Dental X-Ray Image Segmentation and Object Detection Based on ...

Dental X-Ray Image Segmentation and Object Detection Based on Phase Congruency F. Sattar and F.O. Karray Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON N2L 3G1, Canada {fsattar,karray}@uwaterloo.ca

Abstract. Dental radiographs are essential in oral diagnostic procedures. This paper presents a new method for segmentation and object detection of dental radiograph images based on phase congruency. This phase congruency based approach provides local image structure and is invariant to image scaling, rotation, translation, variable lightning conditions, as well as process noise. Comparative experimental results and quantitative measures show the effectiveness of the proposed approach. Keywords: Dental Radiographs, Segmentation, Object Detection, Phase Congruency.

1

Introduction

A dental radiograph is a photographic image produced on film by the passage of X-rays through teeth and supporting structures [1]. Dental radiographs are essential in oral diagnostic procedures. They may suffer from poor quality, low contrast and uneven exposure that complicate the task of segmentations. The goal of radiograph segmentation is to localize the region of each tooth in a dental X-ray image [2]. This radiographic segmentation thus for example helps the dentist to detect/identify dental caries and periodontal disease which are the most common dental diseases in the world. Dental caries is an infectious microbiological disease that results in localized dissolution and destruction of the calcified tissues of the teeth. If untreated the caries results in the progressive distraction of the tooth and infection of the dental pulp takes place. Identification of dental caries is important for the diagnosis and treatment planning of the dental disease, which has been affecting a very large population throughout the world. It is also helpful for conducting detailed study and investigations about the nature of the dental disease [3]. The production of diagnostic quality radiographs depends on many factors including proper film positioning, appropriate X-ray exposure and correct film processing techniques. An error in any of these factors will result in less than optimal or non-diagnostic radiographic image [4]. Thus the purpose is to provide a diagnostic quality image through segmentation which could enable the dentist to identify many conditions that may otherwise remain undetected. In [5], A. Campilho and M. Kamel (Eds.): ICIAR 2012, Part II, LNCS 7325, pp. 172–179, 2012. c Springer-Verlag Berlin Heidelberg 2012

Dental X-Ray Image Segmentation and Object Detection

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segmentation and contour extraction are applied to extract features for automatic identification of dental radiographs. In [2] an automated morphological filtering wavelet based approach for tooth segmentation in dental X-ray images is proposed. In the boundary-based image-segmentation approach, several postprocedures, such as edge tracking, gap filling, smoothing, or thinning, should be performed on these detected edge points [6]. Obviously, all these post-procedures are very time-consuming and not easy. Hence, we would like to propose a simple effective approach avoiding such complex post-procedures required by the boundary-based approach. This paper presents a new method to detect objects of dental radiographs (such as crown, cavity, root, etc) automatically based on phase congruency and edge detection. Extracting objects based on phase congruency has the following advantages: firstly, phase congruency detects step change, line and angle features in all directions; secondly, it detects image contours rather than edges; thirdly, it is not sensitive to variations of brightness and contrast. We have shown here that the phase congruency has a significant role in extracting the boundaries of dental objects.

2

Proposed Approach

The proposed method constitutes on the generation of phase congruency based on the local energy model of salient feature detection postulates that features are perceived at points where the components of the Fourier series expansion of the image is maximally in phase, i.e. where the phase congruency is high. Phase congruency provides a contrast invariant way of identifying features within the images. It has been shown in [7] that phase information rather than magnitude information provides the most significant information within the image. It is calculated in two dimensions through 2D log-Gabor filters with different scales and orientations. Let |Ws,m (x, y)| and φs,m (x, y), are magnitude and phase of the outputs of the log-Gabor wavelets at a given scale, s, and orientation, m, respectively. Then the 2D phase congruency at point (x, y) is calculated for each scale s and orientation m as: P Cs,m (x, y) =

|Ws,m (x, y)|ΔΦs,m (x, y) |Ws,m (x, y)| +

(1)

In Eq. (1), is a very small positive real number used to prevent the division of zero and the phase deviation ΔΦs,m (x, y) = cos(φs,m (x, y) − φm (x, y)) − |sin(φs,m (x, y) − φm (x, y))| and φm (x, y) is mean phase angle at orientation m. Also, |Ws,m (x, y)| =

e2s,m (x, y) + o2s,m (x, y)

φs,m (x, y) = atan2(os,m (x, y)/es,m (x, y)) even odd even and [es,m (x, y), os,m (x, y)] = [I(x, y) ∗ Ms,m , I(x, y) ∗ Ms,m (x, y)] where Ms,m odd and Ms,m denote the even-symmetric and odd-symmetric filters at scale s and orientation m and ∗ denotes the convolution.

