Robust Epiphyseal Extraction Method Based on Horizontal Profile Analysis of Finger Images

 

 

 


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 estimated. 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 ~, ~ and ~. 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 whichthat are calculated 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.


 [JH1]*Write “the existing” if you are referring to ALL existing methods, not just some of them.

 [JH2]This sentence was repositioned here from below.

 [JH3]“gradient values”--?

--passim…

 [JH4]?—Do you mean, “using the same method” (i.e. Hsieh’s method)? If you do not mean this, delete “using their own method” and insert a comma after EDGES.

 [JH5]Unnecessary: implicit in the foregoing

 [JH6]You need to insert a comma after the following equation.