(E-Mail Removed) writes:

>Hi all,

> can we do Bicubic Interpolation with5x5 pixels of image

>instead of 4x4
No, yes, and no, depending on how deeply you look.

If you used 5x5 pixels, you'd have enough data to use 4th-degree

polynomials instead of 3rd degree, so it would be "biquartic"

interpolation instead of bicubic. Thus your terminology is not quite

right.

You *could* build an interpolation method that used 5 points and 5

4th-degree polynomial segments in each direction. You just wouldn't

want to.

Polynomial interpolation is always done with odd-degree polynomials and

an even number of points, because that allows building an interpolating

function that goes through the points (0, 1), (-1, 0), (1, 0), (-2, 0),

(2, 0), and so on. In other words the function is 1 at X=0 and zero at

all integer offsets from that. This, in turn, has the nice property

that interpolating an image to exactly the same size without any shift

gives the original image back.

With an even-degree polynomial and an odd number of input points, the

"joints" in the polynomial are at X=0.5, -0.5, 1.5, -1.5, etc. You

can't create an interpolating function that goes through (0, 1) and has

zero crossings at other integer offsets (while keeping the integral of

the function equal to 1) so using even-degree polynomial interpolation

never gives the original image even at the same size. There's always

some blurring.

So in practice, interpolation methods jump from linear interpolation

(which is the trivial case of polynomial interpolation, using a 1st

degree polynomial and 2 points) to cubic using 3rd-degree polynomial and

4 points, to 5th, 7th, etc degrees using 6, 8, ... points.

Dave