Design and Implementation - Segmentation of Hand Bone for Bone Age Assessment - page 64

1

g 2 ( ∇ I ) =

1 +α

∇ I ( x , y , t )
κ

1 +

(3.29)

where α > 0

The ' κ ' denotes an adjustable constant that is used to manipulate the 'definition
of edge'. This value is conventionally decided from the noise degree in the image
and the intensity of the edges in image. It is important for diffusion function to
identify the edges so that diffusion strength is reduced on them with the purpose of
smoothing the texture of the bone and to ease the following processes of segmen-
tation, especially segmentation that involves clustering.
The following shows the 2D discrete implementation:

∂
∂ t I ( x , y , t ) − div [ g ( x , y , t ) ∗ I ( x , y , t )]
For the relative distance, ∆ x = ∆ y = 1

(3.30)

∂
∂ t I ( x , y , t + ∆ t )
≈ I ( x , y , t ) + ∆ t · [ Φ east + Φ west + Φ north + Φ south ]
+ 1

(3.31)

∆ d 2 (Φ northeast + Φ northwest
+Φ southeast + Φ southwest )
where ∆ d = √ 2

3.3.2.1 Parameter-Free Diffusion Strength Function

Anisotropic diffusion is adopted in the segmentation framework with some modi-
fication so that it conforms to the desired properties P6 where the conventionally
manually tuned parameter κ is made to be automated. Instead of finding κ in dif-
fusion strength function, we used coefficient of variance. Referring to Eq. ( 3.27 ),
the conventional anisotropic diffusion adopts diffusion strength function governed
by image gradient and thus we have to determine the edge threshold, κ . Therefore,
the aim is to modify it by using the automated noise estimation scheme from [ 12 ].
Thus g ( ∇ I ) in Eq. ( 3.27 ) has been changed to c(q) in Eq. ( 3.32 ).

∇( I , x , y , t )
∂ t

(3.32)

= div ( c ( q )∇ I ))

1

c ( q ) =

(3.33)

q 2 − q 0 ( t ) /[ 1 + q 0 ( t )] 1 +

var ( I m , n )
µ I m , n

(3.34)

q =