International Journal of Computer Applications (0975 – 8887)
Volume 76– No.9, August 2013
Tibia Bone Segmentation in X-ray Images - A
Comparative Analysis
Nathanael .E. Jacob
Department of E & Tc.
VIT, Pune. Country- India
M.V. Wyawahare
Department of E & Tc. VIT, Pune. Country- India
ABSTRACT
Segmentation techniques in the medical field are used to segment anatomical structures or other regio
n of interest from medical images obtained from different modalities. This paper deals with segmentation techniques like manual thresholding, Otsu thresholding, watershed, traditional active contours and growcut in X-ray modality, for segmenting the tibia bone. This paper analyzes the performance of these algorithms on a database of 48 clinical X-ray images. The images have been obtained from different X-ray machines and vary in their resolution and dimensions. The performance of the algorithms have been measured and validated empirically.
General Terms
Medical imaging, machine vision, biomedical image analysis.
Keywords
X-ray, tibia bone, segmentation, growcut, validation.
1. INTRODUCTION
A common ailment that affects the tibia bone is fractures and account for approximately 20% occupancy in hospitals [1]. The fractures that occur in tibia bones are varied and pose difficulties to a doctor in finding and assessing them accurately. Misdiagnosis of fractures can occur in clinical setting
due to factors such as a tired radiologist, huge volume of data to be analyzed; satisfaction of search etc [2].This can result in loss of money, time and litigations. Therefore there is a need to design systems that can aid experts in assessing bone anomalies.
Development in machine vision can enable doctors to use computers as second opinion to diagnose fractures in bone. [3]. Such systems called Computer aided diagnosis (CAD) systems can prove very useful to analyze large volumes of medical data, as well as improve the accuracy of interpretation while reducing time for diagnosis. A CAD for fracture detection system consists of four blocks: preprocessing, segmentation, fracture detection and location of fracture [4].
This is shown in the Fig 1 below.
Fig 1: Block diagram of bone fracture CAD system This paper deals with the first and second blocks. It focuses on applying threshold based, region based, deformable model and cellular automata based segmentation techniques to solve the problem of segmenting tibia bone accurately from X-ray images.
This is followed by validation of segmentation using
time, sensitivity, specificity, Jaccard and Dice coefficients as performance metrics.
2. RELATED WORK
Segmentation of bones plays an important role not only in fracture detection [5] but also surgery, quantitative analysis and planning for surgery. Segmentation has been researched in different modalities like CT, MRI and X-ray. In case of X-ray images the segmentation is quite challenging. This is because of bone boundaries being less clear in X-ray images as compared to images in CT or MRI [6].
Region based algorithm involving region growing, region merging and region labelling has been applied by [7] Manos et al. to segment hand and wrist bones. [8] El-Feghi et al. used a fuzzy set algorithm to segment bone in lateral skull x-ray images. The algorithm however suffers from the problem of disjoined segmented regions. [9] Vinhais et al. segmented the rib cage in posterior-anterior chest X-ray images using a deformable prior model, which is deformed using    a deformation grid. The segmented output defines the lung region, which is used in Computer aided diagnosis system. On the other hand [10] Zhanjun Yue et al., rib finding algorithm uses Hough transform to approximate and final
ly localize the rib bones using active contour model in chest radiographs. Geodesic active contour incorporating prior shape information has been used by [11] Yuchong Jiang et al. to segment the leg bone. The algorithm is robust to background noise of the casting material overlaying on the fractured leg. [12] Ying Chen et al. worked on developing a model based code to automatically extract femur bone from X-ray images. Initially a model femur contour is registered to the x-ray image, followed by active contour with shape constrains to refine the contour. [13] G. Behielset al. uses active shape model (ASM), involving a regularizing smoothness constrain to segment femur, humer and calcaneus bones in the human body.
3. PREPROCESSINGresized
The database consists of x-ray images obtained from different x-ray machines and is very large in size. The size falls in following range: height = 2068 – 3072 (in pixels) and width = 956 – 2844 (in pixels). To process such images is extremely time consuming and real time implementation of segmentation algorithms for such images is not possible. Also the orientation of the leg in the images is non uniform and need to be corrected for uniformity and to aid automation. To address these issues a pre-processing technique that corrects alignment and also reduces the size of the images has been devised. The method takes care that important information is not lost from the x-ray images.
