Towards Segmentation of Pedicles on - Synchromedia

Towards Segmentation of Pedicles on

Posteroanterior X-ray Views of Scoliotic Patients

Vincent Dore1, Luc Duong2,3, Farida Cheriet2,3, and Mohamed Cheriet1

1 Department of GPA, Ecole de Technologie Superieure,Montreal Qc H3C 1K3, Canada

2 Research Center, Sainte-Justine Hospital, Montreal Qc H3T 1C5, Canada3 Department of Computer Engineering, Ecole Polytechnique de Montreal, Montreal

Qc H3C 3A7, Canada

Abstract. The objective of this work is to provide a feasible study todevelop an automatic segmentation of pedicles of vertebrae on X-ray im-ages of scoliotic patients, with the ultimate goal of the extraction of highlevel primitives leading to an accurate 3D spine reconstruction based onstereo-radiographic views.Our approach relies on coarse and fine parameter free segmentation.First, active contour is performed on a probability score table built fromthe input pedicle sub-space yielding to a coarse shape. The prior knowl-edge induced from the latter shape is introduced within a level set modelto refine the segmentation, resulting in a fine shape.For validation purposes, the result obtained by the estimation of the ro-tation of scoliotic deformations using the resulting fine shape is comparedwith a gold standard obtained by manual identification by an expert. Theresults are promising in finding the orientation of scoliotic deformations,and hence can be used for subsequent tools for clinicians.

Key words: X-ray images, idiopathic scoliosis, active contour, vertebralorientation.

1 Introduction

Adolescent idiopathic scoliosis is a disease characterized by frontal deviation ofthe spine from the normal alignment plane. This deviation is principally lat-eral but it also includes a three dimensional component. Present technologiesonly allow X-ray view in two dimensions ( posteroanterior or PA and lateral orLAT) which only reveals partially the deformation. To provide clinicians withadditional information, 3D spine are nowadays reconstructed by extracting man-ually landmark points from both views. Reconstruction by manual identificationis a tedious task, and might introduce a variability depending on the operatorperforming it. The ultimate goal of our work is to automate the reconstructionprocess and to enrich it by integrating basic primitives on different objects suchas vertebrae, clavicle, pelvis, ribs. Already several works treat of spine X-ray im-ages [1], those researches deal with vertebrae shape matching [2] or classification

2 Vincent Dore, Luc Duong, Farida Cheriet, and Mohamed Cheriet

[3, 4] of vertebrae or of spinal curve [5].In such perspective, we present in this paper a feasible study to automate thesegmentation of pedicles at every vertebral level. Pedicles are two short roundedstructures that extend from the lateral posterior margin of the vertebral body.They can be identified on both views and are thus used as landmark for 3D re-construction. In addition of giving insights about the vertebral rotation, segmen-tation of pedicle would lead to an automatic 3D-reconstruction. Furthermore,by extracting objects rather than points, high level primitives can be used toimprove the quality of the 3D model. This work could also be used to detectpedicle intra-operatively since pedicle screws are used for surgical correction ofscoliosis.LAT views are highly noisy due to several object superpositions. Presently, onlycervical and lumbar vertebrae are segmented on this view. The segmentation ofpedicles on LAT should thus be driven by segmentation information from thePA view; projective geometry computed from a known object can be used forthis purpose. The accuracy of the segmentation on LAT view is thus dependanton the segmentation quality on the PA. Hence, in this paper, we focus on thesegmentation on the PA view.Because of pedicles are small and low contrasted objects on highly noisy images,they are hard to identify and even harder for non expert clinicians. Moreover,since pedicles shape are deformed in AIS, segmentation becomes really tedious.It is thus difficult to perform segmentation directly on those images. The firststep of this kind of segmentation is to characterize the pixels belonging to thesame pedicle. In fact, pedicles can be identified (after training) because some oftheir pixels are locally and slightly darker than the background. They also forma ring around lighter pixels belonging to the inner of the pedicle. To enhance thischaracteristic, we built a score table which assigns to each pixel a probabilityto be in the darker object present in a certain neighborhood. In this table, thering is hardly identified and often mistaken for vertebrae edges. To simplify andwithout loss of generality, only the inner part is detected. Thus, on the table, weinitialized around the inner part an active contour. This kind of model enables usto extract closed curves from noisy images [6, 7]. Recently, models incorporatingshape knowledge on snake [8] or in active contour [9, 11] have appeared in theliterature. We applied [11] to our segmentation problem with bad results . Thishappened because of the large variability of the shapes, their small and variablesize as well as the lack of singularity points. We then decided to use the simpleconstant piecewise model developed by Chan and Vese [10] on the probabilityscore table and embedded it in a coarse-fine segmentation. By using such tableinstead of the original image, we group together pixels, which have the samelocal characteristics; moreover, this table enables us to have the same initializa-tion for all the pedicles. Initially as the ring in these score tables may containholes, the regularity parameter is set high. A priori information about the sizeof the pedicle enables the model to automatically and dynamically update thecharacteristic and regularity parameters. As a result of such a process, coarseshape of the inner part of the pedicle is obtained. In order to reach the summits

