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+.help fit1d Jul85 images.imfit
+.ih
+NAME
+fit1d -- fit a function to image lines
+.ih
+USAGE	
+.nf
+fit1d input output type
+.fi
+.ih
+PARAMETERS
+.ls input
+Images to be fit.  The images may contain image sections.  Only the region
+covered by the section will be modified in the output image.
+.le
+.ls output
+Output images to be created or modified.  The number of output images
+must match the number of input images.  If an output image does not exist
+it is first created and initialized to zero for fit types "fit" and
+"difference" and to one for fit type "ratio".
+.le
+.ls type
+Type of output.  The choices are:
+.ls fit      
+An image created from the function fits to the image lines.
+.le
+.ls difference
+The difference between the image and the fit (i.e. residuals).
+.le
+.ls ratio
+The ratio of the image and fit.
+.le
+.le
+.ls bpm = ""
+List of bad pixel masks.  This may be a null string to not use a
+bad pixel mask, a single mask that applies to all input images, or
+a matching list.  The value may also be !<keyword> to specify a keyword whose
+value is the mask to use.
+.le
+.ls axis = 1
+Axis along which the one dimensional fitting is done.  Axis 1 corresponds
+to fitting the image lines and axis 2 corresponds to fitting the columns.
+.le
+.ls interactive = yes
+If \fBinteractive\fR is set to yes, a plot of the fit is drawn and the
+cursor is available for interactively examining and adjusting the fit.
+.le
+.ls sample = "*"
+Lines or columns to be used in the fits.
+.le
+.ls naverage = 1
+Number of sample points to combined to create a fitting point.
+A positive value specifies an average and a negative value specifies
+a median.
+.le
+.ls function = spline3
+Function to be fit to the image lines or columns.  The functions are
+"legendre" (legendre polynomial), "chebyshev" (chebyshev polynomial),
+"spline1" (linear spline), and "spline3" (cubic spline).  The functions
+may be abbreviated.
+.le
+.ls order = 1
+The order of the polynomials or the number of spline pieces.
+.le
+.ls low_reject = 0., high_reject = 0.
+Rejection limits below and above the fit in units of the residual sigma.
+.le
+.ls niterate = 1
+Number of rejection iterations.
+.le
+.ls grow = 0.
+When a pixel is rejected, pixels within this distance of the rejected pixel
+are also rejected.
+.le
+.ls graphics = "stdgraph"
+Graphics output device for interactive graphics.
+.le
+.ls cursor = "stdgcur"
+Graphics cursor input.
+.le
+.ih
+DESCRIPTION
+A one dimensional function is fit to each line or column of the input images.
+The function may be a legendre polynomial, chebyshev polynomial,
+linear spline, or cubic spline of a given order or number of spline pieces.
+The output image is of pixel type real and is formed from the fitted
+function values, the difference or residuals of the fit (pixel value -
+fitted value), or the ratio between the pixel values and the fitted values.
+
+The output image may exist in which case a section in the input image is
+applied to the output image.  Thus, a section on the input image causes only
+that part of the output image to be changed.  If the output image does not
+exist it is first created with a size given by the full (without a section)
+input image and initialized to zero for fit and difference output types
+and one for ratio output types.
+
+A bad pixel mask may be specified to exclude data from the fitting.  Any
+non-zero value in the mask is excluded.   It appears in the interactive
+fitting in the same way as manually deleted points.  The mask is matched to
+the input image(s) as described by \fBpmmatch\fR.  The default is matching
+in physical coordinates.
+
+The points fit are determined by selecting a sample of lines or columns
+specified by the parameter \fIsample\fR and taking either the average or
+median of the number of points specified by the parameter \fInaverage\fR.
+The type of averaging is selected by the sign of the parameter and the number
+of points is selected by the absolute value of the parameter.
+The sample points are specified relative to any image sections.
+
+If \fIlow_reject\fR and/or \fIhigh_reject\fR are greater than zero the sigma
+of the residuals between the fitted points and the fitted function is computed
+and those points whose residuals are less than \fI-low_reject\fR * sigma
+and greater than \fIhigh_reject\fR * sigma are excluded from the fit.
+Points within a distance of \fIgrow\fR pixels of a rejected pixel are also
+excluded from the fit.  The function is then refit without the rejected points.
+This rejection procedure may be iterated a number of times given by the
+parameter \fIniterate\fR.
+
+The fitting parameters (\fIsample, naverage, function, order, low_reject,
+high_reject, niterate, grow\fR)
+may be adjusted interactively if the parameter \fIinteractive\fR is yes.
+Lines or columns from the image are selected to be fit with the \fBicfit\fR
+package.  A single column or line may be chosen or a blank-separated range
+may be averaged.  Note that the averaging applies only to the graphed
+data used to set the fitting parameters.  The actual image lines and columns
+are fit individually.  The interactive cursor mode commands for this package
+are described in a separate help entry under "icfit".  Line 1 is automatically
+selected for one dimensional images and any number of lines or columns may be
+selected for two dimensional images.  Note that the lines or columns are
+relative to the input image section; for example line 1 is the first line of
+the image section and not the first line of the image.  When an end-of-file or
+no line(s) or column(s) are given then the last selected fitting parameters
+are used on each line or column of the image.  This step is repeated for
+each image in the input list.
+.ih
+EXAMPLES
+1.  To create a smoothed version of an image by fitting the image lines:
+
+    cl> fit1d image fitimage fit
+
+If the interactive flag is set and the image is two dimensional then a prompt
+for an image line is printed:
+
+    image: Fit line = 100 200
+
+The selected lines are averaged, graphed, and the interactive options for
+setting and fitting the line are used.  Exiting with 'q' or return prompts for
+another line if the image is two dimensional.  When the fitting parameters
+are suitably set then respond with end-of-file or return to fit all the lines
+of the image and create the output image.
+
+2.  To subtract a linear function fit to columns 10 to 20 and 80 to 100 from
+columns 10 to 100 and to subtract another linear function fit to lines
+110 to 120 and 180 to 200 from columns 110 to 200:
+
+.nf
+    cl> fit1d image1[10:100,*] output diff axis=2 sample="1:11,71:91"
+    cl> fit1d image1[110:200,*] output diff axis=2 sample="1:11,71:91"
+.fi
+
+Pixels outside columns 10 to 100 and 110 to 200 are not affected.  Note that the
+sample points are specified relative to the image sections.  The script
+\fBbackground\fR is available in other packages for doing background
+subtractions.
+
+3.  To determine a small scale response image:
+
+    cl> fit1d image1 flat ratio
+
+The task \fBimred.generic.flat1d\fR is available for making flat field images
+by this method with the addition of an extra parameter to limit the data values
+for which the ratio is computed.
+.ih
+SEE ALSO
+imred.generic.background, imred.generic.flat1d
+xtools.icfit, lineclean, imsurfit
+.endhelp