Int J CARS (2014) 9:177–187 DOI 10.1007/s11548-013-0927-2
REVIEW ARTICLE
Vertebra identification using template matching modelmp and K -means clustering Mohamed Amine Larhmam · Mohammed Benjelloun · Saïd Mahmoudi
Received: 10 January 2013 / Accepted: 4 July 2013 / Published online: 24 July 2013 © CARS 2013
Abstract Purpose Accurate vertebra detection and segmentation are essential steps for automating the diagnosis of spinal disorders. This study is dedicated to vertebra alignment measurement, the first step in a computer-aided diagnosis tool for cervical spine trauma. Automated vertebral segment alignment determination is a challenging task due to low contrast imaging and noise. A software tool for segmenting vertebrae and detecting subluxations has clinical significance. A robust method was developed and tested for cervical vertebra identification and segmentation that extracts parameters used for vertebra alignment measurement. Methods Our contribution involves a novel combination of a template matching method and an unsupervised clustering algorithm. In this method, we build a geometric vertebra mean model. To achieve vertebra detection, manual selection of the region of interest is performed initially on the input image. Subsequent preprocessing is done to enhance image contrast and detect edges. Candidate vertebra localization is then carried out by using a modified generalized Hough transform (GHT). Next, an adapted cost function is used to compute local voted centers and filter boundary data. Thereafter, a K -means clustering algorithm is applied to obtain clusters distribution corresponding to the targeted vertebrae. These clusters are combined with the vote parameters to detect vertebra centers. Rigid segmentation is then carried out by using GHT parameters. Finally, cervical spine curves are extracted to measure vertebra alignment. Results The proposed approach was successfully applied to a set of 66 high-resolution X-ray images. Robust detection was achieved in 97.5 % of the 330 tested cervical vertebrae. M. A. Larhmam (B) · M. Benjelloun · S. Mahmoudi Computer Science Department, Faculty of Engineering, University of Mons, Place du Parc, 20-7000 Mons, Belgium e-mail:
[email protected]
Conclusions An automated vertebral identification method was developed and demonstrated to be robust to noise and occlusion. This work presents a first step toward an automated computer-aided diagnosis system for cervical spine trauma detection. Keywords Medical image analysis · Vertebra segmentation · Generalized Hough transform · K -means clustering.
Introduction Medical image segmentation presents a necessary tool for clinical purposes, especially for diagnosing many orthopedic conditions, such as osteoporosis, spinal fractures, and cervical trauma. Indeed, back pain has been considered as one of the most common medical conditions over the last century and, in many cases, it is caused by vertebra abnormalities. In order to obtain an efficient spine analysis, accurate vertebra detection and segmentation are of a great importance as they provide important information for disease recognition and surgical planning. However, vertebra localization is a difficult task to achieve manually due to their complex shape, their various appearances between patients, and density variability in image modalities (MRI, CT, X-ray, etc.) of vertebrae. Moreover, the segmentation of vertebrae remains a challenging task in conventional radiography, where projectional superimposition of other skeletal structures may partly prevent identification of vertebra bodies. In the context of cervical trauma, which is a serious complication of car accident, the examination generally used in the urgencies department is cervical column radiography [1]. The evaluation of this X-ray examination is critical for the management of the patient. Due to work overload in the urgencies department, many of these cervical subluxations
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Fig. 1 a Normal vertebra alignment, b vertebra subluxation [1]
are not detected [2]. Thus, an automated computer-aided diagnosis tool for detecting possible subluxations (Fig. 1) yields a major help to the clinician. In this paper, we demonstrate an improvement of our previous work on vertebra detection [3]. Therefore, we present a novel method for vertebra identification in cervical spine X-ray images, which combines a template matching approach and unsupervised clustering. This work is based first on a modified GHT technique in order to determine candidate vertebra centers. Next, an adapted cost function is used to filter data point before applying a K -means-based clustering algorithm. Rigid segmentation is then carried out using GHT parameters. Finally, cervical spine curves are extracted to measure vertebra alignment. This paper is organized as follows: section “Related work” describes related work, while section “The generalized Hough transform (GHT)” presents the background of the GHT; section “Framework overview” clarifies our framework overview; experimental results are presented in section “Experiments and results”; general discussion is presented in section “Discussion”; and finally, section “Conclusion” concludes and describes future works.
