ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

Maximization (EM) algorithm witch estimates best fitting of GMM parameters.
Before these two steps, we applied smoothing (denoising) and enhancing method to
enhance breast image [11]. Respectively, an anisotropic filter diffusion SRAD (Speckle
Reducing Anisotropic Diffusion) [12] and Contrast-limited Adaptive Histogram
Equalization (CLAHE) are used.
We applied the proposed algorithm to some challenging breast images in BIRADS
database including poor contrast tissue density (fatty, dense or granular) and the
segmented mass done by our algorithm is compared to segmentation carried by an
expert radiologist by measuring Dice coefficient.
3. GMM FOR MASSE SEGMENTATION:
3.1 Mass Density estimation:
GMM model can give important information about intensities probability distribution of
the mammogram images, and specialy about intensities variations in mass region.
Indeed, the region mass is not in reality a completely homogeneous region. In other
words, she can be represented by several under homogeneous regions (under classes).
For estimating their densities distributions in several suspicious regions (ROIs), we
should introduce number of these class regions as prior information.
Expectation maximization (EM) is the most popular technique used to determine the
parameters of a mixture with an a priori given number of components. We used
iterative EM algorithm to estimate best fitting of GMM parameters.
On the other hand, as quoted in introduction, another important information which must
be take account is intensities distributions of region of tissue. These distributions are
introduced as the data completed of EM algorithm.
Then, we can give the parameters of GMM by leaving of its first definition (1):
M
g x, f ( x,
)
(1)
k 1
k k
Where x is a data vector (pixels values), k , k 1,..., M , are the mixture weights, and
f( x, k ) , are the component Gaussian densities, where k k, k , k
,
k 1,... M .
M represents number of class in region mass, estimate by K-means algorithm, with
mean vector k and variance vector k . The mixture weight satisfy the constraint that
M
k 1
1.
k
Each component density is Gaussian function of the form (2):
2
x
1
k
f x, k f x, k , k exp
(2)
2
2
k
k