Microscope Image Processing

Notice that the hyperbolic paraboloid has four parameters and can be made

to fit through all four points in the neighborhood of Fig. 5.2. Similarly, the

bicubic function has 16 parameters and can fit all 16 points in a 4  4 neigh-

borhood. If a higher-order interpolating function has the same number of

coefficients as the neighborhood has points, then the interpolating surface can

likewise be made to fit at every point. However, if there are more points in the

neighborhood than there are coefficients, then the surface cannot fit all the

points, and a curve-fitting or error-minimization procedure must be used.

Higher-order interpolating functions that are widely used include cubic splines,

Legendre centered functions, and the truncated sinc(x) function