12.2.1 The Accumulation Buffer: Interpolation and Extrapolation

 

Haeberli and Voorhies [27] have suggested several interesting image processing techniques using linear interpolation and extrapolation. Each technique is stated in terms of the formula:
 
This equation is evaluated on a per-pixel basis. and 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 [27].

In the limited case where , these equations may be implemented using the accumulation buffer via the following steps:

• Draw into the color buffer.
• Load , scaling by (1-x) (glAccumGL_LOAD, (1-x)(GL_LOAD, (1-x))).
• Draw into the color buffer.
• Accumulate , scaling by x (glAccumGL_ACCUM,x(GL_ACCUM,x)).
• Return the results (glAccumGL_RETURN, 1(GL_RETURN, 1)).

It is assumed that and 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 6 and derive a list of accumulation buffer operations to perform the operation. Define a scale factor s such that:

Equation 6 becomes:

and the list of steps becomes:

• Compute s.
• Draw into the color buffer.
• Load , scaling by (glAccumGL_LOAD, (1-x)/s(GL_LOAD, (1-x)/s)).
• Draw into the color buffer.
• Accumulate , scaling by (glAccumGL_ACCUM, x/s(GL_ACCUM, x/s)).
• Return the results, scaling by s (glAccumGL_RETURN, s(GL_RETURN, s)).

The techniques suggested by Haeberli and Voorhies use a degenerate image as and an appropriate value of x to move toward or away from that image. To increase brightness, is set to a black image and x > 1. To change contrast, is set to a gray image of the average luminance value of . Decreasing x (toward the gray image) decreases contrast; increasing x increases contrast. Saturation may be varied using a luminance version of as . (For information on converting RGB images to luminance, see Section 12.2.4.) Sharpening may be accomplished by setting to a blurred version of [27].