Polynomials

A 1d-polynomial is defined as:

(D25) |

A 2d-polynomial is defined as:

Thus the order of the coefficients (line,pixel) is independent of degree d:

d=0: (1)

d=1:
(2, 3)

d=2:
(4, 5, 6)

d=3:
(7, 8, 9, 10)

Thus the number of coefficients (unknowns in least squares estimation) equals for a 2d-polynomial of degree d:

(D27) |

And the degree of a polynomial with

(D28) |

Leijen 2009-04-14