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2.1

F. Sattar and F.O. Karray

Log-Gabor Wavelets

In order to have local phase information, log-Gabor wavelets are considered. In [8], Field proposes an improvement of Gabor wavelets by introducing logGabor wavelets. Log-Gabor filters can be constructed with arbitrary bandwidth and the bandwidth can be optimized to produce a filter with minimal spatial extent [9]. Log-Gabor filters have Gaussian transfer functions when viewed on the logarithmic frequency scale and has the following transfer function if viewed in the linear frequency scale. G(f ) = e

(log(f /f ))2 2 0 ))

− 2(log(σ/f0

(2)

where, f0 is the filter’s center frequency. σ/f0 controls the shape ratio of the filter. The 2D log-Gabor filters can be constructed in the frequency domain around some central frequency (fi , θi ), where θi is the orientation angle of the filter, and fi is the central radial frequency [10,11]: G(f, θ) = e

(log(f /fi ))2 2 fi /fi ))

− 2(log(σ

e

−

(θ−θi )2 2σ2 θi

(3)

where, σfi defines the radial bandwidth B in octaves with B = 2 2/log2|log(σfi /fi )|

(4)

and σθi defines the angular bandwidth 2log2

(5)

(log(f /fi ))2 2 fi /fi ))

(6)

ΔΩ = 2σθi Here, G(f ) = e

− 2(log(σ

is the radial component, which controls the frequency band that the filter responds to G(θ) = e

−

(θ−θi )2 2σ2 θi

(7)

is the angular component, which controls the orientation. The two components are multiplied together to construct the overall filter. 2.2

Denoising

The phase congruency has an implicit denoising scheme without causing blurring. It is based on estimating the noise response of the sum of the filters σG , it is assumed that the smallest scale filter mainly detects noise. We can obtain a robust estimate of the mean of the magnitude response of the smallest scale


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filter via median response. Thus based on Rayleigh distribution, the median of the magnitude |Wsmin | of the smallest scale filter smin is τ=

median(|Wsmin |) ln(4)

(8)

And the overall noise response is the sum of the individual noise contributions of each filter. Since the noise spectrum is assumed to be uniform then the wavelets will gather energy from the noise as a function of their bandwidth which, in turn, is a function of their center frequency. Then the overall noise response reduces to a geometric sum of the ratio of center frequencies of successive filters (mult) across S number of wavelet scales. S τ 1− 1 mult σG = (9) 1− 1 mult Using (8) and (9), it is possible to calculate the mean μR = σG π2 and also 2 2 calculate the standard deviation of the noise σR = ( 4−π 2 )σG . Then the estimated noise threshold T calculated to be twice the standard deviations beyond the mean of the distribution, is given by T = μR + 2σR

(10)

This noise threshold T will be subtracted from the numerator in Eq. (1). Eq. (10) thus allows us to set threshold automatically from the statistics of the smallest scale filter response.

3

Experimental Results

Fig. 1 shows the segmentation and object detection results for a dental radiograph. To achieve that first we apply phase congruency method on the dental x-ray image displayed in Fig. 1(a). We obtain the boundary contours as shown in Fig. 1(b) in which tooth areas such as crown part are extracted. After this we apply the optimal Canny edge detection algorithm. The resulting binary image of the detected objects is shown in Fig. 1(d). Fig. 1(c) is the smoothed image of Fig. 1(b) by morphological opening and closing operations. The result shows no further improvement in noise reduction which is mainly due to the effects of denoising described in section 2.2. Similarly, the results in Fig. 2 shows the tooth isolation of a normal dental x-ray image. Here the number of wavelet scales and number of filter orientations are set to 4 and 9, respectively and the parameters used for Canny edge detection are the same as shown in Table 1. In order to evaluate the performance, we firstly compared the results of our approach with other magnitude based edge detection algorithms including the Canny edge detector, the Sobel edge detector, and the Laplacian of Gaussian (LoG) edge detector. The parameters for these detectors can be found in Table 1.

