extendedopacity
Created: 17 April 2003
This page is a copy of http://www.sgi.com/grafica/interp/ on
April 17, 2003,
with some slight formatting changes, included in the Netpbm
documentation
for convenience.
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 process‐
ing 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 consid‐
ered 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/extrapo‐
lation 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 accelera‐
tion.
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 degener‐
ate (zero
alpha) image. Interpolation darkens the image, and extrapola‐
tion brightens
it. In both cases, brighter pixels are affected more. bright‐
ness
Changing Contrast
Contrast can be controlled using a constant gray image with
the average
image luminance. Interpolation reduces contrast and extrapola‐
tion boosts it.
Negative alpha generates inverted images with varying con‐
trast. 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 unaf‐
fected. 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 expen‐
sive conversions
to and from HSV space. Repeated update in an interactive ap‐
plication 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 ad‐
justed by this
approach. If a blurred image is used as the degenerate image,
interpolation
attenuates high frequencies to varying degrees, and extrapola‐
tion boosts
them, sharpening the image by unsharp masking. Varying alpha
acts as a
kernel scale factor, so a series of convolutions differing on‐
ly 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 to‐
wards or away
from the average image luminance. Local contrast is similar,
but uses local
area luminance. Unsharp masking is the extreme case, using on‐
ly the color of
nearby pixels.
Combined Processing
An unusual property of this interpolation/extrapolation ap‐
proach 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 extrapo‐
lation 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, ex‐
trapolation 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 in‐
accuracy.
These image manipulation techniques can be used in paint pro‐
grams 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.
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 Inter‐
polation and
Extrapolation. IRIS Universe Magazine No. 28, Silicon Graph‐
ics, Aug, 1994.
