正交函数基


最近做image warping,把image从一个camera warp到另外一个camera。最开始用了homography的方法,不好用;又试了一下使用depth map和camera calibration,但是因为depth map不精确,加上estimated的focal length也不精确,所以这种方法也不行;也试了使用函数warping的方法,使用1, x, x^2, x^3, …函数基,也不行。现在准备试一试正交的函数基。

http://en.wikipedia.org/wiki/Basis_function

Polynomial bases

The collection of quadratic polynomials with real coefficients has {1, t, t²} as a basis. Every quadratic can be written as a1+bt+ct², that is, as a linear combination of the basis functions 1, t, and t². The set {(1/2)(t-1)(t-2), –t(t-2), (1/2)t(t-1)} is another basis for quadratic polynomials, called the Lagrange basis.

http://en.wikipedia.org/wiki/Lagrange_polynomial

Orthogonal polynomials

http://en.wikipedia.org/wiki/Orthogonal_polynomials

Legendre polynomials

http://en.wikipedia.org/wiki/Legendre_polynomials

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