NAME

       extendedopacity - theory of netpbm interpolation and extrapolation

DESCRIPTION

       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

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

       Linear interpolation is often used to blend two images.  Blend fractions (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 acceleration.

       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
       cursor.

   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.

       brightness

   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.

       contrast

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

   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.

       saturation

   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 convolutions differing only in scale can be done easily, independent of the size
       of the kernel.  Since blurring,  unlike  sharpening,  is  often  a  separable  operation,  sharpening  by
       extrapolation may be far more efficient for large kernels.

       sharpening

       Note  that  global  contrast  control,  local  contrast control, and sharpening 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.

       combined

   Conclusion
       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 can do many common image processing operations.

       Since  a  degenerate  image  is  sometimes  easier to calculate, extrapolation 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
       work with 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.   Application  developers should allow users to extrapolate parameters when
       practical.

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

DOCUMENT SOURCE

       This  manual  page was generated by the Netpbm tool 'makeman' from HTML source.  The master documentation
       is at

              http://netpbm.sourceforge.net/doc/extendedopacity.html