International Journal of Computer Applications (0975 – 8887)
Volume 76– No.9, August 2013
Algorithm:
1.Start
2.Read input image, I
3.Resize the input image I,by a scale of 0.15 to get the
resized image I resized.
4.Apply Otsu segmentation [14] to the image, I resized.
5.Calculate area of every region in the threshold image,
I otsu.
6.Select the region with maximum area as the ROI.
7.Calculate its inclination.
8.Correct the inclination of the bone using the formula
8.1.If the bone is inclined to the right, then it is rotated
in anti-clockwise direction by an angle equal to
“90-angle” (i.e. Angle corrected= 90 - Angle original)
8.2.But if the bone is inclined to the left, then it is
rotated in clockwise direction by an angle equal to
“-90-angle” (i.e. Angle corrected= - 90 -
Angle original). Here the value obtained will be
negative. This denotes that the image should be
rotated in clockwise direction.
9.The new image obtained is I rot. Next, the co-ordinates of
the bounding box of the maximum area region in the above image are obtained.
10.Using these coordinates a rectangle containing the bone
region (ROI) is cropped from the image I rot. The new image obtained is I crop, which is the final pre-processed image I new.
11.Stop
The size of test images obtained after pre-processing fall in the following range: height = 367 – 530 (in pixels) and width = 50 – 191 (in pixels).One of the results is shown in Table 1.
Table 1. Preprocessing result
The segmentation algorithms adopted must be robust to such interpolated images, obtained due to pre-processing. Once the ROI is obtained from segmentation, the binary mask of the ROI is rescaled and rotated back to its original size and inclination. The binary mask is then used to crop the ROI from the original, unaltered medical image. This ensures that the final ROI obtained contains pixels having intensities that have been originally provided to the segmentation system and the system is in no way modifying the intensities of the ROI by processing it.
Prior to segmentation, the images are rotated and scaled. Scaling and rotation of images involve interpolation. The less frequently this technique is used, the lesser is the distortion in the image. This is because interpolation never adds additional details to an image other than what is already present. Interpolation adopts the strategy of guessing pixel values at additional new locations based on the neighbouring pixel values of those locations. This causes loss of quality of images and hence is generally avoided on sensitive medical images
4.SEGMENTATION METHODS
The methods discussed in this section are categorized in Table 2.
Table 2. Segmentation Techniques
The the segmentation techniques.
4.1MANUAL THRESHOLDING
Manual thresholding requires user effort for selecting the right threshold value and is usually done with the help of a histogram, using trial and error method. It involves converting the input image into binary image based on a fixed threshold. The input image pixels having intensities greater than the threshold level are assigned the value 1 and all the other pixels are assigned the value 0 in the output image. The manual thresholding does not hold good since the intensity distribution range for the    3 classes (Skin, bone and background) is not unique and varies with different images as well as the X-ray modality used. Often the three classes are found to overlap for a given area on the histogram. Due to these reasons this method is not suitable for tibia bone segmentation problem. The segmentation result for    a threshold value of 153 is shown in Table 3.
4.2OTSU THRESHOLDING
Otsu thresholding [14] attempts to find that threshold value for which the sum of variances of the foreground and background pixels is at its minimum. It is an automated technique and is easy to implement. However the regions in the image need to be well separated in the histogram to give perfect results.
International Journal of Computer Applications (0975 – 8887)
Volume 76– No.9, August 2013
Table 3. Manual thresholding results
Here three thresholds are found using Otsu method. The first threshold (T 1) is only good enough to segment the leg from the background. So in order to get the bone the leg region is provided to the Otsu algorithm to get the second threshold (T 2). But this results in over segmentation. So the region having intensities between T 1 and T 2 is provided to the algorithm to get a third threshold (T 3). This has been tested to give better results than T 1 and T 2.
The Threshold values can be shown on the intensity axis as follows:-
Fig 2: Threshold values on the intensity axis
The threshold values are: T1 = 108, T2 = 191 and T3 = 151 for the example shown in Table 4.
