Improved Curve Fitter in ImageJ 1.46f

• Simplex Minimizer is now a separate class, allowing users to minimize other functions or to fit a curve with a custom fit function.
• Slightly improved simplex algorithm.
• There is no limit on the number of reinitializations (formerly called 'restarts'), apart form the maximum iteration count.
• Two threads with two independent minimization runs, with repetition until two identical results are found, to avoid local minima or keeping the result of a stuck simplex. Redefined the former 'restarts' public methods to apply to these retries, with the default of 2 restarts meaning up to 6 minimization runs (2 threads, each 1 initial run and up to 2 retries). This means that for equal performance, you will see twice the number of iterations, because a minimum of two runs are performed.
• The Curve Fitter supports linear regression, which is used for most built-in functions to eliminate one or two parameters. This costs some overhead, so it does not reduce fitting time, but generally increases the quality of the result. E.g., the 'exp+offset' easily finds whether to use a positive or negative exponent.
• In addition to initial parameters, 'initial parameter variations' can be specified, giving the order of magnitude of parameters. For the built-in functions, this helps e.g. for polynomials if the numbers are not between 0.01 and 10 but e.g. around 10^6.
• Fixed 'Rodbard NIH Image' display: The fit in ImageJ is ok, the graphics are not. This function actually fits x = Rodbard(y); the graph has x&y of the points exchanged.
• Added polynomials of degree 5-8. As with most fitting software, this works reasonably well only if the x values encompass x=0; not for e.g. x values all between 10 to 15.
• New "Exponential (linear regression)" and "Power (linear regression)" fits. They behave like the "exp" and "power" fits in most other programs (Excel, etc.).
• UserFunction interface for user-defined minimization or fit functions.
• Analyze>Tools>Curve Fitting usability enhancements: color graphics, warning in case of problems, nicely sorted list of functions.
• More source code documentation.