FRACLAB Functions

alphaimage

Computes corresponding alpha image from original, normalized, image. The pixels in the alpha image are estimated values of Holder exponent at these points and they describe the local regularity.

NOTE: In the FracLab graphical interface this function is associated with the falphaimage function and the spotted function.

Syntax

A = alphaimage(x,rmax)
A = alphaimage(...,'Method')
A = alphaimage(...,'Scale')

Description

A = alphaimage(x,rmax) Estimates the Holder "alpha" image, A, of the normalized grayscale input image, x using a specific radius, rmax. The parameter rmax is an integer in (1:5) which defines the largest measure domain.

Let Mi(m,n) denotes the amount of the chosen measure within measure domain of size i, at particular image pixel with spatial coordinates (m,n). The Holder exponent at this point, alpha(m,n), is estimated from bi-logarithmic diagram. Natural logarithms of measure values, ln(Mi(m,n)), and of the domain sizes, ln(i), are calculated and plotted on corresponding points in bi-logarithmic diagram ln(Mi(m,n)) vs. ln(i). Then, the limiting value of alpha(m,n) is estimated as a slope of linear regression line in this log-log diagram. After finding alpha value for every pixel in input image, x, we may create an "alpha" image : an image of the same dimension as initial image but filled by values of alpha(m,n) with one-by-one correspondence to input image pixels.

A = alphaimage(...,'Method') Estimates the Holder "alpha" image, A, using a specific measure type. The supported measure Methods can be choosen from the list below :

Method Specifiers

Specifier	Method
'max'	Maximum, square shaped domain
'min'	Minimum, square shaped domain
'sum'	Sum, square shaped domain
'iso'	Iso, square shaped domain When this mehtod is selected, is necessary to specified the degree of sensitivity. This parameter is a positive integer in (25:255), which allows to tune the discretization of the gray levels in the input image. A large value will result in larger number of detected small objects.
'maxi'	Maximum, diamond shaped domain
'mini'	Minimum, diamond shaped domain (default)

A = alphaimage(...,'Scale') Estimates the Holder "alpha" image A using a specific grayscale of the image. The supported Scales can be choosen from the list below :

Scale Specifiers

Specifier	Action Type
'normal'	Use the original image (default)
'neg'	Use the negative image of x

Examples

Example 1 : Choosing a specific grayscale

images_loc = which('alphaimage.html');
x = imread(fullfile(fileparts(images_loc),'images_examples','Segmentation','m213.pgm'));
x = ima2mat(x);
A1 = alphaimage(x,2); A2 = alphaimage(x,2,'neg');
figure; subplot(1,3,1); imagesc(x); title('Original image x');
subplot(1,3,2); imagesc(A1); title('Alpha image from x');
subplot(1,3,3); imagesc(A2); title('Alpha image from negative x');

Example 2 : Choosing a specific measure Method

x = imread(fullfile(fileparts(images_loc),'images_examples','Segmentation','m213.pgm'));
x = ima2mat(x);
A1 = alphaimage(x,2,'neg');
A2 = alphaimage(x,2,'iso',200,'neg'); A3 = alphaimage(x,2,'iso',100,'neg');
figure; subplot(1,3,1); imagesc(A1); title('Method = mini');
subplot(1,3,2); imagesc(A2); title('Method = iso Sensitivity = 200');
subplot(1,3,3); imagesc(A3); title('Method = iso Sensitivity = 100');

See Also

falphaimage, spotted

References

[1] J. Lévy-Véhel, P. Mignot "Multifractal segmentation of images", Fractals, Vol. 2 No. 3, (2004) 379-382.

[2] T. Stojic, I. Reljin, B. Reljin "Adaptation of multifractal analysis to segmentation of microcalcifications in digital mammograms", Physica A: Statistical Mechanics and its Applications, Vol. 367 No. 15, (2006) 494-508.

Functions -- Alphabetical List

asmlevy