Table 4. Otsu segmentation results 123
4.3 WATERSHED SEGMENTATION [15]
The watershed segmentation is known to face over segmentation error due to irregularities in the gradient of the image to be segmented. To overcome this markers are defined on the image from where, the topological surface is flooded. The algorithm used
in Matlab for watershed segmentation is the Meyer‟s flooding algorithm developed in the early 1990‟s. A disc marker of radius 5 or 10 has been used to obtain the results. The size of marker to be used for a given image is empirically set. The results obtained using the above approach is shown below.
Different regions of the Watershed output for one of the input images have been indicated by different colours in Table 5.
Table 5. Watershed segmentation results
At the end of the program, a user intervention is needed in order to indicate the actual region of the watershed transform that one is interested in. This can be avoided by determining the region properties of the segmented regions and then classifying a region as bone if it satisfies the region properties of a bone. Also there is a need to automatically determine the radius of the marker disc. The code for marker controlled watershed is part of the demos section of Matlab 2012a and can be run by typing ipexwatershed  in the command window.
International Journal of Computer Applications (0975 – 8887)
Volume 76– No.9, August 2013
4.4 ACTIVE CONTOUR SEGMENTATION
Active contours [16] or Snakes are widely used for edge detection in the field of image processing. A snake can be defined as a spline curve which tends to minimize its energy. The energy of the snake is
dependent on its shape (internal energy) and its location (external energy). The total energy of
the snake is given by:-
The above equation involves a parametric snake given by s(p) = (x(p),y(p)). E int  and E ext  are the internal and external energies of the snake.
E int
can is given by the formula,
It controls the mechanical behaviour of the snake by determining its shape. Here α and β are constants. If alpha is less, the snake can elongate more and if beta is less the snake can bend more. The internal energy is meant to force the snake to be small and smooth. E ext
is given by the equation,
It depends on the properties of the image. The simplest form of external energy is the inverse of the gradient magnitude of the input image.
Internal and external forces determine the shape and position of the snake. The internal force keeps the snake smooth whereas the external force guides the snake towards the image features.
The output of the snake model is a closed contour. This is very advantages if the region boundary has discontinuities. The snake tends to take the general shape of the image boundary. Also the edges of output of the snake model are very fine. This will prove to be advantages if ones interest lies in extracting features pertaining to the edges.
Table 6. Active contour segmentation results
However the active contour method is known to face problems at concavities. Furthermore the snake n
eeds to be initialized close to the ROI. This is often done manually. The snake is found to be highly sensitive to its parameters which are initialized empirically to values that vary for different types of images. The result for AC model is given in Table 6.
4.5 GROWCUT
GrowCut [17] segmentation is an interactive process, modelled by evolution of cellular automata. Here every pixel in an image can be considered as a cell. The cells can be initialized as foreground, background, or undefined. As the algorithm proceeds, these cells compete to dominate the image domain. Some cells capture their neighbours, replacing their labels. The ability of a cell to spread depends on its feature vector and strength. There can be more than 2 class labels in an image. It can be extended to N dimensions.  The growcut involves …for‟ loops which prove to be computationally expensive in Matlab. To solve this problem, the code for growcut has been written in C in Matlab (i.e.  as a binary mex file). Mex stands for Matlab executable.
The most important challenged faced in applying the growcut algorithm is the computation time for large medical images. The results reported in the original paper of growcut [17], mention a segmentation time of 4 sec for a 256x256 image on a    2.5 GHz processor. However for large images
the computation time required is 10 minutes, which is quite large. To address this problem the images were resized.
The mex code for growcut has been implemented by Shawn Lankton and can be downloaded from [18]. The results obtained are given in Table 7.
Table 7. Active contour segmentation results
5. VALIDATION
It is not possible to visually inspect the subtle differences between an expert segmented image and a user segmented image at all times [19]. In order to compare different segmentation techniques and to encourage programmers to
International Journal of Computer Applications (0975 – 8887)
Volume 76– No.9, August 2013
develop more better and efficient codes, evaluation parameters will be needed [20] .These parameters help to evaluate the quality or “goodness” of image segmented by the above algorithms. In general validation techniques can be categorized as follows:-
1. Analytical
2. Empirical
a.
