Abstract
InBy
previousexisting[JH1] epiphyseal extraction methods,
epiphyses often wereare not extracted accurately, in a certain finger
because as
errors can occurs
in the detection of a finger’s
central axesaxis.
This paper proposes a new, more accurate
epiphyseal extraction method whichthat estimates the central axesaxis more robustly from the top of the distal
phalange to the upper
part of the metacarpal. In this method, The method
entails an analysis of a finger’s horizontal profile that
detects that finger’s
central axis, on and
from which epiphyses are detected and extracted,
respectively. central axes of
fingers are
detected by the
analysis of finger’s horizontal profile, and epiphyses are extracted
on the detected
central axis. The result of In thean experiment, the
result showsshowed
that this method robustlyaccurately extracts epiphyses
even from finger images thatfor which
the detection of finger’s the central
axesaxis is difficult.
1. Introduction
Since the shapes of epiphyses vary
largely according to a subject’s age,
epiphyses are usedutilized foras
the
significant features forin
the bone age
assessment. The
point-detection range over which epiphyses are detected and extracted is from
the top of the distal phalange to the upper part of the metacarpal.[JH2]
Previous works of
epiphyseal extraction algorithms are based on a process that detects the point
where, on the central axis of a finger, the
differential of gray values appeared highly on central axis of a
finger is most apparent. In order to extract three
epiphyses on a finger, the range of
point detection is from top of distal phalange to upper part of
metacarpal. Pietka’s method is a representative
of
previous work ofon automatic
bone age estimation. In this method, after the soft tissue-background edges of
a finger image are detected, the central axis is estimated using a third-order
polynomial fit [1][2][3][4]. However, the central axis from the lower part of the proximal phalange
to the upper part of the metacarpal is
derived byfrom the
interpolation value calculated on the upper phalange, because bones
located under the lower part of the proximal phalange have not edges of soft tissue-background. Therefore, if the
direction of the metacarpal’s
edges is different withfrom the
direction of the finger’s soft tissue-background
edges, a detection of proximal epiphyses maymight
be
fail. AnotherAn
alternative method iswas proposed by Seouk-Hwan
Jang [5]. In this method, first
of all, each region of a finger is extracted in
order to make finger images, and then those
images are utilized , in estimating
the
angles of each of the fingers. are estimated on
finger images. According to these
angles, the Ffinger images are rotated
and aligned to the vertical, by
rotating according to estimated angles,
and the each of
central axesaxis of each finger is estimated by analysisanalyzing with
the vertical projected gray value of theits
rotated finger
image. However, if a finger is bent, an error of
finger’sits angle estimation maycan
occur,
rendering inaccurate the. Then an epiphyseal
extraction result. becomes not accurate.
Besides
these methods,A third method is Chi-Wen Hsieh’s proposed phalange extraction
infrom a finger image using the
Gabor filter and the Canny edge detector to finddetermine the position of epiphyses. However, itthis
method also has a problem of is
prone to the same type of epiphyseal extraction
error because of a finger’s angle estimation error on the bent finger image [6] [7]. Ana Maria Marques Da
Silva’s method uses the gradient value[JH3] to detect the
edge of fingersfinger
edges using
their own method[JH4] , but the parameters of the
method are not selected automatically [8].
In order to solve these problems, with the above statement,
this paper proposes thean epiphyseal extraction method whichthat estimates a
finger’s central axesaxis
from the top
of the
distal phalange to the upper part of the metacarpal
by analyzing thethat finger’s horizontal profile. The paper is organized
as follows. Section 2 introduces
explains the processes which is accomplished
before of detecting epiphyses, and then estimating central axes, and detecting epiphyseal coordinates. are explained.
Section 3 discusses the Experimental results of an
experiment conducted are shown
to evaluate the proposed method. in Section 3. The
conclusions are summarized in Section 4
summarizes the conclusions.
2. Epiphyseal extraction process
The eEpiphyseal extraction is performed inaccording to the following steps. First, the background
region is removed to obtain the hand
region from the radiograph of a
left hand, and then the finger positions are detected onfrom within the
hand region. 3Three
fingers, of the
index, the middle and the ring finger, are used forin
the epiphyseal extraction. Second,
the
central axes are estimmated. in the
finger region.[JH5] And
finally, the epiphyses are extracted onby reference to the estimated central axes. The
procedure of epiphyseal extraction is shown in Figure 1.
2.1. Background removal and finger region detection
First of all, the background
region is removed from the left-hand radiograph in order to obtain
the hand region. The background 
is assumed asto be
a 2-dimensional third-order polynomial defined as[JH6]
|
|
(1) |
and 
are calculated using the least square algorithm [9]
|
|
(2) |
|
|
(3) |
where z is the sampled background pixel on the 
coordinates of the input
radiograph. The background is removed by thresholding according to the
estimated value, using Equations (1), (2)
and (3).
After the background removal, the boundary
tracing method is performedused
to detect the position of the 3 fingers onfrom
within the background-removed hand region. The boundary of the hand is traced, and then
the
hand’s inflection points, which include the finger’s-tip
points, are extracted, as shown in Figure 2,
using angle variation of the hand boundary. Each of fingers has the 3 inflection points of
①~③, ③~⑤ and ⑤~⑦. Each
finger image is extracted byaccording to a
rectangle that can be drawn using the 3 inflection points. Finally, the finger
images are rotated to vertical, as shown in Figure
3(a). An angle to rotate the finger image The
rotation angle is calculated by the least square algorithm [9] using
the
detected finger’s pixel coordinates.
