, Munson PJ, Rodbard D.
Simultaneous analysis of families of sigmoidal
curves: application to bioassay, radioligand assay,
and physiological dose-response curves. Am J
Physiol. 1978 Aug;235(2):E97–102 [PMID: 686171]
(x−c)2
2d2
[42]
x−a
d )
RodbardSigmoidFit and
149
PlotSigmoidDerivatives macros,
Last updated: 2012/10/02