Related work Several segmentation techniques have been investigated in the literature on vertebra shape extraction, such as generalized Hough transform (GHT) [4], active shape model (ASM) [5], and level set [6]. Segmentation methods in this context can be classified into different approaches: (1) Edge-based methods that recognize the area of transition and localize the boundary between the regions, (2) Region-based methods that use techniques for identification and localization of homogeneous regions, and (3) Shape-based approaches tend to look for regions that match a reference shape. Klinder et al. [7] developed an automated model-based vertebra detection, identification and segmentation framework applied to CT images. First, they extract the spine curve,
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followed by the application of a curved planar reformation (CPR). Detection is subsequently performed using the GHT models of all vertebrae. Finally, identification and segmentation of individual vertebrae are performed using appearance models and adapted triangulated shapes. Identification accuracy was reported at around 70 %. Yao et al. [8] proposed an automated spinal column extraction and partitioning by using a watershed algorithm for CT images. Many automated approaches for detecting the spine in MR images are highlighted in the literature. Schmidt et al. [9] proposed a probabilistic graphical solution to the localization of vertebral column. They used a combination of classification trees and a graphical model. The approach proposed in this work considers the position of intervertebral disks. A robust identification was announced by the authors even for missing imaging features. The algorithm fails in case of fractures, which are not covered by training data. Similar to this method, Corso et al. [10] developed a probabilistic model on both pixel and object features for lumbar disk localization and labeling which deal with lumbar spine MR images. Peng et al. [11] provided an automated vertebra detection and segmentation from a set of sagittal image slices. They used disk template for vertebra region detection, and they performed vertebra boundary extraction using the Canny edge detector. Shape-based models, such as active shape models (ASM) and active appearance models (AAM), are exploited in [12, 13] and [14] for vertebra segmentation and classification on X-ray and CT images. Some previous works have used digital videofluoroscopic images, which present more noise than MRI images. Zeng et al. [15] proposed an automatic segmentation of lumbar vertebrae from videofluoroscopic images based on optimized Hough transform and shape descriptors. Wong et al. [16] used edge enhancement, Markov Random Fields (MRFs), and support vector machines (SVMs) for lumbar vertebra segmentation. Dealing with X-ray images of vertebrae, Benjelloun et al. [17] proposed a segmentation approach based on polar signature representation associated with polygonal regions to detect boundaries of vertebra bodies. This method was applied for vertebra mobility analysis. Recently, they successfully applied the active shape model recognition approach to vertebra segmentation in [18]. Dong et al. [19] presented a graphical- model-based solution for vertebra identification from X-ray images. They claim an automatic calculation of the number of visible vertebrae in the image. Casciaro et al. [20] used local phase symmetry measure in order to localize vertebrae and determine vertebral morphometry. They announced a detection rate of 83 %. Authors in [21,22] proposed an accelerated method for vertebra detection and segmentation on X-ray images using ASM. These methods proposed to exploit the new parallel (GPU) and heterogeneous platforms.
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In our recent work, Raby et al. [1], we presented a semiautomatic approach used to detect cervical vertebrae in X-ray images. The objective was to localize the cervical spine centers. We conducted a GHT algorithm in order to find potential vertebrae centers. Then, we proceeded by an adaptive filter exploiting linear regression fitting to achieve vertebrae centers detection. Despite the good global accuracy of detection of 89 %, the C7 vertebra is detected with a rate of 60 % which is lower than the mean accuracy.
The generalized Hough transform (GHT) Hough transform is a pattern recognition technique widely used in computer vision and image processing. It was initially developed to detect analytic curves (lines, circles, parabolas, etc.) and was generalized by Ballard [4] to detect arbitrary shapes. Therefore, the GHT becomes a powerful pattern recognition method which is robust to scale change, rotation and translation as well as recognition under occlusion. The GHT employs a voting process to locate possible candidates that match the reference image, also called the template model. The detection process of the GHT is composed of two steps: R-table construction The R-table is a discrete lookup table created to describe the reference image. It contains information about position and orientation of the template shape. The construction of this table was completed during a training phase, as follows: Given an arbitrary shape of a target object, the first step was to determine a reference point c = (cx , c y ) in the object. The shape was defined according to the distance and angle from the boundary to the reference point. For each point of the edges, we computed the orientation ϕ and the relative position r = (r x , r y ) from the reference point. Next, we stored the distance r and the direction from the edge point to the reference point β in the R-table as a function of the orientation ϕ. Many occurrences of the same orientation occurred as we moved around the boundary. Therefore, the R-table is able to summarize a parametric representation of the template model. Accumulator creation The accumulator is a four-dimensional voting scheme, which was constructed in the following manner: for each edge point p in the image, we computed the gradient direction ϕ p . We then voted for all possible positions p − ri of the reference point in the accumulator array, where ri were the positions (ri , βi ) indexed under ϕ = ϕ p in the R-Table. The shape was indicated by finding local maxima in the voting scheme.
