2-D Savitzky-Golay Smoothing and Differentiation Filter.

2-D Savitzky-Golay smoothing and differentiation filters, including those for mixed partial ...

2-D Savitzky-Golay (SG) Smoothing and Differentiation Filter.
The filter coefficients are calculated from the decomposation property of the 2-D SG filters.
In addition, the filter coefficients for mixed partial derivative can be obtained by this function.

h=sgsdf_2d3(x,y,nx,ny,d,flag_coupling)
x = x data point, e.g., -3:3 (both odd-length and even-lenght
are accepted, symmetry is prefered but not restricted)
y = y data point, e.g., -2:2 (both odd-length and even-lenght
are accepted, symmetry is prefered but not restricted)
nx =x polynomial order default=1
ny =y polynomial order default=1
dx = differentiation order in x direction (0<=d<=nx) default=0
dy = differentiation order in y direction (0<=d<=ny) default=0
flag_coupling = with or without the consideration of the coupling
terms, between x and y. default=0
h = filter coefficients obtained.

Example:
sgsdf_2d2(-2:2,-3:3,1,1,0,0,0)
sgsdf_2d2(-2:2,-3:3,1,1,0,0,1)
sgsdf_2d2(-2:2,-3:3,2,2,0,1,0)
sgsdf_2d2(-2:2,-3:3,2,2,0,1,1)
sgsdf_2d2((-3:2)+1/2,-3:3,2,2,1,0,0)
sgsdf_2d2((-3:2)+1/2,-3:3,2,2,1,0,1)
sgsdf_2d2(-1:1,-1:1,1,1,1,1,1)
sgsdf_2d2((-3:2)+1/2,(-4:3)+1/2,2,2,1,1,1)
sgsdf_2d2(-3:3,-4:4,2,3,2,1,1)

Author:
Jianwen Luo <[e-mail]>
11/23/2005

References:
[1] J. W. Luo, K. Ying, P. He, and J. Bai, "Properties of Savitzky-Golay Digital Differentiators,"
Digital Signal Processing, vol. 15, pp. 122-136, 2005.
[2] A. Savitzky and M. J. E. Golay, "Smoothing and Differentiation of Data by Simplified Least Squares Procedures,"
Analytical Chemistry, vol. 36, pp. 1627-1639, 1964.
[3] K. L. Ratzlaff and J. T. Johnson, "Computation of Two-Dimensional Polynomial Least-Squares Convolution Smoothing Integers,"
Analytical Chemistry, vol. 61, pp. 1303-1305, 1989.
[4] J. E. Kuo, H. Wang, and S. Pickup, "Multidimensional Least-Squares Smoothing Using Orthogonal Polynomials,"
Analytical Chemistry, vol. 63, pp. 630-635, 1991.
[5] http://research.microsoft.com/users/jckrumm/SavGol/SavGol.htm
[6] T. A. Sakharuk, "Computation of Weighting Functions for Smoothing 2-Dimensional Data by Local Polynomial-Approximation Techniques,"
Analytica Chimica Acta, vol. 249, pp. 331-336, 1991.
[7] P. Meer and I. Weiss, "Smoothed Differentiation Filters for Images,"
Journal of Visual Communication and Image Representation, vol. 3, pp. 58-72, 1992.
[8] P. Nikitas and A. Pappa-Louisi, "Comments on the two-dimensional smoothing of data,"
Analytica Chimica Acta, vol. 415, pp. 117-125, 2000.