Result and Discussion - Segmentation of Hand Bone for Bone Age Assessment - page 116

segmentation algorithms and the ideally segmented image (ground truth). The met-
ric returns a numerical value after comparing the segmented image with the reference
image that is manually segmented indicating the similarity between them to rank the
segmentation algorithms performance. The ground truths are defined differently in dif-
ferent segmentation quality metrics; for FOM, the ground truth refers to the edges of
hand bones; for FOC, the ground truth refer to the pixel intensity of hand bones; for
FRAG, the ground truth refers to the number of isolated fragmented bones resides in
hand bone radiographs. The details of each metric are explained below:

(1) Figure of Merits (FOM)

It is the commonly adopted edge detection evaluation that measures the discrep-
ancy between the detected edge pixels and the actual edge pixels. The metric is
defined as follows:

N

1
N

1
1 + ω[ E ( i )]

(4.8)

FOM =

i = 1

where N denotes the maximum number between the detected edge pixels and
actual edge pixels. E ( i ) denotes the distance between the i ith detected edge pixel
with its according actual spatial location. The parameter ω denotes the scaling
parameter that manipulates the influence of errors to the metric; this scaling ena-
bles us to model the relative importance of edges in ossification sites and edges in
non-ossification sites.

(2) Figure of Certainty (FOC)

It is a metric that measures the discrepancy of the gray level intensity of specific
spatial location between the segmented hand bone and the gray level intensity in
reference hand bone. The value reflects the degree of false labeling. Specifically,
false labeling occurs if a pixel that constitutes the bone region is labeled as back-
ground pixel or if a pixel that constitutes soft-tissue region or background pixel is
labeled as bone region. The FOC is defined as follows:

N

1
N

1
1 + α | R ( i ) − S ( i )| β

(4.9)

FOC =

i = 1

where N denotes the total number of hand bone pixels. R ( i ) refers to the ith pixel
of hand bone in reference hand bone. S ( i ) refers to the i ith pixel of hand bone in
segmented hand bone. The scaling parameter α determines the impact of small
deviation between the reference pixels and segmented pixels whereas the scaling
parameter β determines the impact of large deviations between the reference pixels
and segmented pixels.

(3) Fragmentation (FRAG)

For accurate bone age assessment, the condition in which the total number
of bones in actual hand bone radiograph amounts to total number of bones in