Fits a polynomial of x&y to the image data, also subtracts the polynomial as a background.

This plugin-filter fits a polynomial of variable order to an image.

The selection (if any) determines the image area the polynomial is fitted to. Output can be the polynomial fit or the image with the fit subtracted. Output area is always the whole image, irrespective of the selection.

Dialog parameters

• The order of the polynomial can be selected separately for x, y and mixed terms. E.g. with orders 2, 3, and 2 for x, y, and xy, respectively, the polynomial will be a + b*x + c*x² + d*y + e*y² + f*y³ + g*xy (note that the lowest-order mixed term, xy, has order 2).
• “Output Fit (Don't Subtract)” determines whether the output should be the polynomial fit. If unchecked, the polynomial is subtracted from the image.
• “Shift Values to Display Range” uses the mean value of the current display range, (max+min)/2, as zero for the subtracted output image. If unchecked, zero output corresponds to 128 for 8-bit and RGB, 32768 for 16-bit and 0 for float images. This option has no effect if “Output Fit (Don't Subtract)” is checked.

For 8-bit and 16-bit images with no or linear calibration, the image will be calibrated by shifting the zero value appropriately.

Hints for usage

• To exclude particles or other foreground objects from the fit, select a threshold to include the background only, then run Edit>Selection>Create Selection to restrict the fit to the selection (i.e., to the background).
• For subtracting the background of 8-bit, 16-bit and RGB images, saturation of the output can be avoided by setting “Brightness&Contrast” to such a values that desired background level is in the middle of the displayed range, and selecting “Shift Values to Display Range”. Example: For an 8-bit image with background values around 30 and no significant area of foreground objects in the selection, it makes sense to set a display range of 0-60 before running the filter, and check “Shift Values to Display Range”.

• Undo will revert only the image contents, not the calibration.
• In some cases (very high order of the polynomials and/or some non-rectangular selections), a “Fit failed” message may appear although the fit is mathematically possible. On the other hand, in some cases (some non-rectangular selections), it may run without a “Fit failed” message although there are not enough points for a unique solution with the given order of the polynomial.

Download the sourcecode (file Fit_Polynomial.java), save it in the “plugins” folder or a subfolder thereof and compile it with Plugins>Compile and Run… (make sure you name the downloaded file ”Fit_Polynomial.java”; uppercase/lowercase matters).

The plugin is in the public domain.

— Michael Schmid 2008/09/30 15:19