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Framework overview The proposed approach presents a semi-automatic framework for vertebra segmentation. Our method was based on a combination of a template matching method and a K -means clustering algorithm applied to X-ray images of cervical vertebrae. As an output, an identification of vertebra centers and edges segmentation is provided and spine cervical curves are extracted. Our approach is based on the following steps (Fig. 2): Building vertebra model: Using manual annotation of landmark points on vertebrae X-ray images, we built a geometric vertebra body mean shape; Parametric representation of the model: A lookup table was created to make a parametric template of vertebra body based on the GHT; Candidate vertebra localization: We constructed an accumulator array to cluster all voted locations of possible vertebra candidates based on the GHT algorithm; Cost function filter: We applied a vote density filter in order to find local maxima in the accumulator; K-means clustering: In this step, we clustered data points corresponding to each vertebra and we computed spatial centers. Vertebra labeling: Vertebra body labeling was achieved combining a weighted formula including clusters data and vote information from the accumulator array with a distance and position process; Vertebra shape segmentation: Shape reconstruction was performed using parametric representation of the model; Vertebra alignment measurement: In this step, we extracted three cervical curves using a polynomial regression fitting. Vertebra model definition An accurate vertebra detection based on the GHT method relies on efficient representation of the target object. Model definition step aims to build a geometric representation of vertebra body shape, which can be used as a reference image of the GHT algorithm. Thus, we constructed in this step one mean model of cervical vertebrae body in order to reduce computation cost during the template matching process. To compute the mean vertebra model, we performed manual annotations of landmark points across vertebra edges. We used a set of 25 random vertebrae from cervical X-ray images. The landmark points were used to compute one mean shape model z¯ using the following Eq. (1): z¯ =
n 1 z i , z i = [(xi1 , yi1 ) ; . . . ; (xim , yim )]T n
(1)
i=0
where n is the number of training vertebrae (n = 25), m is the number of landmark points on each vertebra z i and (xi1 , yi1 ) are the coordinates of the first landmark point.
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Fig. 2 Overview of the different steps of the proposed framework
Finally, we carried out a gradient computation and edge detection in order to extract the mean model edge and capture information related to shape direction.
Table 1 The general R-table form Orientation ϕ
2Δϕ
Positions (r, β) ri , β i /ϕi = 0 (ri , β i )/ϕi = Δϕ ri , β i /ϕi = 2Δϕ
…
…
0 Δϕ
Parametric representation of the model In this offline phase of the GHT, we made the R-table, which is a parametric representation of the template shape of vertebra, using information about position and direction of edge points computed in the last step. The R-table was constructed in the following manner: It is assumed that n denotes the number of model edge points pi (xi , yi )(i = 1 . . . n) and ϕi is the corresponding gradient. The reference point c = (cx , c y ) was calculated using the following Eq. (2):
c =
1 pi n
(2)
The R-table was therefore constructed by analyzing all the boundary points of the model shape. For each point pi , we computed the distance ri and βi , the angle between the horizontal direction and the reference point c, which are computed as shown in Eqs. 3 and 4. (3) ri = (xc − xi )2 + (yc − yi )2 yi − yc (4) βi = artan xi − xc Then, (ri , βi ) are stored in the R-table as a function of ϕ. The final form of the R-table is shown in Table 1.
