Image Processing By Interp andFImageoProcessingaBy Interp 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 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 im-
age 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 im-
ages, each differing in brightness, contrast, sharpness, color, or sat-
uration, 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 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 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 af-
fected.
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 in-
teractive 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, in-
terpolation attenuates high frequencies to varying degrees, and extrap-
olation boosts them, sharpening the image by unsharp masking. Varying
alpha acts as a kernel scale factor, so a series of convolutions dif-
fering only in scale can be done easily, independent of the size of the
kernel. Since blurring, unlike sharpening, is often a separable opera-
tion, sharpening by extrapolation may be far more efficient for large
kernels.
sharpening
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.
combined
Conclusion
Image applications frequently need to produce multiple degrees of ma-
nipulation interactively. Image applications frequently need to inter-
actively manipulate an image by continuously changing a single parame-
ter. 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, 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 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. Applica-
tion developers should allow users to extrapolate parameters when prac-
tical.
References
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.
DOCUMENT SOURCE
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netpbm documentation Image Processing By Interp and Extrapolation(5)
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