;+ ; NAME: ; ASINHSCL ; ; PURPOSE: ; ; 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.) ; ; AUTHOR: ; ; FANNING SOFTWARE CONSULTING ; David Fanning, Ph.D. ; 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 ; ; CATEGORY: ; ; Utilities ; ; CALLING SEQUENCE: ; ; outputImage = ASINHSCL(image) ; ; ARGUMENTS: ; ; image: The image or signal to be scaled. Written for 2D images, but arrays ; of any size are treated alike. ; ; KEYWORDS: ; ; BETA: 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: Any value in the input image greater than this value is ; set to this value before scaling. ; ; MIN: Any value in the input image less than this value is ; set to this value before scaling. ; ; OMAX: The output image is scaled between OMIN and OMAX. The ; default value is 255. ; ; OMIN: The output image is scaled between OMIN and OMAX. The ; default value is 0. ; RETURN VALUE: ; ; outputImage: The output, scaled into the range OMIN to OMAX. A byte array. ; ; COMMON BLOCKS: ; None. ; ; EXAMPLES: ; ; Plot, ASinhScl(Indgen(256), Beta=0.0), LineStyle=0 ; OPlot, ASinhScl(Indgen(256), Beta=0.1), LineStyle=1 ; OPlot, ASinhScl(Indgen(256), Beta=1.0), LineStyle=2 ; OPlot, ASinhScl(Indgen(256), Beta=10.), LineStyle=3 ; OPlot, ASinhScl(Indgen(256), Beta=100), LineStyle=4 ; ; RESTRICTIONS: ; ; Requires cgScaleVector from the Coyote Library: ; ; http://www.idlcoyote.com/programs/cgScaleVector.pro ; ; Incorporates ASINH from the NASA Astronomy Library and renamed ASINHSCL_ASINH. ; ; http://idlastro.gsfc.nasa.gov/homepage.html ; ; MODIFICATION 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. ;- ;******************************************************************************************; ; Copyright (c) 2008, by Fanning Software Consulting, Inc. ; ; All rights reserved. ; ; ; ; Redistribution and use in source and binary forms, with or without ; ; modification, are permitted provided that the following conditions are met: ; ; ; ; * Redistributions of source code must retain the above copyright ; ; notice, this list of conditions and the following disclaimer. ; ; * Redistributions in binary form must reproduce the above copyright ; ; notice, this list of conditions and the following disclaimer in the ; ; documentation and/or other materials provided with the distribution. ; ; * Neither the name of Fanning Software Consulting, Inc. nor the names of its ; ; contributors may be used to endorse or promote products derived from this ; ; software without specific prior written permission. ; ; ; ; THIS SOFTWARE IS PROVIDED BY FANNING SOFTWARE CONSULTING, INC. ''AS IS'' AND ANY ; ; EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES ; ; OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT ; ; SHALL FANNING SOFTWARE CONSULTING, INC. BE LIABLE FOR ANY DIRECT, INDIRECT, ; ; INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED ; ; TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; ; ; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ; ; ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT ; ; (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS ; ; SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. ; ;******************************************************************************************; FUNCTION ASinhScl_ASinh, x ; ; NAME: ; ASINH ; PURPOSE: ; Return the inverse hyperbolic sine of the argument ; EXPLANATION: ; The inverse hyperbolic sine is used for the calculation of asinh ; magnitudes, see Lupton et al. (1999, AJ, 118, 1406) ; ; CALLING SEQUENCE ; result = asinh( x) ; INPUTS: ; X - hyperbolic sine, numeric scalar or vector or multidimensional array ; (not complex) ; ; OUTPUT: ; result - inverse hyperbolic sine, same number of elements as X ; double precision if X is double, otherwise floating pt. ; ; METHOD: ; 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). ; ; REVISION HISTORY: ; Written W. Landsman February, 2001 ; Work for multi-dimensional arrays W. Landsman August 2002 ; Simplify coding, and work for scalars again W. Landsman October 2003 ; On_Error, 2 y = ALog( Abs(x) + SQRT( x^2 + 1.0) ) index = Where(x LT 0 ,count) IF count GT 0 THEN y[index] = -y[index] RETURN, y END ;------------------------------------------------------------------------------- FUNCTION ASinhScl, image, $ BETA=beta, $ NEGATIVE=negative, $ MAX=maxValue, $ MIN=minValue, $ OMAX=maxOut, $ OMIN=minOut ; Return to caller on error. On_Error, 2 ; Check arguments. IF N_Elements(image) EQ 0 THEN Message, 'Must pass IMAGE argument.' ; Check for underflow of values near 0. Yuck! curExcept = !Except !Except = 0 i = Where(image GT -1e-35 AND image LT 1e-35, count) IF count GT 0 THEN image[i] = 0.0 void = Check_Math() !Except = curExcept ; Work in double precision. output = Double(image) ; Too damn many floating underflow warnings, no matter WHAT I do! :-( thisExcept = !Except !Except = 0 ; Perform initial scaling of the image into 0 to 1.0. output = cgScaleVector(Temporary(output), 0.0, 1.0, MaxValue=maxValue, $ MinValue=minValue, /NAN, Double=1) ; Check keywords. IF N_Elements(beta) EQ 0 THEN beta = 3.0D IF N_Elements(maxOut) EQ 0 THEN maxOut = 255B ELSE maxout = 0 > Byte(maxOut) < 255 IF N_Elements(minOut) EQ 0 THEN minOut = 0B ELSE minOut = 0 > Byte(minOut) < 255 IF minOut GE maxout THEN Message, 'OMIN must be less than OMAX.' ; Create a non-linear factor from the BETA value. scaled_beta = ((beta > 0) - minValue)/(maxValue - minValue) nonlinearity = 1.0D/(scaled_beta > 1e-12) ; Find out where 0 and 1 map in ASINH, then set these as MINVALUE and MAXVALUE ; in next cgScaleVector call. This is necessary to preserve proper scaling. extrema = ASinhScl_ASinh([0, 1.0D] * nonlinearity) ; Inverse hyperbolic sine scaling. output = cgScaleVector(ASinhScl_ASinh(Temporary(output)*nonlinearity), $ minOut, maxOut, /NAN, Double=1, MinValue=extrema[0], MaxValue=extrema[1]) ; Clear math errors. void = Check_Math() !Except = thisExcept ; Does the user want the negative result? IF Keyword_Set(negative) THEN RETURN, BYTE(maxout - Round(output) + minOut) $ ELSE RETURN, BYTE(Round(output)) END ;-------------------------------------------------------------------------------