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Candidate vertebra localization In order to determine possible vertebra candidate in the input images, we proposed to perform a semi-automatic approach using a manual selection of the region of interest (ROI). Two points were placed to cover an inclined area of the five cervical vertebrae (Fig. 3). We achieved a preliminary preprocessing step based on histogram equalization to enhance contrast in X-ray images. Next, we used the Canny detector [23] for edge detection since it is highly recommended for X-ray images [24]. The gradient magnitude was computed using the Sobel filter. We then created the accumulator array that summarized all voted locations. The steps of candidate identification are outlined as follows: – Contrast-Limited Adaptive Histogram Equalization (CLAHE) [25]: In order to improve image contrast, we applied CLAHE to the input X-rays images. In general terms, this filter first computes different local histograms corresponding to each part of the image and uses them to
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Cost function Filter Fig. 3 The ROI selection with candidate vertebra localization
change the contrast of distinct regions of the image. This method is well known by limiting noise amplification. – Gradient computation and edge detection: In this step, edge detection with the Canny edge detector was applied to the improved image, and the Sobel operator was performed in −x and −y directions in order to compute the gradient of each edge point of the images. – Accumulator creation: Vertebra candidate identification was carried out using a four-dimensional voting schema, representing the Hough domain. In practice, each edge point voted for different possible locations according to its gradient direction and the corresponding information in the R-table. These votes were stored in an accumulator. We added two parameters s to make a range of scale and α to overcome different possible rotations of vertebrae. This modification of the GHT enabled us to enhance the detection process. Therefore, a voted c(x, y) point can be expressed by its two coordinates as shown in Eq. (5): ⎤ ⎡ j
cos β + α ϕ x x ⎦ (5) = i + s ∗rϕj ⎣ j yi y sin βϕ + α where s and g are the scale and the angle of rotation of the j j vertebra, (rϕ , βϕ ) the parameters obtained in Eqs. (3) and (4) correspond to the ϕ value in the R-table. Figure 3 presents the obtained GHT voting procedure result, and Listing 1 summarizes the detection algorithm.
In order to comprehensively consider the result given by the voting procedure, we propose a new adapted cost function, which computes one mean voted location for small areas. We divided the image into small squares of which the sizes depend on the image resolution. To each of these areas, we attributed a value vr determined by a cost function depending only on the number of votes in each region. Then, we applied an automatic threshold based on the value of vr , the regions under the threshold value are filtered. The used formula is detailed in Eq. (6): nr 1 vi vr = nr
(6)
i
where nr is the number of voted points in the region r , and vi = A [x, y] is the vote value attributed to a point c(x, y) of the region r . False positives are quickly replaced by local maxima. The result of this step is shown in Fig. 4. K -means clustering K -means (KM) clustering is an unsupervised machine learning algorithm introduced by MacQueen [26]. The main idea of this method is to partition observed data points into k cohesive clusters. Each point is assigned to the mean of its cluster using the Euclidian distance. K -means is appropriate for vertebra segmentation since the number of clusters (K ) is already known, which presents the number of the five targeted cervical vertebrae. The steps of the K -means algorithm are summarized as follows:
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Fig. 4 Image grid filter result
Fig. 5 K -means generated clusters with the centroids printed in black
1. Initialization • Data are the filtered accumulator points (xi ). • K centroids cn (n = 1 . . . 5) are chosen randomly to define the initial clusters. 2. Repeat • Each candidate vertebra point is assigned to the closest cluster center (7). z n = arg min d (xi , cn ) i
(7)
i
3. Until convergence Convergence of the algorithm is defined as the minimization of the within-cluster sum of squares (WCSS) Eq. (9):
n
k (n) d xi − vn n
(9)
i
The K -means algorithm clusters the spatial accumulator data by iteratively computing the geometric centroid of each class. The final result is sensitive to initialization. Since KM is a fast computed algorithm, we ran the process several times and chose the best result which minimized the WCSS. Finally, we obtained a distribution of five clusters corresponding to the cervical vertebra positions (Fig. 5).
