12.2.1 The Accumulation Buffer: Interpolation and Extrapolation

 

Haeberli and Voorhies have suggested several interesting image processing techniques using linear interpolation and extrapolation. Each technique is stated in terms of the formula:
 
The 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], extrapolation results.[19]

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))

We assume 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, we can modify equation 6 and derive a list of accumulation buffer operations to perform the operation. We 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 grey image of the average luminance value of . Moving toward (x < 1) the grey image increases contrast; moving away decreases it. Saturation may be varied using a black and white 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 .[19] For more details, readers are encouraged to visit http://www.sgi.com/grafica/interp/index.html