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F. Sattar and F.O. Karray

Original Image

(a)

Morphological smoothing

(c)

Phase congruency representation

(b)

Edge tracing

(d)

Fig. 1. Result of segmentation and object detection for a dental x-ray image (example 1)

Original Image

(a)

Morphological smoothing

(c)

Phase congruency representation

(b)

Edge tracing

(d)

Fig. 2. Result of segmentation and object detection for a dental x-ray image (example 2)

Note that all the parameters are particularly chosen respectively from their best results of a series of experiments. Fig. 3 and Fig. 4 show the input dental radiographs and their corresponding detection results. It can be seen that none of the magnitude-based detectors can locate the dental objects properly.


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Table 1. Parameters used for different types of edge detectors Method Canny Sobel LoG

Original Image

(a)

Sobel Edge Image

(c)

Parameters t1 = 0.1, t2 = 0.2, σ = 1 t = 0.03 t = 0.0045, σ = 2

Canny Edge Image

(b)

LoG Edge Image

(d)

Fig. 3. Results for a dental x-ray image based on magnitude based detectors (example 1)

3.1

Quantitative Measure

For quantitative performance evaluation, we measure the average ridgeness content of the output image. In order to measure it, we construct the Hessian matrix, Γ at image pixel (x, y) defined as ∂2L Lxx Lxy (11) , with Lab = Γ = Lyx Lyy ∂a∂b where L is an image obtained by convolving the output image Y with a (3 × 3) derivative masks along x and y directions followed by smoothing using a Gaussian filter with bandwidth σD [12]. Here, the subscripts xx and yy represent the second-order derivatives in the x and y directions. Then the ridge intensity at each point (x, y) is measured as Aγ = (λ2 )2γ ((Lxx − Lyy )2 + 4L2xy )

(12)

where the eigenvalues of the (2 × 2) Hessian matrix shown in Eq. (11) is obtained as

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F. Sattar and F.O. Karray Original Image

(a)

Sobel Edge Image

(c)

Canny Edge Image

(b)

LoG Edge Image

(d)

Fig. 4. Results for a dental x-ray image based on magnitude based detectors (example 2)

λ1,2 =

1 1 2 (Lxx + Lyy ) ± 4Lxy + (Lxx − Lyy )2 2 2

(13)

The σD and γ parameters are set to 10 and 0.5, respectively. As indicated in Table 2, the proposed approach is found to be more effective as it provides the highest average ridgeness intensity of Aγ . Table 2. Average ridgeness content of the output images Method Proposed Canny Sobel LoG

4

Aγ 2.2959 (Fig.1(d)) 2.9950 (Fig.2(d)) 1.1281 Fig.3(b)) 0.7586 Fig.4(b)) 0.5499 Fig.3(c)) 0.4107 Fig.4(c)) 0.3440 Fig.3(d)) 0.3015 Fig.4(d))

Conclusion and Future Work

This paper presents a new method for extracting the object boundaries of dental x-ray images. The dental radiographs are commonly used for dental treatment


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in order to analyze significant or unexpected conditions. The proposed approach is based on calculating the phase congruency by exploiting the orientation and scale over which the local image feature exists. The boundaries of the dental objects extracted by the presented method have a better precision. The comparative experimental results and quantitative measures on dental radiographs demonstrate the effectiveness of the proposed method. The issues like the choice of optimal parameters such as number of scales and number of orientations related to phase congruency as well as more detailed evaluation will be studied in the future. Moreover, for edge detection we would like to work on the similarity graph for further improvement. Acknowledgment. We would like to thank Department of Restorative Dentistry, Faculty of Dentistry, National University of Singapore (NUS) for their help in obtaining the dental radiographs used in our investigations.

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