Lecture Notes in Computer Science: Pedicle segmentation 3

of the real shape, we perform a second algorithm with ”a priori” knowledge onthe coarse shape that searches for more details around it.To validate the relevancy of the segmentation, we show a comparison between theorientation of each vertebra (frontal rotation) estimated by our pedicle extrac-tion and the one obtained manually. In addition, the assessment of this rotation,as described in [12], might be used as a good indicator of the severity of thecurve. Even though those rotations are not accurate, they are still used by clin-icians, due to the lack of 3D-reconstruction. Hence, our automatic estimation isa useful clinical result.In the first part of the paper, we present the Chan-Vese model and its limi-tations when applied to our problem. Then, we introduced the new model tosegment pedicles. Discussions on the estimation results of the vertebral orienta-tions are provided in the following section. Finally in the conclusion we presentthe perspective opened by this feasible study.

2 The Active Contour Model of Chan-Vese

The constant piecewise model developed by Chan Vese [10] is a segmentationalgorithm based on the minimization of the following simplified Mumford-Shahenergy functional:

infu,C

FMS(u,C) =

∫

Ω

(u− u0)2dxdy + ν|C|

(1)

Where u is considered to be a two phases image; a single object of characteristicc1 is separated from the background of characteristic c2 by a contour C. Thefirst term in (1) corresponds to the energy attachment of u to the input imageu0 while the second one is the length of the contour C. The two phases imagethat minimize (1), is close to u0 and has a regular contour. ν is the regularitycoefficient, which enables to privilege the contour regularity on the data attach-ment or vice versa. In the level set method, C is represented by the zero levelset of an implicit function:

φ(s) =

0 if s ∈ C

−ε if s ∈ Cinε if s ∈ Cout

(2)

Where ε is a positive constant, Cin the area inside the curve C and Cout thearea outside it. The evolving image u can thus be decomposed as:

u = c1H(φ) + c2(1−H(φ)) (3)

With H is the heaviside function:

H(φ) =

1 if φ > 0−1 otherwise

(4)


By using this decomposition, the functional (1) can be rewritten as:

infc1,c2,φ

FMS(c1, c2, φ) =∫

Ω(c1 − u0)

2H(φ)dxdy+∫

Ω(c2 − u0)

2(1−H(φ))dxdy + ν∫

Ω|∇H(φ)|dxdy

(5)The Euler Lagrange equations can be easily computed by minimizing (5) underc1, c2 and φ:

c1 =

∫∫

u0H(φ)∫∫

H(φ)and c2 =

∫∫

u0(1−H(φ))∫∫

(1−H(φ))(6)

c1 and c2 correspond to the mean value of u0 inside and outside the curveC, respectively. To solve the practical problem of the level set function, (5) isembedded in a gradient descent by introducing an artificial time t. The authorsthus obtain the following equation:

