53 CHAPTER 5 DECISION TREE APPROACH FOR BONE AGE ASSESSMENT The decision tree approach for BAA makes use of the radius and ulna wrist bones to estimate the bone age. From the radius and ulna bones, 11 epiphyseal features, that reflect the degree of maturation of the bones, are extracted. They are fed into the new decision tree classifier (different for males and females), which outputs the bone age class of the input image. 5.1 INTRODUCTION For a computerized system to have accuracy over the entire 0-19 year age range, the radius and ulna bone information have to be integrated with the BAA system. The difficulty lies in the fact that at lower age ranges, the ulna bone maturation information will not be sufficient to determine bone age. This is because the ulna bones do not ossify until the age of 6-7 years in males and 4-5 years in females. For the age group below the above specified range, the ulna bones do not contribute toward BAA. But for those age groups, the information from radius bone can be utilized in assessing bone age. Therefore, a reliable method has to be developed to cover the whole range by efficiently integrating information from each of the different regions. This chapter presents one such proposed system for BAA by incorporating the features from the radius and ulna wrist bones. possible 5.2 GROWTH PATTERN OF RADIUS AND ULNA BONES The radiographic appearance of the carpal bones and growth plates of the distal radius and ulna begin progressively from birth. Figure 5.1 shows the TW stages of maturation from stage B to stage I for the radius and ulna bones. The initial stage A is characterized by the absence of the epiphysis. Stage B is demonstrated by
the ossification of the epiphysis as a small circular deposit of calcium. In stage C, the epiphysis becomes elongated and non-circular. During stage D, its diameter becomes half or more the width if the metaphysis. In stage E, the surface becomes rough and concave, and in stage F the epiphysis becomes as wide as the metaphysis. During stage G, the epiphysis begins to cap the metaphysis. Stage F is distinguished by the beginning of fusion of the epiphysis and metaphysis. Stage I is recognized by the completion of the fusion. 54 Figure 5.1 TW stages of the radius bone 5.3 MATERIALS AND METHODS 5.3.1 Dataset The common dataset of 220 images with 110 male and 110 female images are used for this approach too (as given in section 3.3.4). 5.3.2 Pre-processing The input radiograph is initially thresholded (Gonzalez and Woods 2009) to detect the foreground and background pixels. A threshold image partitions the image into two regions, foreground and background, based on the intensity values. The thresholded image is superimposed on the input image to remove the hand borders in the image. Then the epiphyseal ROI of radius and ulna bones are cropped and isolated. The cropped ROI are pre-processed for noise reduction using anisotropic diffusion filter. Figure 5.2 shows a sample input, thresholded and superimposed image
during preprocessing. Figure 5.3 depicts samples for cropped and filtered radius ROI (RROI) and ulna ROI (UROI) for feature extraction. 55 (a) (b) (c) Figure 5.2 Pre-processing results for Decision Tree approach (a) Input image (b) Thresholded image (c) Superimposed image (a) (b) (c) (d) (e) (f) (g) Figure 5.3 Cropped RROI/ UROI for various age groups (a) 1 year (b) 2 years (c) 3 years (d) 5 years (e) 7 years (f) 9 years (g) 10 years ( a to d are samples of RROI and e to g are samples of UROI respectively)
56 5.3.3 Feature set For both radius and ulna bones, the degree of maturity is based on the extent of ossification of their epiphysis. So, for both the categories, the same five epiphyseal features given below are considered for feature extraction. i) Presence whether the epiphysis of the bone is present or absent ii) Circularity whether the epiphysis is circular in shape or not iii) Roughness whether the epiphysis surface is smooth or irregular iv) Capping whether the epiphysis capping has begun or not v) Fusion whether the epiphysis fusion has begun or not. The features are extracted from the radius and ulna epiphysis as given below. i) Presence The presence of the radius or ulna epiphysis is marked by a TRUE value for Presence and returning a FALSE value if absent. ii) Circularity Circularity is defined as a simple shape factor based on the projected area of the sample and the overall perimeter of the projection given by, 4 A Circularit y 2 (5.1) P where A is the area and P is the perimeter of the epiphysis sample. Values for Circularity range from 1 for a perfect circle to 0 for a line. The Circularity value of the bone is checked. If it is greater than or equal to 0.5, it returns a TRUE value. In the FALSE case, when it is non-circular, the diameter of the epiphysis, R_diameter is calculated and checked if it is above or below the threshold (which is calculated as the mean of the R_diameter values of both the extreme age classes) and assigned a class to it accordingly.
