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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
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
supports 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
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
Interpolation and
Extrapolation. IRIS Universe Magazine No. 28, Silicon
Graphics, Aug, 1994.
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