∂φ

∂t= ν δε(φ)∇

(

∇φ

|∇φ|

)

+ δε(φ)(

−(c1 − u0)2 + (c2 − u0)

2)

(7)

A finite differences implicit scheme is used to discretize equation (7). At timet = 0, the level set function φt is initialized by the user. The algorithm iterates,until convergence of the system, the three following steps:

– compute c1(φt) and c2(φt)– compute φt+1 by discretizing (7)– increment t = t+ 1

One of the major drawbacks of the constant piecewise model is the determinationof the characteristics which are constant over the object and the background.Indeed, in real life those characteristics are not constant but homogeneous (reg-ular). In some extreme cases, characteristics c1 and c2 can be very close whencomputed over the objects, but different when evaluated locally. For instance, inthis study, the mean intensities of the inner and outer parts of the pedicle areoften separated by less than three gray levels. It is clear that this difference ofcontrast is not obvious. Nevertheless, we are able to perceive the pedicle as adark ring on a lighter background. The difference in the evaluation of the localcharacteristics that is generally larger than that of the global ones, enables usto have a better visual perception of the pedicles.

3 Overview of the system

To allow the Chan Vese model in segmenting pedicles, we adopt the followingfour steps ( Figure 2):

– Initialisation: The algorithm is initialized by clicking in the inner pedicle.– Probability score table: In a neigbourhood of the initialization point, a

probability score table is constructed by assigning to each pixel a probabilityof locally belonging to the darker object.


(a) (b)

Fig. 1. a) X-ray of a L1 vertebra, b) in green what we call the outer part and in yellowthe inner part of the pedicle. The X-ray has been enhanced for visual facilities.

– Coarse segmentation: The active contour is processed on the table with ahigh regularity parameter ν. Hence, pixels having a high (or low) probabilityare grouped together. If the output segmentation is not suitable, the activecontour is reinitialized with a different regularity parameter depending onthe resulting segmentation.

– Fine segmentation: This segmentation enables high cuvature on the activecontour and thus to reach the entire inner part. The model is increased witha shape consistency term, forcing the fine shape to be close to the coarseone.

The three latter steps are detailed in the next following subsections.

Fig. 2. Bloc diagram of the system.

3.1 Probability Score Table

For each pixel x ∈ Ω, let Va(x) ∈ Ω be its neighborhood of size a. All the pixelsx in the inner part of the pedicle should contain in their neighborhood Va(x),at least one pixel belonging to the outer part. a should thus be quite large. This


parameter is set to seven for the first ten vertebrae and to nine for the otherones. Then, the histogram of Va(x) ∈ Ω is separated into two classes: A1(x) thebackground and A2(x), the outer. To do so, Otsu’s algorithm [13] is used to findk∗ that maximizes the intra class variance:

k∗ = argmaxk

p1(k)p2(k)[µ1(k)− µ2(k)]2 (8)

Where k is a variable threshold, pi(k) the weighting of the class Ai and µi(k)its mean. According to the Bayesian theorem, the probability p(x ∈ A1(x, a)) iscomputed as :

p(x ∈ A1(x, a)) =p1P (x|A1(x, a))

p1P (x|A1(x, a)) + p2P (x|A2(x, a))

By assuming that the distribution of the intensity inside each class is Gaussian:

P (x|Ai(x, a)) =1

2πσ2i

e−

(µi−u(x))2

σ2i

We thus obtain :

p(x ∈ A1(x, a)) = p1σ22

1

p1σ22 + p2σ

21e

−(µ2−u(x))2

σ22+

(µ1−u(x))2

σ21

(9)

Probabilities p(x ∈ A1(x, a)) are saved in the probability score table Ta. Thetable subscript is the size of the neighborhood used.By using this probability table, the image is locally split into two-class object;pixels in outer part of the pedicle are highly enhanced by their high probabilities,whereas inner and background pixels get low probabilities. The constant piece-wise model is then performed on the score table. This combination of local andglobal approaches leads to a more robust segmentation algorithm. The latter ispresented with more details in the following subsections.

