boxdim_binaire

Box dimension, computed with the box method, of the white points in a black and white image or, more generally, of non-zero-points in an N-dimensional array.

Syntax

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

Inputs

BWimg :
N-dimensional array. Usually, it is a matrix containing 0 and 1. If BWImg contains values different from 0 and 1, all non-zero values are trated as ones.

Size, Ratio :
Ratio defines the lengths of the sides of a "first box". If BWimg is an image, it is a 1x2 array. (1xN array if BWimg is an N dimensional array). The successive boxes will be deduced from this first box by homotheties with ration Size(i). More precisely, the box at at the i - th iteration will have a length along the k - th axis equal to Ratio(k)*Size(i)

Axes :

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 BWImg are optional. For example, the syntax : boxdim_classique(PointsList) 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_classique, boxdim_listepoints, fl_regression