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 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 By Interp and Extrapolation(5)
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