Unround

Unrounds points on a curve to produce the smoothest curve which is consistent with rounding.

Description

Inverse interpolation using a rounded curve can fail if the rounding operation produces flat spots. In this event, even simple linear interpolation will not result in a unique inverse interpolant.

Unround attempts to find the smoothest possible
curve that will reproduce the original curve after rounding all points to the nearest integer.

Unround finds use in image processing operations,
where shapers (1-d lookup tables) have been
rounded.

Example usage 1:

x = linspace(0,2*pi,20);
vec = round(x);
newvec = unround(vec);
plot(x,vec,'bo',x,newvec,'r-')

Example usage 2:
x = 0:.01:1;
vec = round(10*x.^2);
newvec = unround(vec);
plot(x,vec,'bo',x,newvec,'r-')

If there are requests, I can easily modify the code to allow bound constraints on the unrounding
process. This would allow the user to specify lower or upper bounds on the smoothly unrounded curve.

• Required Products: Optimization Toolbox
• MATLAB release: MATLAB 7.0.1 (R14SP1)
• Other requirements: Because unround solves a quadratic programming problem, vectors of length 10000 or more may take a few seconds to solve.