Teeth Segmentation of Bitewing X-Ray Images Using Wavelet Transform

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Introduction
X-ray radiographs have greatly been used within a variety of medical images. One of the common usages of X-ray imaging is in dentistry and forensic odontology. As tooth is the hardest tissue in our body, it plays an important role in forensic medicine. Individual characteristics such as fingerprints, pupils and face are not always possible for postmortem identification, particularly under the critical circumstances [17]. There are situations such as natural phenomenon (tsunami, hurricane, earthquake, etc.), terrorist attacks, airplane crashes and bomb explosion where victims cannot be identified by visual means. This is where dental features become important for forensic experts [11].
It is widely accepted that image segmentation is the most challenging part of the process of feature extraction from dental X-ray images. In the recent years, several approaches in image segmentation have been introduced and made progress in segmentation in order to overcome the existing shortcomings. The biggest challenges in this process are low quality of X-ray images, noise, and low contrast. However, one of the major problems in dental Xray images is similarity of the pixel intensities between gum tissue and teeth. Although the inhomogeneity in pixel intensities has several effective factors, the basic problem is the device that produces these radiations [1].
Different methods, including thresholding-based segmentation, edge-based segmentation, clustering-based Figure 1: Similarity between gum tissue and teeth in a dental X-ray image. segmentation and region-based segmentation, are being used among automatic processes for teeth segmentation. Thresholding-based techniques rely mainly on the distribution of pixel intensities and they use the information based on the single-band image. Edge-based segmentation methods are prone to produce disjoint edges. Clustering-based methods require training samples; for instance, K-means clustering requires initialization for the number of clusters k. Region-based techniques require objects with similar features in order to segment. These algorithms can segment high contrast simple medical images without noise [15].
The structure of desired segments should be homogeneous. For more complex image segmentation problems, a combination of mentioned segmentation algorithms can be used. Al-sherif, Guo & Ammar [2] use a two-step thresholding technique to binarize the image and then they separate teeth by finding the minimum cumulative energy path. Nomir & Abdel-Mottaleb [3] start segmentation using iterative thresholding followed by adaptive thresholding to segment the teeth from both the background and the bone areas. To separate individual teeth, they use vertical integral protection. Ølberg & Goodwin [4] proposed a path-based technique to segment a dental X-ray image into individual teeth. Abdel-Mottaleb et al. [5] first separate the teeth from the background of the image using a two-step threshold method. In the second stage, they separate each tooth using integral projection.
This study aims to find an automatic approach for teeth segmentation of dental X-ray images with higher accuracy. We propose a novel method that segments the bitewing images according to the edge lines between crowns of the teeth.

Application of wavelet transform
The proposed method consists of two steps; first, separating upper and lower jaws and second, finding the angle of edge lines between the teeth crowns and using morphological operation to separate each tooth according to the corresponding line. Several phases are required to convert a dental X-ray image to the extracted features of each tooth as follows: • Preprocessing • Edge detection • ROI definition • Teeth separation

Preprocessing
The nature of intra-oral radiographs includes poor image quality and so an efficient technique for image enhancement is required. Enhancement is an essential step in preprocessing of X-ray images due to poor quality, noise, unclear region boundaries [6]. Image enhancement techniques are applied in the new method proposed in this paper to reduce noise and increase contrast between different layers of the image [7]. Several efficient sharpening techniques have been employed to enhance dental X-ray images. The newly introduced method is done among homomorphic High Pass Filter (HPF), morphological top hat and bottom hat filter, Butterworth HPF and Gaussian HPF. The results can be seen in Figure  4. It can be seen that the sharpened image by Butterworth HPF has lighter teeth and darker gums. The advantages of Butterworth HPF have been considered in this method by employing a general transfer function as follows: where D0 is the cut-off frequency, n is the order of the filter and D(u, v) is the distance between a point (u, v) in the frequency domain and the center of frequency plane. It has been found that the sharpened image contains high contrast between gap regions and the teeth that makes it easier to find the edge lines.

Edge detection
Edge detection is one of the effective methods to perform image segmentation. There are various types of edge detector operators such as Canny operator, Sobel operator, Prewitt operator, Robert's operator and LoG operator. Various disadvantages have been found about these  methods as difficulties with detection of minor details, and a need to have high quality images to perform the edge detection operators in a satisfiable level [4]. Thus, in noisy images or low-quality images, these methods are not able to distinguish between edges and noise components. A technique for edge detection that can overcome the mentioned problem is to use discrete wavelet transform (DWT) [8]. Down sampling in each sub-band of DWT leads to information loss in the output image. Therefore, Stationary Wavelet Transform (SWT) has been employed in the proposed method to overcome this loss.
The process of applying SWT to an image can be represented as a set of filters [9]. As shown in Figure 6, the image is divided into four bands including LL (approximation), LH (horizontal details), HL (vertical details), and HH (diagonal details). The letters H and L represent High pass and Low pass filtering respectively in each stage.
Among these three detailed images (horizontal, vertical and diagonal) we only need two bands of vertical and diagonal details in order to separate teeth in each jaw. A simple solution for this challenge is to combine vertical and diagonal details.

