（附件中含源代码）
Schoenberg (1964) showed if n≥m, the minimizer is unique and he called it natural polynomial spline.
Statisticians were interested in smoothing the spline other than interpolating  since the existence of noise.
In Practice , especially for applications in Image Registration, m=2,d=2 is pervasively used.

 

f(x,y)=d_1+d_2 x+d_3 y+∑_(i=1)^n▒〖c_i U(‖(x,y)-(x_i,y_i )‖_2 ) 〗

 

The left part ——affine part describes the behavior of f(x,y) at infinity.

The right part——locally small adjustment, bounded and asymptotically flat.

 

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