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Vertebra identification is carried out using the input clustering step. First, we applied an angular filter in order to eliminate points with bad orientation α (with α higher or smaller than the average). Next, we computed a more precise center cn for each cluster using a vote weighted formula, Eq. (10): 1 ∗ (n) cn = vi xi (10) Nn i
• The cluster centers are recomputed as the centroid of their data points (8): 1 (n) xi (8) cn = Nn
arg min
Vertebra identification
Finally, a labelization process based on distance and positions of vertebra centers was applied in order to identify vertebra type. Identification of cervical vertebrae C3–C7 was achieved as shown in Fig. 6. Vertebra shape segmentation In the GHT manner, rigid vertebra segmentation was performed based on the parametric representation of the template shape. Indeed, we reconstructed the vertebra shape on the basis of the corresponding parameters of each detected center in the lookup table. Therefore, the R-table facilitates in recalculating the edge points positions (x, y) of vertebrae using the center point (cx , c y ) and the gradient information for a given scale s and orientation α, Eq. (11). x = cx − r ∗ s ∗ cos (β + α) (11) , ∀ (r, β) Rtable y = c y − r ∗ s ∗ sin(β + α)
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Vertebra alignment measurement In order to analyze vertebra alignment, three parallel lines should be extracted [1]: • Anterior vertebral line • Posterior vertebral line • Posterior Spinous line The extraction of these curves is accomplished by using a polynomial regression fitting applied on the detected key points. The equation of each generated curve is given in Eq. (12). ⎧ ⎨ y = β0 + β1 x + β2 x 2 (12) β1 : Linear effect parameter ⎩ β2 : Quadratic effect parameter
Experiments and results Fig. 6 Vertebra identification result
Image data Experimentations were conducted using two sets of radiographs. First, 46 digitized X-ray films were obtained from the National Health and Nutrition Examination Surveys database, NHANES II, and second, 20 high-resolution X-ray images were obtained from Jolimont Hospital in HaineSaint-Paul, Belgium. All the images focus on the cervical spine area. The second images database was inspected by a radiologist who annotated six landmarks (Fig. 9a) on each cervical vertebra to
Fig. 7 Vertebra reconstruction using the detected center
Fig. 8 Vertebra key point printed on the used template. Anterior face in red, posterior face in green, and Spinous in blue
Figure 7 shows the reconstructed vertebra using the detected center. After that, we localize three key points describing anterior face corner, posterior face corner, and posterior Spinous of vertebrae as shown in Fig. 8.
Fig. 9 Vertebra orientation computed from landmarks. a The radiologist annotation in blue and the two generated mid-points in green. b The vertebra midplane in green and the orientation angle in red
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Table 2 Recognition accuracy with a sample of 45 images
Table 3 Comparison of vertebra detection rate with other methods
Vertebra type
Method
Type
Approach
Detection rate (%)
Dong et al. [16]
X-ray
Semi-automatic
92.4
Klinder et al. [7]
CT
Fully automatic
92.0
Casciaro et al. [20]
X-ray
Fully automatic
83.0
Our previous work [1]
X-ray
Semi-automatic
89.0
Proposed method
X-ray
Semi-automatic
97.5
Detection rate NHANES II (%)
Jolimont DB (%)
Mean (%)
C3
100
100
100
C4
100
100
100
C5
100
100
100
C6
97.8
100
98.9
C7
97.8
80
88.9
Total
99.1
96
97.5
generate ground truth data for the segmentation validation step (a total of 100 vertebrae). We notice that the mean model was built using a set of 25 cervical vertebrae (from NHANES II) which were not included in the test data. Vertebra detection The proposed method is a semi-automatic approach initialized by a manual selection of the ROI. Two points were placed to cover an inclined area of the five cervical vertebrae. The detection of cervical vertebrae operated successfully on the input radiographs. Intermediate results are shown in Figs. 3, 4, 5, and 6. The range of scale change used in the vote process is shown in Eq. (13). s ∈ {0.8 + p×0.1, p ∈ [0, . . . , 4]}
(13)
Fig. 10 Robustness of the detection and the clustering steps to three different initializations. a, b Random initializations, c Illustration of the positions of initializations Segmentation evalution 20.00% 15.00% 10.00% 5.00% 0.00%
Missed segmentation
C3
C4
C5
8.80%
8.80%
4.40%
C6
C7
8.80% 17.70%
Fig. 11 Segmentation evaluation—missed vertebrae
The size of the small squares used in the cost function step is fixed to 10 × 10 pixels. The validation of the results was led by using visual examination and clinical expert landmarking, for NHANES II and Jolimont Hospital databases, respectively. Therefore, candidate vertebra centers had to be located within the vertebra body or the polygon formed by the six landmarks. The method correctly identified the cervical vertebrae with a robust success rate of 97.5 %. Table 2 compares the detection rate of the different cervical vertebrae from C3 to C7. The final identification of C3–C7 vertebra result is shown in Fig. 6 Table 3 presents a comparison of vertebra detection rate of the proposed method with other methods. We focused on methods where the rate of detection was announced. To evaluate the impact of the inter-operator variability on the robustness of the clustering and detection steps, three different initializations have been made on a noisy X-ray image from NHANES II. Figure 10 illustrates the result of clustering and detection of vertebrae in three cases.