57 iii) Roughness Roughness of the bone is measured by employing Fractal dimension. Fractal dimension is found to be a measure of roughness and is given by, log N Roughness 1 (5.2) log r where, N is the number of copies of a self similar set, which has been scaled down and r is the scaled ratio of the self similar set. If Roughness is above the threshold value (which is calculated as the mean of the Roughness values of both the extremes), it returns TRUE. iv) Capping This is calculated as the difference between the horizontal diameter of the sample bone and the horizontal diameter of the corresponding epiphysis, as given in equation (5.3). If Capping value is negative, then it returns TRUE. v) Fusion Capping Diameter Bone Diameter Epiphysis (5.3) Fusion is computed by simply measuring the Euclidean distance between the bone and the epiphysis. If it is negative, then it returns TRUE. The above features are extracted from the radius and ulna bones, leading to the following features, R_Presence, U_Presence, R_Diameter, R_Circularity, U_Circularity, R_Roughness, U_Roughness, R_Capping, U_Capping, R_Fusion, and U_Fusion. Thus the feature extraction phase results in 11 morphological features for further processing.
58 5.3.4 Bone Age Estimation Feature extraction is followed by either the training phase or testing phase. In case of training, the classifier is trained with the range of values taken by each feature with respect to each age class. During testing, the extracted features are translated into corresponding skeletal bone age. The selected features occupy positions in the decision tree based on the order of ossification of the bones, which influence their contribution towards the bone age estimation procedure. 5.3.5 Decision Tree classifier The morphological features extracted from the wrist bones have a certain degree of overlapping between them, since the growth pattern is gradual. But the features can fall into only any one of the categories, since they are mutually exclusive. So the decision tree classifier is more suitable for this proposed BAA method. Decision trees have proved to be simple and robust method to divide the space in attributes and to make decisions based on symbolic inputs (Liu et al 2000). They are by nature readily interpretable and well suited to classification problems. A decision tree consists of nodes for testing attributes, edges for branching by values of symbols and leaves for deciding class names to be classified. Fig 5.3 (a) shows the decision tree constructed for males and Figure 5.4 (b) for females. The inputs to the decision tree are the 11 features modeled as Boolean values, and the output will be the skeletal class or category. The selected class is then mapped onto the skeletal bone age, based on the criteria shown in Table 5.1 for males and Table 5.2 for females. 5.4 RESULTS AND DISCUSSION The performance of the proposed decision tree method in estimating the bone age was evaluated using a dataset consisting of 100 radiographs (50 for boys and 50 for girls). The ease and accuracy of feature extraction for the UROI were slightly imprecise when compared to the RROI, the reason being that the epiphysis of the
ulna bone was smaller in size and less contributing. Also, the accuracy of feature extraction tend to decline slightly as the age increases, since at later stages the system relied much on the ulna ROI. On the other hand, the accuracy of feature extraction from RROI was outstanding, thus improving age estimation during early stages. The accuracy of the classification was measured in terms of four metrics, precision, recall, specificity and accuracy. The above four metrics were measured for each class A J, using True Positive(TP), False Negative(FN), False Positive(FP), and True Negative(TN) cases, as done in the previous chapters. 59 (a) (b) Figure 5.4 Decision Tree (a) Males (b) Females
60 Table 5.1 Criteria Selection for Male in Decision Tree approach Age Class Age Value v (Years) Table 5.2 Criteria Selection for Female in Decision Tree approach Age Class Age Value v (Years) A 1 month < v < 1 year A 1 month < v < 3 months B 1 year < v < 2 year B 3 months < v < 6 months C 2 year < v < 3 year C 7 months < v < 1 year D 3 year < v < 4 year D 1 year < v < 2 year E 4 year < v < 5 year E 2 year < v < 4 year F 5 year < v < 6 year F 4 year < v < 5 year G 6 year < v < 7 year G 5 year < v < 5 year 5 months H 7 year < v < 8 year H 5 year 5 months < v < 6 year I 8 year < v < 9 year I 6 year < v < 7 year J 9 year < v < 10 year J 7 year < v < 8 year The performance metrics were calculated using the following formulae: TP precision TP FP (5.4) recall TP TP FN (5.5) TN specificit y (5.6) TN FP accuracy TP TP TN TN FP FN (5.7)