2.2. Epiphyses extraction
process
The central coordinates of the phalanges are estimated byby
reference to the central coordinates of the bone-soft
tissue edge’s coordinates
or those
of the soft tissue-background edge. ’s
coordinates. Each of The edge
coordinates are locateds
on both sides of the finger, and isare
calculated using the horizontal profile of finger
image. BeforePrior to the
estimation of the central axis, athe
finger image is blurred by a Gaussian filter [10] to reduce
noise.
Figure 3(a) is an extracted finger image, and Figure
3(b) is a horizontal profile centered on the marked line of Figure
3(a). The x-axis of Figure 3(b) represents the x-coordinates
of the finger image on the profile line, and the y-axis of Figure 3(b)
represents the gray values of the finger image on
the profile line. The horizontal profile existsis
centered on
each of the y-coordinates
of the
finger image. Figure 3(c)
shows the variation
of the horizontal profile,:
significant variation appears on the bone-soft tissue edge or the soft
tissue-background edge positions.
The central axis of a finger consists of central coordinates usingby reference to the
edge coordinates on each y-coordinate of a finger image. The start point
of edge detection is the finger’s tip, which is detected
onin the
process of the finger region detection. Starting
from the finger’s tip, each of the edge
coordinates located on both sides of the
finger are extracteddetected by
detection ofaccording to significant variation of
the
gray values, and then extracted. The direction of
edge detection is from inside to outside, along the
horizontal profile of the current
y-coordinate. And thenSubsequently,
the central coordinate of both edge’s x-axis coordinate is calculated.
In order to avoid using a different kind of edge in calculating a central
coordinate, the bone-soft tissue edge and the soft tissue-background edge are
each assorted byaccording to
the gray value of the extracted edge point. The central
coordinate which is calculated on the current
y-coordinate becomes the coordinate of the start
point onfor the next
y-coordinate, and then the above process is performed iteratively.
The set of central coordinates has a form ofrepresents
the
finger’s central axis, but this
set is rough, and so maymight
contain errors because ofowing to a
fault in the detection of each edge. Therefore,
the set of central coordinates are
reshaped into a line of a third-order
polynomial. A This
third-order polynomial mostmust be
matched to the shape of the phalange in statistical analysis
of finger data. The reshaped line is given by the equation
|
|
(4) |
where y is athe
y-coordinate value of the finger image, and 
are calculated using the least square algorithm [9] with the set of mean values. The calculated line becomes the central axis
of the
finger.
Figure 4 isshows an example
of central axis estimation. Figure 4(a) isshows
the extracted fingers. Figure 4(b) is an image that shows
the detected edges are marked with the white point set
and the central coordinates are
marked with the black point set. Figure 4(c) is a shows the result of the
estimated
central axis after performingestimated by
the least square algorithm.
After detecting the central axis, epiphyses are extracted on the
central axis from it. Each epiphysis coordinate
of
epiphyses is detected according to the differential of the
horizontal projection of the gray values. Figure
5(a) shows the horizontal projected value of the finger
image’s gray value with the black line, and Figure 5(b) shows the
variation of the projected value. As shown in Figure 5(b), the projected value
varies visibly at the positions of the epiphysis.
Therefore, coordinates of epiphyses isare
determined at the positions which hasshowing
significant variation from the projected values.
3. Experiment
In order to evaluate the
efficiency of the proposed method, an
experiment of the in
epiphyseal extraction was doneconducted
using 749 left-hand
radiographs of patients ranging in chronological age from 5 to 16 years. The Ssuccess
rate iswas
calculated byaccording to
the
ratio of epiphysis extraction success aboutfor
all of the sample radiographs. We defined the success case of successful epiphyseal extraction underby this criterion. (1) 9Nine epiphyseal images must be
extracted from each of the left-hand radiographs. (2) Each of the epiphyseal images must be
corresponded withto each distal, middle, and proximal parts of the phalanges. (3) The detected coordinates of epiphysis
must be belonged to fall within the range from the
top of an epiphysis
to theits bottom. of epiphysis. In this time,
iIt
is under the assumptionwas assumed that the epiphyseal image has
parallel directionwas
parallel with to
the detected central axis of a finger.
The performance of the proposed
method iswas compared towith those
of the methods of the
S. H. Jang’s method and the Pietka’s. method.
Table 1 shows the comparison. of success rate with S. H. Jang’s Method, Pietka’s method and
proposed method. Figure 6 shows a result of thethe results for
S. H. Jang’s method and the
proposed method, and Figure 7 shows a the results
offor
the
Pietka’s method and the proposed method.
In the S. H. Jang’s method, an
epiphyseal extraction mostly failed when the finger iswas
bent. In the Pietka’s method, an extraction
of proximal epiphyses mostly failed when the metacarpal’s edge hashad
a different
direction differing withfrom
that of the edge of the soft tissue-background. However,
in the case of the proposed method, epiphyseal images
arewere
reliably extracted even in case of bent fingers, images,
and proximal epiphyses also were accurately extracted regardless
of the
upper phalange’s direction.
4. Conclusions
In this paper, we proposed thea robust, more
reliable epiphyseal extraction method that estimates thea
finger’s central axis more reliably by
horizontal profile analysis. Proposed method is the process which
performs extraction after detecting central axes of fingers by the horizontal profile
analysis. ThroughBy
means of thean experiment in epiphyseal extraction,
we verified thatthat
the method showedoffers the high
success rate of 97.8% in the epiphyseal extraction,. we verified acceptable
performance of the proposed method. The case which fails eEpiphyseal
extraction is that failed in the
case where the epiphyseal image was detected with the wrong
angle. As future
works, wWe
are
planning to are planning to fixcorrect
this problem in future work.