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Vertebra segmentation Since the GHT assists in computing vertebra inclination, we propose to use the angle of orientation in order to evaluate our segmentation step. We compared our results with the manual landmarking, annotated by expert radiologist, by using the four vertebra landmarks that determine the corners. We used these corners to generate vertebra body midplane. Thus, the orientation of vertebra is determined as the angle of the inclination of the midplane. Figure 9 shows the computing process of vertebra orientation from landmark points (Fig. 11). Table 4 shows the result of cervical orientation evaluation. Our approach is characterized by a RMS (root means square) error of 6.70◦ . Figure 12 shows the final result for this database. In order to evaluate the segmentation of the images obtained from the NHANES II, which were not annotated, we propose a visual evaluation of the missed segmentation
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Table 4 Cervical spine angular error analysis Vertebra type
RMS angle error
C3
8.22
C4
5.55
C5
5.65
C6
7.48
C7
6.58
(◦ )
Mean 6.70
result. Figure 11 shows the final evaluation result of the 46 X-ray images. Finally, Fig. 13a, b show the final segmentation results, while Fig. 13c shows an example of missed segmentation of the C6 vertebra. Vertebra alignment The proposed identification and segmentation method enabled us to extract the three parallel lines used for vertebra alignment measurement. This is a first step toward a computer-aided diagnosis (CAD) tool used to exclude cervical spine trauma. The curves were extracted by fitting three key points per vertebra. These key points are computed from the segmentation step, and they represent the anterior face, posterior face, and vertebra Spinous. Figure 13 shows the curves extraction step result.
enables to extract the parameters used for vertebra alignment measurement. The evaluation of the algorithm has been conducted using 66 radiographs of normal patients. The detection succeeded for all normal sagittal plane images, including cases with extreme spine curvature. We notice that the detection process for Jolimont DB showed a good accuracy of 96 %. However, we used a trained model from NHANES II. C7 vertebra was also detected with a rate of 88.9 % (Table 2) which is lower than the mean accuracy. The C7 vertebra also called vertebra prominens is located in the base of the neck. Therefore, the projectional superimposition of other body skeletal structures in radiographs can partly prevent the identification. Also, the edge detection step did not efficiently localize this vertebra which explains the low detection of this vertebra. The segmentation of the annotated database showed an RMS error of 6.70◦ . Compared to the inter-operator variability shown in [27], which is equal to 3.14◦ for X-ray image in case of vertebral motion analysis, we notice that our angular error is greater. This is due to the use of a general model shape, which was not trained on the same dataset. In addition, the rigid segmentation did not give a great accuracy. For the second database, the evaluation of missed segmentation showed a high miss rate of 17.7 % of C7 vertebra. The extraction of the three curves used for vertebra alignment measurement is performed based on polynomial regression. The behavior of the algorithm on normal exams is shown in Fig. 14c.
Discussion
Conclusion
In this work, we developed and tested a robust method for cervical vertebra identification and segmentation. Thismethod
We presented a novel method that combines a template matching model and K -means clustering to identify cer-
Fig. 12 The final segmentation result for two cases from the Jolimont DB
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Fig. 13 The final segmentation result for three images from NHANES II database. a, b Identification of C3 to C7 vertebrae for 2 cases, c example of missed segmentation of C4 vertebra
Fig. 14 Vertebra alignment measurement steps. a Vertebra segmentation, b key points localization, c curves extraction
vical vertebrae in X-ray images. We conducted an offline process to build a vertebra model and create a parametric representation of it. Thereafter, a candidate vertebra localization based on the GHT was performed. Then, we applied an adapted cost function and K -means clustering in order to achieve vertebra identification. Finally, we extracted three curves used to analyze vertebra align-
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ment. This method proved to be robust to noise and occlusion and can also be applied to different image databases. As regards future work, we plan to develop a fully automatic computer-aided diagnosis system for cervical trauma detection. We also intend to improve our learning model and segmentation process.
Int J CARS (2014) 9:177–187 Acknowledgments The authors acknowledge the Jolimont Hospital for providing the annotated radiographs used in this study. The authors would like to thank S. Drisis, physician in the imaging department at Jules Bordet Hospital, for his helpful advice on cervical spine trauma. The authors thank also the anonymous reviewers for their insightful comments that improved the quality of this paper Conflict of interest M. A. Larhmam, M. Benjelloun, and S. Mahmoudi declare that they have no conflict of interest.
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