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Image Processing By Interp and ImagepProcessing By Interp and Extrapolation(5)

Created: 17 April 2003

       extendedopacity - theory of netpbm interpolation and extrapolation

       This page is a copy of http://www.sgi.com/misc/grafica/interp/ on April
       17, 2003, with some slight formatting changes, included in  the  Netpbm
       documentation  for  convenience.   Since  at  least  June 11, 2005, the
       source page has been missing.

Image Processing By Interpolation and Extrapolation
       Paul Haeberli and Douglas Voorhies

       Interpolation and extrapolation between two images  offers  a  general,
       unifying approach to many common point and area image processing opera-
       tions.  Brightness, contrast, saturation, tint, and sharpness  can  all
       be  controlled with one formula, separately or simultaneously.  In sev-
       eral cases, there are also performance benefits.

       Linear interpolation is often used to blend two  images.   Blend  frac-
       tions  (alpha)  and  (1 - alpha) are used in a weighted average of each
       component of each pixel:

             out = (1 - alpha)*in0 + alpha*in1

       Typically alpha is a number in the range 0.0 to 1.0.  This is  commonly
       used to linearly interpolate two images.  What is less often considered
       is that alpha may range beyond the interval 0.0 to 1.0.   Values  above
       one subtract a portion of in0 while scaling in1.  Values below 0.0 have
       the opposite effect.

       Extrapolation is particularly useful if a  degenerate  version  of  the
       image is used as the image to get "away from."  Extrapolating away from
       a black-and-white image increases saturation.  Extrapolating away  from
       a  blurred  image increases sharpness.  The interpolation/extrapolation
       formula offers one-parameter control, making display  of  a  series  of
       images,  each  differing  in brightness, contrast, sharpness, color, or
       saturation, particularly easy to compute, and inviting hardware  accel-

       In  the  following  examples,  a  single alpha value is used per image.
       However other processing is possible, for  example  where  alpha  is  a
       function of X and Y, or where a brush footprint controls alpha near the

   Changing Brightness
       To control image brightness, we use pure black as the degenerate  (zero
       alpha)  image.   Interpolation  darkens  the  image,  and extrapolation
       brightens it.  In both cases, brighter pixels are affected more.


   Changing Contrast
       Contrast can be controlled using a constant gray image with the average
       image  luminance.   Interpolation  reduces  contrast  and extrapolation
       boosts it.  Negative  alpha  generates  inverted  images  with  varying
       contrast.  In all cases, the average image luminance is constant.


       If  middle gray or the average pixel color is used instead, contrast is
       again altered, but with middle gray or the  average  color  left  unaf-
       fected.   Shades  and  colors  far  away from the chosen value are most

   Changing Saturation
       To alter saturation, pixel components must move towards  or  away  from
       the  pixel's  luminance  value. By using a black-and-white image as the
       degenerate version, saturation can be  decreased  using  interpolation,
       and  increased  using  extrapolation.  This avoids computationally more
       expensive conversions to and from HSV space.   Repeated  update  in  an
       interactive application is especially fast, since the luminance of each
       pixel need not be recomputed.  Negative alpha preserves  luminance  but
       inverts the hue of the input image.


   Sharpening an Image
       Any  convolution,  such  as  sharpening or blurring, can be adjusted by
       this approach.  If a blurred image is used  as  the  degenerate  image,
       interpolation  attenuates  high  frequencies  to  varying  degrees, and
       extrapolation boosts them, sharpening the  image  by  unsharp  masking.
       Varying  alpha  acts  as a kernel scale factor, so a series of convolu-
       tions differing only in scale can be done easily,  independent  of  the
       size of the kernel.  Since blurring, unlike sharpening, is often a sep-
       arable operation, sharpening by extrapolation may be far more efficient
       for large kernels.


       Note that global contrast control, local contrast control, and sharpen-
       ing form a continuum.  Global contrast pushes pixel components  towards
       or  away  from the average image luminance.  Local contrast is similar,
       but uses local area luminance.  Unsharp masking is  the  extreme  case,
       using only the color of nearby pixels.

   Combined Processing
       An  unusual  property  of  this interpolation/extrapolation approach is
       that all of these image parameters may be altered simultaneously.  Here
       sharpness, tint, and saturation are all altered.


       Image  applications  frequently  need  to  produce  multiple degrees of
       manipulation interactively.   Image  applications  frequently  need  to
       interactively  manipulate  an  image  by continuously changing a single
       parameter.  The best hardware mechanisms employ a single  "inner  loop"
       to  achieve a wide variety of effects.  Interpolation and extrapolation
       of images can be a unifying approach, providing a single function  that
       supports many common image processing operations.

       Since  a  degenerate image is sometimes easier to calculate, extrapola-
       tion may offer a more efficient  method  to  achieve  effects  such  as
       sharpening  or  saturation.   Blending is a linear operation, and so it
       must be performed in linear, not gamma-warped space.   Component  range
       must  also  be  monitored, since clamping, especially of the degenerate
       image, causes inaccuracy.

       These image manipulation techniques can be used in  paint  programs  to
       easily  implement  brushes  that saturate, sharpen, lighten, darken, or
       modify contrast and color.  The only major change needed is to  support
       alpha values outside the range 0.0 to 1.0.

       It  is  surprising  and unfortunate how many graphics software packages
       needlessly limit interpolant values to the range 0.0 to 1.0.   Applica-
       tion developers should allow users to extrapolate parameters when prac-

       For a slightly extended version of this article, see: P.  Haeberli  and
       D.  Voorhies.  Image  Processing by Linear Interpolation and Extrapola-
       tion.  IRIS Universe Magazine No. 28, Silicon Graphics, Aug, 1994.

       <a  href=../index.html#interp>  <img  src=gobot.gif  alt=""   width=564
       height=25 border=0></a>

netpbm documentation           Image Processing By Interp and Extrapolation(5)

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