3.2 Coarse segmentation of pedicles

At t = 0, the initial level set function is a distance function whose 0-level line is a5 radius circle centered on an inner pixel pt, chosen manually. Then, the objectiveis to group together all the pixels having a strong probability p2 of belongingto the inner part. Consequently, the characteristics c1 and c2 of the model arerepresented by the probabilities p2 and p1 = 1 − p2. At the initialisation, thecharacteristics are set as c10 = 0 and c20 = 1.The only a priori knowledge that has been fixed to the level set function is:

– A minimum area size Amin of the set H(φ) and a maximal one Amax.– A parameter ν corresponding to the weight of the regularity part in the

energy (1).


Those three parameters have been estimated experimentally for each kind ofvertebra on 5 x-rays. ν is set high in order to get a regular shape and avoidthe active contour to come through the eventual holes of the outer part. Theequation that handles the evolution of the level set function is :

φt+1 = φt+ ν δε(φt)∇

(

∇φt+1

|∇φt|

)

+ δε(φt)(

−(c2t − Ta)2 + (c1t − Ta)

2)

(10)

Since the level set method allows change of topology, at each iteration the con-nected component C of H(φt) > 0 that contains the initial point is extracted. φtis then reinitialized with the signed distance function (2) from the border ∂C. LetAt be the area |C| at time t. If At is higher than Amax, some pixels included inthe set H(φt) > 0 should not belong to the inner part. In other words, the outerbeing the border of the inner part of the pedicle, those pixels should belong tothe outer part. They have been included in the set H(φt) > 0 because of theirlow probability p1 (noisy score table). The characteristic c1t is thus reduced tomake the condition of being in the outer part less selective. So, some pixels inH(φt) > 0 and at the border of this condition at time t, will be excluded of thepositive part of φ at time t+ 1 reducing the size area.This process is iterated until the system reaches convergence. Due to character-

(a) after 5 iterations of theprocess

(b) at the end of the process

Fig. 3. A(φt = 0) is higher than Amax, the characteristic c2t decreases to 0.84.

istics updating, there may be situation where c1t ' c2t or the number of iterationsis above a threshold τ . It is obvious that in the first case, the model will notconverge to an acceptable segmentation. In the second one, experiments showthat the 0 level line could not be limited to the inner part of the pedicle. In bothsituations the process is stopped since it has encountered a problem of area size:

– If At < Amin then the problem of convergence is not due to the qualityof the score table as we defined it previously but due to the pedicle shape.When the pedicle is too thin (this is the case for high axial rotation of thevertebra) and the regularity constraint term ν is too strong, the active shapeencounters difficulties in growing, especially where its curvature is strong.


Thus the algorithm is reinitialized with the same initial conditions exceptfor the regularity term that is reduced.

– If At > Amax, mostly the pedicle has a hole in its outer part ( due to thesuperposition of the pedicle with another object). The table is badly defined.If the parameter ν is too small then the 0 level line fills the hole and enablesthe shape to evolve outside the inner part. The algorithm is thus reinitializedwith a higher parameter ν, this prevents the evolution of the shape on strongcurvature locations, and hence to proceed outside the inner part.

The way characteristics c1, c2 and regularity term ν are updated enables themodel to segment coarse shapes of pedicles from all vertebral spine levels (tho-racic and lumbar) without any manual parameter adjustments. This is an im-portant result for the model automation.

