boxdim_classique

Box dimension of the graph of a function from R^N to R computed using the box-method.

Syntax

[boxdim,Nboxes,handlefig]=boxdim_binaire(Signal, Size, Ratio, Axes, Waitbar ,reg, lrstr, optvarargin)

Inputs

Signal :
Usually, Signal is a 1-D array (values of a function), but it can also be a matrix 2-D array (Grayscale image, white pixels considered as peaks and dark pixels as valleys) or an N dimensional array with any N, where the function goes from R^N to R

Size, Ratio :
Ratio defines the lengths of the sides of a reference box. The length among the k-th axis of this reference box is Ratio(k) The successive boxes will be deduced from this first box by homotheties with ration Size(i). More precisely, the box at the i - th iteration will have a length along the k - th axis equal to Ratio(k)*Size(i)

Axes :
Domain of definition of the signal. For example, if f goes from [0,1]x[0,1] to R, then Axes=[0,1;0,1].
For a graphical explanation of Size, Ratio and Axes, see Example 1

Waitbar :
1 if you want a waitbar to appear during the calculation, else 0

reg :
The way you choose the bounds. See the help on fl_regression for more information.

lrstr,optvarargin :
Regression parameters. They define the regression type. Type " help monolr" for more information

Outputs

boxdim :
The estimated box dimension

Nboxes :
Nboxes is a vector. Nboxes(i) is the number of non-empty boxes at the i - th iteration. A non-empty box is a box that contains at least one point of the graph of the function.

handlefig :
If reg~=0, a window appears to help you choosing the linearity bounds. handlefig is the handle of this figure.

bounds :
Bounds of linearity of log2(Nboxes) in function of log2(Size). Interesting if reg==1.

Optional arguments

All arguments except Signal are optional. For example, the syntax : boxdim_classique(Signal) is correct. If you don't want to precise an argument, you can also type []. The missing arguments take their default values:

Size=[1 1/2 1/4 ... 1/2048 1/4096]
Ratio =[1 1 ...]
Axes=[0 1;0 1 ; ...]
Waitbar = 0
reg=0
lrstr='ls'

These default values are not always relevant, especially Size, so when you don't know how to define Size, try to use reg ~= 0 in order to precise manually the correct box sizes.

Examples

See Also

boxdim_binaire, boxdim_listepoints, fl_regression