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dimR2d(2) Scilab Function dimR2d(2)
NAME
dimR2d - Regularization dimension of the surface of a 2d function
Author: Francois Roueff
Computes the regularization dimension of the surface of a 2d function. Two
kernels are available: the Gaussian or the Rectangle.
Usage
[dim, handlefig]=dimR(x,sigma,voices,Nmin,Nmax,kernel,mirror,reg,graphs)
Input parameters
o x : Real or complex matrix [nt,pt] Space samples of the signal to be
analyzed.
o sigma : Real positive number Standard Deviation of the noise. Its
default value is null (noisefree)
o voices : Positive integer. number of analyzing voices. When not
specified, this parameter is set to 128.
o Nmin : Integer in [2,nt/3] Lower scale bound (lower width) of the
analysing kernel. When not specified, this parameter is set to
around nt/12.
o Nmax : Integer in [Nmin,2nt/3] Upper scale bound (upper width) of
the analysing kernel. When not specified, this parameter is set to
nt/3.
o kernel : String specifies the analyzing kernel: "gauss": Gaussian
kernel (default) "rect": Rectangle kernel
o mirror : Boolean
specifies wether the signal is to be mirrorized for the analyse
(default: 0).
o reg : Boolean
specifies wether the regression is to be done by the user or
automatically (default: 0).
o graphs : Boolean:
specifies wether the regularized graphs have to be displayed
(default: 0).
Output parameters
o dim : Real Estimated regularization dimension.
o handlefig : Integer vector Handles of the figures opened during the
procedure.
Description
This function is the same as dimR but adapted to 2d signals. For a more
complete explanation of the regularization dimension, one can refer to: "A
regularization approach to fractionnal dimension estimation", F. Roueff, J.
Levy-Vehel, submitted to Fractal 98 conference. The regularized graphs of
x are computed via convolutions of x with dilated versions of the kernel at
different scales. The lengths of the regularized graphs are computed via
convolutions of x with the derivatives of the dilated versions of the ker-
nel. The regularization dimension is computed either via an automatic range
regression or via a regression by hand on the loglog plot of the lengths
versus scales. If sigma is strictly positive, an estimation of the lengths
without noise is used for the regression. These lengths are displayed in
red while those of the noisy signal are in black. They should seperate at
fine scales. When one specifies the range regression, the loglog plot of
the lengths versus scales appears. Above are either increments (when sigma
is null) or a loglog plot of the noise prevalence in the lengths. One
selects the scale range of the regression. In the case of noisefree sig-
nals, select a scale region with stable increments. In the case of a
strictly positive sigma, select a scale region where the noise prevalence
is not too close to 1 (0 in log10): it should correspond to an approxi-
mately linear region for the red estimations. The number of scales
(voices) tells how many convolutions are computed. The bigger it is, the
slower the computation is. The scale axis is geometrically sampled (i.e.
its log is arithmetically sampled). The gaussian kernel should give a
better result but the rectangle is faster. As a general rule, be careful
of the size of the input signal and of the maximal size of the kernel (Nmax
x Nmax) to avoid too long computing times.
See also:
cwttrack, cwtspec.
Example:
Signal synthesis
x = GeneWei(100,0.6,2,1.0,0);
y = GeneWei(100,0.4,3,1.0,1);
w = x'*y;
mesh(w);
Dimension of the graph with a regression by hand
[dim,H] = dimR2d(w,0,25,5,30,'gauss',0,1,0);
Close the figures
close(H)
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