3.3 A fine segmentation

The Chan Vese algorithm with a high coefficient of regularity ν gives a regularshape approximating the pedicle. In this section, we present a way to get a finesegmentation for better pedicle shapes estimation. At first, we build a signeddistance function φG from the coarse shape. The latter has been segmented inthe previous subsection. Then, we use a second algorithm to better estimatethe pedicle segmentation on a score table Tb. The neigbourhood b is set toseven for the first ten vertebrae. For the others, smaller neighborhood sizesare to be used because a 9-neighborhood produces too coarse tables. Moreover,important axial rotation on those vertebrae implies thin pedicles. The shapeof those latter pedicles presents two region with strong curvation, that we callsummits. Thus, in order to reach upper and lower summits of theses thin pedicles,the algorithm must be processed on a T5 probability table. The approach thatwe recommend is to process the second algorithm iteratively on different tables(from T8 to T5). Once the process has converged on a table, the resulting levelset function φ is used as the new coarse level set φG of the next level (figure4). This second algorithm is based on the model presented by Rousson andParagios [11]. According to this model, a new energy is added to the MumfordShah functional. This energy, called shape energy, forces the level set functionφ to evolve according to a certain shape database[11]. However, in our modelφ evolves according to φG, which is the distance function to the coarse shapeboundary extracted in the previous section. The energy to be minimized is :

E(φ) =

∫

Ω(c1 − Tb)

2H(φ)dxdy +∫

Ω(c2 − Tb)

2(1−H(φ))dxdy

+ ν∫

Ω|∇H(φ)|dxdy + µ

∫

Ω(φ− φG)

2dΩ

(11)

The evolution scheme of φ associated to this energy is found in figure 4. Inaddition, the energy parameter µ is not taken constant over all the definitionspace of φ as in [11]. It is set φ1

t and φG dependant, and it follows a sigmoidalshape:

µt(φ1t , φG) =

1

1 + e−λ(‖φ1t−φG‖−P )

(12)


Fig. 4. Shape superposing for neighborhoods sizing from 9 to 5.

φ0 = φG

φ1t+1 = φt + ν δε(φt)∇

(

∇φt+1

|∇φt|

)

+ δε(φt)(

(c1t − Tb)2− (c2t − Tb)

2)

φ2t+1 = φt − 2× dt(φt − φG)

update of µt thanks to φ1t+1 and φG

φt+1 = (1− µt) φ1t+1 + µt φ

2t+1

update of c2t+1 et c1t+1 thanks to Amax and to Amin

Fig. 5. algorithm for fine segmentation

When φ1t is close to φG, it can evolve to find details. Whereas when the distance

between φ and φG is high on some pixels, its evolution will locally slow down untilstopping. The coefficient parameters λ and P are set in our experimentations insuch a way that the inflexion point is at 4 and the evolution is almost stoppedfor ‖φ−φG‖ < 5. From a shape point of view, this is to allow the active contourto evolve in a narrow band of ten pixels width with a speed that is proportionalto its local distance from φG.

3.4 Experimental results

To quantify the results of our method, we have tested our algorithm on five x-ray images of patients with Adolescent Idiopathic Scoliosis. We focused on thetwelve thoracic level and the first four lumbar vertebrae. On those x-ray images,nine pedicles could not be segmented due to the presence of calibration balls andsixteen were not visible due to strong axial rotations. We do not consider those


pedicles in our study. Hence, on the remaining hundred thirty five we succeededin correctly segmenting one hundred one (i.e. 74% of accuracy rate). Consideringthe quality of the images, the difficulty of the task and the diversity of the spinaland vertebral deformations, this segmentation rate is rather promising. For theother non detected pedicles, the algorithm failed due to two main reasons. Firstsome pedicles do not respect the thresholds Amin and Amax especially fromT2 to T6 vertebrae where variability is high. But those pedicles, to which wemay design more specific methods, could be segmented separately as outliers.Secondly, some others may be intersected by the upper endplate. In this case,the algorithm may encounter difficulties in segmenting the complete pedicles.Hence, our segmentation accuracy rate might be promising for the estimation ofthe vertebral rotation.

