Miscellaneous Analysis Tasks

• The task imdiff can be used to compare two images. It finds optimum parameters (in a maximum likelihood sense) for making one image approximate another image. The parameters are an amplitude scale factor, dc offset, shifts in the x and y directions and an expansion factor. Any of these parameters can be fixed at a given value, and the others allowed to vary.

  Note that this task is suited only to small shifts, expansions and scale factors. You can use the self-explanatory task shifty for large integral pixel shifts. The keyword in2 gives the image which must be adjusted to look like the image given by keyword in1. Task imdiff can also output a residual image - see the help file for the definition of the residual, but it is basically a combination of all the residuals of all the adjustable parameters.

  To hold any particular parameter fixed, you simply specify the appropriate options string (see help file). Otherwise, imdiff will solve for that parameter. Initial guesses can be entered through the keyword for each parameter.

  IMDIFF
  in1=vela.atca	Template image
  in2=vela.vla	Adjust this image
  adjust=vela.vla-atca	Adjusted image
  resid=vela.resid	The residual image
  region	Unset for entire image
  guard	Unset for default OK
  xshift	Unset for initial guess of 0
  yshift	Unset for initial guess of 0
  expand	Unset for initial guess of 1
  amp	Unset for initial guess of 1
  offset	Unset for initial guess of 0
  options=expand	Unset to vary everything and x
  	and y expansions separately

• A very useful tool for diagnosing errors in images is to Fourier Transform them. The error may, under some conditions, be easier to recognise in the Fourier plane. Miriad offers the task fft for this purpose. It can Fourier Transform real or complex images (you input there real and imaginary parts with separate keywords). Note that blanked pixels in the input are treated as if their value was zero.

  In the following example, we FFT a CLEANed image and form the amplitude and phase images of the Fourier Transform.

  FFT
  rin=ic4296.icln	Input real image
  iin	Unset
  sign=+1	Forwards transform
  center	Use ref. pix. for centre of transform
  rout	Unset
  iout	Unset
  mag=fftp.amp	Amplitude image
  phase=fft.phase	Phase image

  Task fft produces gridded images, so you can use all the usual display tools to look at them (see Chapter 17).

• For those of you wrestling with optical data in Miriad, the task impoly may be of benefit. You may like to make a polynomial sky subtraction. impoly allows you to define a region over which a 2-D polynomial is fit. The fit is the subtracted from the the full image, not just the designated fit region.

  IMPOLY
  in=cluster.deep	Input image
  out=cluster-sub.deep	Output image
  order=#	Order of polynomial
  coeffs	Unset not to see coefficients of fit
  region=@cgcurs.region	Fit over this region

• As is discussed in Chapter 17, there are a variety of transfer functions that you can apply to your image with the display tasks. One that is particularly useful is histogram equalisation. Essentially, this method assesses, via a histogram, which image intensities have the most pixels. It then optimally expends the dynamic range of the device in displaying these pixels, rather than the pixels which have intensities that occur seldom.

  It may be that you would like the image to be written out with histogram equalisation applied, rather than it just being computed but not saved by the display task. The task imheq will do this for you. You can specify the intensity range in which pixels will be included when computing the histogram. It is useful to use this if you have outliers significantly from the bulk of the distribution. imheq will equalised each plane of a cube, and by default, use the image minimum and maximum of that plane. If you set options=global it will take the minimum and maximum from the whole cube instead.

  If you set the device keyword, imheq will draw a plot of the image histogram and discretized cumulative histogram (see help file). The latter is essentially the transfer function that is applied. This plot is drawn after every plane of a cube.

  IMHEQ
  in=cluster.deep	Input image
  out=cluster-heq.deep	Output image
  nbins	Default for 128 histogram bins
  range	Default is image min to max
  options	Unset for plane by plane equalisation
  device=/xs	PGPLOT device for histogram

• It is sometimes useful to replace the value of all image pixels which are blanked by some number (often zero). Task imblr offers this facility; it unblanks all blanked pixels and replaces their value with the one specified.

  IMBLR
  in=test.m1	Input image
  out=test-2.m1	Output image
  value=0.0	Replacement value