Design and Implementation - Segmentation of Hand Bone for Bone Age Assessment - page 63

sub-image X U , over the range of ( X S + 1 , X L − 1 ) . In other words, the grey level on
input image has been remapped to the entire dynamic range in the output image.

3.3.2 The Application of Anisotropic Diffusion

Before implementing image processing techniques such as segmentation and pattern
recognition, a prior filtering is used to decrease the level of noise in the input radio-
graph. There is, nonetheless, an inevitable problem associated with the conventional
linear filtering such as Gaussian filtering: as the noise is being diffused, the bounda-
ries are also diffused simultaneously. The diffusion of noise of first condition is desir-
able; but the second condition of boundary smoothing is inferior to segmentation.
To avoid this undesired diffusion, a non-linear anisotropic diffusion method are con-
structed via partial differential equation, designed by Perona and Malik [ 9 ], termed
as the Perona-Malik Anisotropic Diffusion (PMAD) which is based on scale-space
filtering [ 10 ]. This method gains popularity by advancing the non-linear filtering
algorithm for image smoothing. Traditionally, noises are eliminated by using diffu-
sion algorithms in use of the isotropic diffusion equation as defined as follow [ 11 ]:

∂ I ( x , y , t )
∂ t

(3.26)

= div (∇ I )

Suppose the I ( x , y , t ) denotes the input image at t stage in the continuous
domain, where ∇ I denotes image gradient, ( x , y ,0 ) : R 2 → R + , ( x , y ) denotes the
spatial coordination of the image, t denotes the time parameter. The enhanced iso-
tropic partial diffusion equation proposed by Perona and Malik is as follows:

∇( I , x , y , t )
∂ t

(3.27)

= div ( g ( ∇ I ∇ I ))

where ∇ I represents gradient magnitude, g (∇ I ) represents the diffusion strength
functions. The diffusion function manipulates the diffusion intensity relying on the
image gradient. The characteristic that is uniquely possessed by this anisotropic
diffusion makes it having advantage over the conventional scale-space filtering. This
characteristic is the existence of the diffusion function—the diffusion intensity vary-
ing function. This function changes accordingly depending on the image gradient. If
the gradient magnitude is large, then diffusion intensity is low; whereas, if the gra-
dient magnitude is small, the diffusion intensity is high. This complies to the final
objectives of the smoothing the image: 1) the texture inside region is smoothed; 2)
the object boundaries are preserved to sharpen the edges of object to preserve the
details of the image. To fulfil this property of the diffusion function, Perona and
Malik proposed monotonically decreasing diffusion functions as follows (2D image):

2

∇ I ( x , y , t )
κ

(3.28)

g 1 ( ∇ I ) = exp −