3.5 Frontal rotation estimation

The orientation of the vertebral body (frontal rotation) could be derived fromthe orientation of the endplates on healthy subjects. However, for patients withscoliosis, vertebrae are often deformed and the orientation of the endplates doesnot always coincide with the orientation of the vertebra. Using the pedicles maypresent a more reliable evaluation of this rotation and it has been widely acceptedby the spine community [14]. The frontal rotation of a vertebra, as described in[12], is estimated on the PA view by computing the angle between the abscissaaxis of this view and the line going through the centers of the pedicles (figure6(a)). Since the fine shape is nosy comparing to the coarse shape, the latterseems to be more robust to estimate those centers. However, extracting a suffi-cient number of points from a fine contour implies also a good center estimation.Furthermore, since fine shape reaches the entire pedicle, the estimated centermight be better.The rotations must only be estimated by the algorithm without those centers be-ing dependent on the initialization point. To this end, the experiment compriseda set of ten pedicles from different levels. The algorithm has been initializedwith various points for each pedicle. The resulting mean variance on the centerlocation is about 0.0616 pixel (corresponding to 0.02mm). As it will be explainedbelow, this result is considerably insensitive to the starting point. This makesthe model robust and user independent. First let consider the simple case of twodifferent initialisations on the same pedicle. If the three mentioned parametersdo not change, the algorithm will be driven by the probability score table. Thisproduces the same segmentation and thus the same center. Secondly, in a moregeneral case, as the inside of the pedicle is quite small, the initialization pointsmust be close. After a few iterations both level set functions will be very close.Consequently, areas of positive parts of both level set functions will change sim-ilarly as the parameters. This results at the end in similar segmentations; bothcenter will match.The frontal rotation estimation is currently done manually by extracting the up-per and lower summits of the pedicle; the centers being just the middle points.On figure 6(b) we show the frontal rotation obtained manually (in red) and our


semi-automatic evaluation of the angle (in blue). When the segmentation couldnot be found, the center was extracted manually from the x-ray. Our results maylook noisy. Nevertheless, we conserve the intra vertebra smoothness. Moreover,we notice that our estimated rotations are as accurate as those extracted man-ually on the same PA view (such as vertebrae 4 and 13). By comparing all therotations, we obtain a mean difference of 2.3 degrees between the manual andthe semi-automatic estimation. This error is considered more than acceptablesince the manual error is about five degrees. This result is really promising forthe evaluation of the scoliotic deformation.

(a)

−20 −10 0 10 200

2

4

6

8

10

12

14

16Rotation X (O2)

−20 −10 0 10 200

2

4

6

8

10

12

14

16Rotation X (Auto)

(b)

Fig. 6. (a) Rx is an estimation of the frontal rotation. Vectors X and Y define thePA view. (b) Representation of the planar rotation in degree (abscissa) of differentvertebrae (ordinate) of a patient. In red, manually extracted rotations and in bluerotations extracted by our semi automated algorithm.

4 Conclusion

In this paper we have introduced a technique to segment pedicles on the PAview. We first perform active contours on score tables that assign to each pixela probability of being in the outer part. Setting a high regularity parameter, weget a coarse shape of the pedicle. Hence, we used a second algorithm that looksfor details around it to reach the summit points.This paper is, to our knowledge, the first study to segment the intrinsic shapeof pedicles from image of pathologic spine. Moreover, segmentation on digitalradiography is often limited to the lumbar segment of the spine and do not treatsuch fine details as the vertebra pedicles. Our study demonstrated good-to-fairresults on such task, hence paved the road for other studies to automate thesegmentation process by injecting some prior knowledge into the process. Otherresearches on the vertebrae [1] described techniques to either provide informa-tion of the global spine shape or to provide local information on the vertebralbodies location. For instance, the vertebral shape location could be injected inour model to improve the segmentation of this kind of pedicles. Moreover, state


of the art researches on vertebra and spine segmentation allow us to think thatat term the initialization can be automated.The conclusions of this feasible study offer good perspectives in automaticallysegmenting pedicles on a pair of stereo-radiographic views to automate 3D recon-struction of the vertebral spine. Furthermore, by segmenting pedicles, high levelprimitives can be extracted to generate a more accurate and more representative3D model than those reconstructed manually.

References

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