# Coyote Graphics Routines

## Date: Fri Mar 27 12:14:20 2015

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# cgasinhscl.pro

Image Processing

This is a utility routine to perform an inverse hyperbolic sine function intensity transformation on an image. I think of this as a sort of "tuned" gamma or power-law function. The algorithm, and notion of "asinh magnitudes", comes from a paper by Lupton, et. al, in The Astronomical Journal, 118:1406-1410, 1999 September. I've relied on the implementation of Erin Sheldon, found here:

``` http://cheops1.uchicago.edu/idlhelp/sdssidl/plotting/tvasinh.html ```
I'm also grateful of discussions with Marshall Perrin on the IDL newsgroup with respect to the meaning of the "softening parameter", beta, and for finding (and fixing!) small problems with the code.

Essentially this transformation allow linear scaling of noise values, and logarithmic scaling of signal values, since there is a small linear portion of the curve and a much large logarithmic portion of the curve. (See the EXAMPLE section for some tips on how to view this transformation curve.)

## Examples

Plot various values of beta:

``` cgPlot, cgASinhScl(Indgen(256), Beta=0.0), LineStyle=0 cgOPlot, cgASinhScl(Indgen(256), Beta=0.1), LineStyle=1 cgOPlot, cgASinhScl(Indgen(256), Beta=1.0), LineStyle=2 cgOPlot, cgASinhScl(Indgen(256), Beta=10.), LineStyle=3 cgOPlot, cgASinhScl(Indgen(256), Beta=100), LineStyle=4 ```

## Author information

Author

FANNING SOFTWARE CONSULTING:

``` David W. Fanning 1645 Sheely Drive Fort Collins, CO 80526 USA Phone: 970-221-0438 E-mail: david@idlcoyote.com Coyote's Guide to IDL Programming: http://www.idlcoyote.com ```

Copyright (c) 2008-2015, Fanning Software Consulting, Inc.

History

Change History:

``` Written by: David W. Fanning, 24 February 2006. Removed ALPHA keyword and redefined the BETA keyword to correspond to the "softening parameter" of Lupton et. al., following the suggestions of Marshall Perrin. 25 April 2006. DWF. Renamed cgASinhScl from ASinhScl. 27 March 2015. DWF. ```

## Routines

`result = cgASinhScl_ASinh(x)`

Return the inverse hyperbolic sine of the argument.

`result = cgASinhScl(image [, BETA=float], NEGATIVE=NEGATIVE [, MAX=MAX] [, MIN=MIN] [, OMAX=byte] [, OMIN=byte])`

The main cgASinhScl function.

## top cgASinhScl_ASinh

`result = cgASinhScl_ASinh(x)`

Return the inverse hyperbolic sine of the argument. Taken from the NASA IDL Astronomy Library and renamed for use in this program. The inverse hyperbolic sine is used for the calculation of asinh magnitudes, see Lupton et al. (1999, AJ, 118, 1406). Expression given in Numerical Recipes, Press et al. (1992), eq. 5.6.7. Note that asinh(-x) = -asinh(x) and that asinh(0) = 0. and that if y = asinh(x) then x = sinh(y).

### Return value

The inverse hyperbolic sine is returned. The output has the same number of elements as X and is double precision if X is double, otherwise floating point.

### Parameters

x in required

The hyperbolic sine, numeric scalar or vector or multidimensional array (not complex).

## top cgASinhScl

`result = cgASinhScl(image [, BETA=float], NEGATIVE=NEGATIVE [, MAX=MAX] [, MIN=MIN] [, OMAX=byte] [, OMIN=byte])`

The main cgASinhScl function.

### Return value

A byte scaled image is returned.

### Parameters

image in required

The image to be scaled. Written for 2D images, but arrays of any size are treated alike.

### Keywords

BETA in optional type=float default=3.0

This keyword corresponds to the "softening parameter" in the Lupon et. al paper. This factor determines the input level at which linear behavior sets in. Beta should be set approximately equal to the amount of "noise" in the input signal. If BETA=0 there is a very small linear portion of the curve; if BETA=200 the curve is essentially all linear. The default value of BETA is set to 3, which is appropriate for a small amount of noise in your signal. The value is always positive.

NEGATIVE

If set, the "negative" of the result is returned.

MAX in optional

Any value in the input image greater than this value is set to this value before scaling.

MIN in optional

Any value in the input image less than this value is set to this value before scaling.

OMAX in optional type=byte default=255

The output image is scaled between OMIN and OMAX.

OMIN in optional type=byte default=0

The output image is scaled between OMIN and OMAX.

## File attributes

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