Empirical Goodness
b. Empirical Discrepancy
The paper uses empirical discrepancy method for validation and analysis.
Since the output of a segmentation algorithm is affected by multiple parameters, it is not possible that a single evaluation parameter will prove effective in evaluating the “goodness” of segmentation. Therefore four metrics have been used to validate the segmentation results. They include: Sensitivity, Specificity, Jaccard and Dice co-efficient. The parameters are chosen, such that they complement each other in their ability to evaluate a segmented output. The ground truth images have been produced manually, by tracing a polygon on the boundaries of the tibia bone in the X-ray images.
The Venn diagram below will help to visualize the spatial differences between a Segmented output (Results set) and its
corresponding gold standard (Truth set) [21]
Fig 3: Venn diagram
Let X be the set of all pixels in the image. Then set A is the set of pixels identified as tibia bone by gold standard segmentation and B is the set of pixels identified as tibia bone by a segmentation algorithm. True positive set (TP) is then defined as the set of pixels identified as tibia bone by both gold standard and user defined segmentation.
< TP = A ∩ B
True Negative set (TN) is the set of pixels identified as non-tibia bone by both the algorithms.
TN =  (A ∪ B)’
Similarly False Positive (FP) and False Negative (FN) are given as,
FP = (A‟ ∩ B) and FN = (A ∩ B‟)
Using these regions four evaluation parameters are defined as,
1. Sensitivity = TP/(TP + FN)
2. Specificity = TN/(TN + FP)
3. Jaccard Co-efficient = TP/(FP + TP + FN)
4. Dice Co-efficient = 2TP/(FP + 2TP + FN)
1. Sensitivity (S)
It measures the proportion of tibia bone pixels that have been accurately segmented by the segmentation algorithm. Using sensitivity, false negative rate (fnr) is obtained and is given by:-
False negative rate (%) = (1-sensitivity) x 100
Since sensitivity gives the amount of foreground pixels correctly segmented as foreground pixels, false negativity rate can be defined at the percentage of foreground pixels classified as background pixels or in other words false negative rate is the percentage of under segmentation error.
2. Specificity (Sp)
Similarly using specificity, false positive rate (fpr) is defined as the percentage of over segmentation error and is given by:-
False positive rate (%) = (1-specificity) x 100 3. Similarity metrics  a) Jaccard co-efficient (J)
The Jaccard co-efficient measures the ratio of area of overlap between the segmented output and the ground truth to the union of their areas. This is defined as:-
J = |A ∩ B| / |A ∪ B|
b) Dice co-efficient (D)
The dice co-efficient is another metric used to define segmentation quality or measure of similarity between the segmented image and the gold standard image. It is defined as:-
J = 2 |A ∩ B| / (|A| ∪ |B|)
The dice co-efficient is more commonly used parameter to measure spatial overlap and is used when the number of non-ROI pixels is greater than the number of ROI pixels [22].  Using the Jaccard co-efficient, the dice co-efficient can be easily obtained, since the dice co-efficient and Jaccard co-efficient are equivalent to each other and there exists a monotonic relationship between
D=2J / (1+J)
Both the coefficients give value between 0 and 1. Here 1 implies perfect similarity of the segmented image to its gold standard and 0 implies total dissimilarity between the two. The Jaccard co-efficient gives a low percentage of similarity as compared to Dice co-efficient for cases where the spatial overlap is very less [23].
However both the Jaccard and dice coefficients are unable to distinguish between over and under seg
mentation errors and assume equal cost for both these errors. Also small errors in the segmented image cannot be identified by these parameters [22].
The segmentation time (t) along with the four evaluation parameters have been calculated for 48 images. The average values of the five parameters for every method are given in Table 8. The segmentation algorithms have been coded in Matlab R2012a (7.14.0.739) and run on a machine with the following configuration:- Intel(R) Core(TM)2 Duo CPU T6600 @ 2.20GHz, 2.20Ghz with RAM: 4.00GB and Windows 7 (64bit) as operating system.

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