ROI definition
The first step in region of interest (ROI) definition phase is jaw separation by finding the gap between jaws. Vertical intensity projection has been used for jaw separation. For the given image with intensity function I(x, y), the vertical intensity projection is defined as follows: The second step in ROI definition is cropping the region that contains crowns. Once cropped, details in the region containing gum tissue and roots cannot be seen anymore.

Morphological processing
After separating the image (containing edge lines) into two upper and lower jaws, it is needed to break branches of the existing edge lines. For this purpose, the morphological operations are used to skeletonize the edge lines and break all the branches, because only those parts of edge lines are of interest where crowns are connected. After breaking the branches, small objects and noise in the binary image can be removed and the orientation of the separating edge lines in both upper and lower jaws can be found. By knowing the orientation of the separating lines, the desired structuring element can be defined and then the morphological image opening can be applied to separate teeth from each other.
Opening an image A by a structuring element B is denoted by A ∘ B and is defined as below:     Morphological opening removes the regions of an object that cannot contain the structuring element. It breaks thin connections, smooths object contours and removes thin protrusions [10]. This leads to separated teeth in both upper and lower jaws. Finally, morphological image thickening is applied to retrieve size decrement due to image opening.

Experimental results
First of all, the dental X-ray radiographs are required to get enhanced due to low quality and contrast. Different techniques have been used for this purpose by different authors; for instance, the morphological top-hat and bottom-hat filtering is used to increase contrast in medical images [11]; [7]; [6]; [12]; [13]; [14]; [15]; [16]; [4]. The histogram equalization as well as a combination of homomorphic and Butterworth HPF for image enhancement are employed for this purpose [17]; [18]; [19]; [20].
To decide which type of filtering results better, a comparison is done among four well-known types of medical images filtering. Table 1 shows the comparison of four bitewing X-ray images based on Peak Signal-to-Noise Ratio (PSNR) value of the input image and the sharpened image.
As can be seen in Figure 10, by applying Butterworth HPF, the teeth parts become lighter and the gum parts become darker that means the increment of contrast in the image.
Expanding the histogram of the image by sharpening strengthens the differences between various tissues in dental X-ray images. This prepares the image for finding directional details in the next phase. The gap between upper and lower jaw creates a valley in the graph of the vertical integral intensity projection. Hence, it can be concluded that this is a suitable approach to separate jaws.
The next step in ROI definition is to remove the undesired details such as roots and top of the teeth. Morphological operators are applied to obtain separating lines. Then, the binary version of approximation image is opened by separating edge lines. In the final stage, the location of individual teeth and extract them has been found by labeling connected components.

Evaluation
The algorithm is implemented in MATLAB R2016b, using an Intel(R) Core(TM) i5 CPU at 1.70GHz and 2.40GHz with 4GB RAM in a Microsoft Windows 8.1 Pro environment.      85 bitewing X-ray images have been used for teeth segmentation experiments with the total 681 separable teeth. Teeth are divided into two groups as the teeth in the upper jaw and the teeth in the lower jaw. The evaluation of segmentation is based on the isolation accuracy.
where Nc is the number of teeth that are correctly isolated and Nt is the total separable teeth.
In the proposed method, 325 teeth in the upper jaw and 292 teeth in the lower jaw are separated correctly out of the total 351 and 330 teeth in the upper and lower jaws, respectively.
Among plenty of different approaches, Table 2 shows the isolation accuracy of four efficient methods for upper/lower jaw and overall teeth separately. It has been shown that the proposed method has the highest performance in correctly separating the teeth at both upper and lower jaws. Consequently, it attains the best isolation accuracy among the other state of the art methods.
The proposed method has also been compared with Ølberg & Goodwin [4], with the best performance in comparison with the other state of the art method, using the same database containing 681 separable teeth and the result of this comparison is shown in Table 3.
Ølberg & Goodwin in [4] use morphological top-hat and bottom-hat filtering to enhance the input image and then they separate teeth by using path-based method. It can be seen that the proposed method achieves better result and can detect and separate the teeth in upper and lower jaws with higher accuracy.

Conclusions
Poor quality of the X-ray images prevents the teeth separation and causes under-or over-segmentation. To solve this problem, a novel method for separating the bitewing X-ray image into individual teeth has been introduced in this paper. At the first phase of the proposed method, the resolution of the image is enhanced and afterwards a wavelet-based edge detection followed by some morphological operations segments and separates each tooth.
The experimental result of 90.6% in terms of isolation accuracy on a database consisting of 681 teeth in 85 bitewing X-ray images has been employed in this paper to show the superiority of the proposed method in comparison to the state-of-the-art teeth segmentation methods. The method can be used as a part of an ADIS for matching purpose.