man > extendedopacity(5)

Image Processing ...and Extrapolation(5) File Formats ManualImage Processing ...and Extrapolation(5)

Created: 17 April 2003

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 - al‐
       pha) 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 in‐
       terpolate two images.  What is less often considered is that alpha may range beyond  the  in‐
       terval 0.0 to 1.0.  Values above one subtract a portion of in0 while scaling in1.  Values be‐
       low 0.0 have the opposite effect.

       Extrapolation  is particularly useful if a degenerate version of the image is used as the im‐
       age to get "away from."  Extrapolating away from a black-and-white  image  increases  satura‐
       tion.   Extrapolating  away  from a blurred image increases sharpness.  The interpolation/ex‐
       trapolation formula offers one-parameter control, making display of a series of images,  each
       differing in brightness, contrast, sharpness, color, or saturation, particularly easy to com‐
       pute, 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.  Inter‐
       polation 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.  In‐
       terpolation  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 de‐
       creased using interpolation, and increased using extrapolation.  This avoids  computationally
       more expensive conversions to and from HSV space.  Repeated update in an interactive applica‐
       tion  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 effi‐
       cient 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 al‐
       tered.

       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 unify‐
       ing approach, providing a single function that can do many  common  image  processing  opera‐
       tions.

       Since a degenerate image is sometimes easier to calculate, extrapolation may offer a more ef‐
       ficient method to achieve effects such as sharpening or saturation.  Blending is a linear op‐
       eration, 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 inter‐
       polant values to the range 0.0 to 1.0.  Application developers should allow users to extrapo‐
       late parameters when practical.

   References
       For a slightly extended version of this article, see: P. Haeberli and D. Voorhies. Image Pro‐
       cessing 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

netpbm documentation                                        Image Processing ...and Extrapolation(5)