13.2.1 The Accumulation Buffer: Interpolation and Extrapolation

Haeberli and Voorhies [40] have suggested several interesting image processing techniques using linear interpolation and extrapolation. Each technique is stated in terms of the formula:

 

out = (1 - x)*in₀ + x*in₁ (12)

This equation is evaluated on a per-pixel basis. in₀ and in₁ are the input images, out is the output image, and x is the blending factor. If x is between 0 and 1, the equations describe a linear interpolation. If x is allowed to range outside [0..1], the result is extrapolation [40].

In the limited case where $0 \leq x \leq 1$, these equations may be implemented using the accumulation buffer via the following steps:

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Draw in₀ into the color buffer.

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Load in₀, scaling by (1-x) (glAccumGL_LOAD, (1-x)(GL_LOAD, (1-x))).

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Draw in₁ into the color buffer.

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Accumulate in₁, scaling by x (glAccumGL_ACCUM,x(GL_ACCUM,x)).

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Return the results (glAccumGL_RETURN, 1(GL_RETURN, 1)).

It is assumed that in₀ and in₁ are between 0 and 1. Since the accumulation buffer can only store values in the range [-1..1], for the case x < 0 or x > 1, the equation must be implemented in a different way. Given the value x, you can modify equation 12 and derive a list of accumulation buffer operations to perform the operation. Define a scale factor ssuch that:

s = max(x, 1-x)

Equation 12 becomes:

$$out = s(\frac{(1-x)}{s}in_0 + \frac{x}{s}in_1)$$

and the list of steps becomes:

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Compute s.

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Draw in₀ into the color buffer.

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Load in₀, scaling by $\frac{(1-x)}{s}$(glAccumGL_LOAD, (1-x)/s(GL_LOAD, (1-x)/s)).

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Draw in₁ into the color buffer.

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Accumulate in₁, scaling by $\frac{x}{s}$(glAccumGL_ACCUM, x/s(GL_ACCUM, x/s)).

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Return the results, scaling by s (glAccumGL_RETURN, s(GL_RETURN, s)).

The techniques suggested by Haeberli and Voorhies use a degenerate image as in₀ and an appropriate value of x to move toward or away from that image. To increase brightness, in₀ is set to a black image and x > 1. To change contrast, in₀ is set to a gray image of the average luminance value of in₁. Decreasing x (toward the gray image) decreases contrast; increasing x increases contrast. Saturation may be varied using a luminance version of in₁ as in₀. (For information on converting RGB images to luminance, see Section 13.2.4.) Sharpening may be accomplished by setting in₀ to a blurred version of in₁ [40].