61 Table 5.3 Classification Metrics for Decision Tree approach Class A B C D E F G H I J Confusion Matrix 10 0 0 80 10 0 0 80 9 0 1 81 8 1 1 82 9 1 0 81 8 2 2 82 8 2 2 82 7 1 2 83 8 1 1 82 9 1 1 81 precision recall specificity accuracy 100 100 100 100 100 100 100 100 90 100 99 99 89 89 99 98 100 90 100 99 80 80 98 96 80 80 98 96 78 88 98 97 89 89 99 98 90 90 99 98 The performance of the system was validated by using the diagnosis results obtained for the data set from two skilled radiologists and the values obtained for the performance metrics are tabulated in Table 5.3. It is found that the minimum value of precision is 78% and obtained for the class H and that of recall is 80% obtained for classes F and G. The minimal value obtained for specificity is 98% obtained for classes F, G and H and that of accuracy is 96% obtained for the classes F and G. Classes F and G found to downgrade the overall performance of the classifier, the reason being the less contribution of UROI or poor ossification of the
epiphysis of the ulna bone for those two age classes. Best performance was found in the earlier classes A and B, since the high contributing RROI are the only bones considered and also due to good inter-class difference. The class-wise performance of the proposed decision tree method is depicted in the graph shown in Figure 5.5. 62 Values of Performance Metrics in % 105 95 85 75 65 A B C D E F G H I J Classes precision recall specificity accuracy Figure 5.5 Performance Metrics Graph for Decision Tree approach The overall accuracy was 98%, specificity was 99%, precision was 90%, and recall was 91%. By applying the alternate partition of 160 train images and 60 test images, the proposed decision tree approach for BAA scored 99% for accuracy, 100% for specificity, 92% for precision and 93% for recall. To achieve further more improvement in the results, yet another partition was introduced with 180 train images and 40 test images and the performance of the system was analyzed. The proposed decision tree method showed much better results for this partition with 100% in all the four performance metrics. The performance of the proposed BAA system using decision tree is compared with the existing BAA methods. Figure 5.6 shows the graphical comparison of the developed new decision tree method with the existing systems using the four performance metrics accuracy, specificity, precision and recall.
63 Values of Performance Metrics in % 105 100 95 90 85 80 75 Zhang et al (2007) Tristan & Arribas (2008) Giordano et al (2010) BAA Systems Somkantha et al (2011) Proposed Decision Tree Approach accuracy% specificity% precision% recall% Figure 5.6 Comparison of Decision Tree approach with existing systems Based on the results obtained for the proposed decision tree method, a paper entitled Computerized Skeletal Bone Age Assessment from Radius and Ulna bones has been published in International Journal of Systems, Algorithms and Applications, Vol. 2, Issue 5, May 2012, pp. 60-66. 5.5 CONCLUSION An efficient computerized approach to estimate the skeletal bone age by deploying decision tree classifier was proposed. The proposed technique utilized features extracted from the radius and ulna bones and their epiphysis. Different decision trees were constructed for males and females, since the growth pattern of the above mentioned bones show variations between males and females. The inputs to the decision tree were the features extracted from the bones and the output was the skeletal age class which corresponds to the final bone age. The system results were validated with the diagnosis results obtained from two radiologists. From the results it is apparent that the developed decision tree approach for BAA was robust and appropriate for the age group of 0-10 years for males and 0-8 years for females. The proposed BAA system using decision tree achieved nearest to 100% in accuracy, specificity, precision and recall.