A 2D Matching Method for Reconstruction of 3D Proximal Femur

using X-ray Images

Sonia Akkoul

, Adel Hafiane

, Rémy Leconge

, Eric Lespessailles

and Rachid Jennane

Laboratoire PRISME, Université d'Orléans, 12 rue de Blois, 45067 Orléans cedex 2, France

Laboratoire PRISME, ENSI de Bourges, 88 avenue Lahitolle, 18020 Bourges cedex, France

Institut 3MTO, Hôpital d'Orléans, 1 rue Porte Madeleine, 45032 Orléans cedex 1, France

Keywords: 3D Reconstruction, Low Dose X-ray Radiograph, Proximal Femur, Matching.

Abstract: The femur shape reconstruction from a limited number of 2D X-ray images is a challenging task but it is

desired as it lowers both the acquisition costs and the radiation dose. The aim of this paper is to use a small

number of 2D X-ray images to reconstruct a 3D proximal femur surface without any prior acknowledge of

the shape model. The proposed method combines a 2D binary contour points coordinates and their normals

to find the best matching between 2D point pairs. The obtained results are promising. The estimated error

shows that it is possible to rebuild the proximal femur shape from a limited number of radiographs.

1 INTRODUCTION

Three dimensional patient bone models play an

important role in pre-operative surgery planning and

improved guidance during surgery, modeling and

simulation. The pre-operative reconstruction of 3D

anatomical models can be achieved using the direct

3D imaging modalities such as Computed

Tomography (CT) (Gamage et al., 2011). However,

the use of such imaging is restricted to a minor

specific procedures; due to constraints placed by

cost, availability and radiation risk. Thus, the

diagnostics and planning of many interventions still

rely on two dimensional (2D) radiographic images,

where the surgeon has to mentally visualize the 3D

anatomy of interest. A direct 3D imaging must be

developed, as an alternative to current pure 2D

radiographs, in order to assist the clinicians on their

medical tasks (Gamage et al., 2011).

Literature on pre-operative reconstruction of

proximal femur based on information collected

through 2D imaging modalities can be divided into

two subgroups. The first group methodology is

based on 2D images and can be considered as

Silhouette Intersection for 3D model reconstruction

(Caponetti and Fanelli, 1993). The second group

contains methods based on a prior knowledge of the

anatomical structure as well as 2D images (Gamage

et al., 2011).

A majority of studies require prior knowledge of the

3D anatomy model to guide the reconstruction

process and to compensate the lack of information in

2D imaging modalities (Gamage et al., 2011). This

information can be provided by the integration of

one generic geometrical surface of the considered

bone structure (Laporte et al., 2003; Le Bras et al.,

2004), or by Statistical Shape Models (SSM) (Baka

et al., 2011; Zheng et al., 2009; Whitmarsh et al.,

2011).

Our aim is to study the accuracy of the 3D femur

reconstruction without using any 3D prior

information. Only, the mathematical projection

model and a limited number of 2D X-ray images are

employed for this purpose. Two successive

projections are used to compute the coordinates of a

3D contour.

The proposed scheme works as follows: after

extracting the contour of the proximal femur on the

2D X-ray images, comes the matching process. This

stage is a very important step for the 3D

reconstruction, because it impacts the accuracy of

the computed 3D coordinates. There exists several

works for contours matching (Park and Han, 1998;

Frenkel and Basri, 2003; Cui et al., 2009). For this

work we examine contour points matching using

merely the position and normal as features to

establish correspondences. The matching between

the points of two contours is performed with the

353

Akkoul S., Haﬁane A., Leconge R., Lespessailles E. and Jennane R..

A 2D Matching Method for Reconstruction of 3D Proximal Femur using X-ray Images.

DOI: 10.5220/0004293403530357

In Proceedings of the International Conference on Computer Vision Theory and Applications (VISAPP-2013), pages 353-357

ISBN: 978-989-8565-47-1

 2013 SCITEPRESS (Science and Technology Publications, Lda.)

Euclidian 2D spatial distance then, the normals of

each point pairwise are used to filter the outliers.

This methods is simple and relatively efficient

allowing a good trade-off between accuracy and

computation complexity, which is important for our

application. The estimated point pairs are then used

to set up a set of 3D points. Since we are using

binary images, the correspondence of the contour 1

towards the contour 2 is not symmetric and may give

different results if contour 2 is used towards contour

1, thus the 3D reconstruction result may be different.

Here, we will discuss this issue and study its

influence on the 3D reconstructed models.

The obtained results, through the proposed

methodology, are benchmarked against real 3D CT

scan data to assess the accuracy of reconstruction.

The cadaver proximal femur was used as the

anatomy of interest throughout this study.

The paper is organized as follow: Section 2

presents the data. Follows the method and

experiments section that presents, the contours

extraction, contours matching, and estimating the 3D

coordinates.

2 MATERIALS

For this work we have used, a cadaver proximal

femur scanned with a resolution of 200µm by the

VISCOM X8060 NDT scanner. The bone was

placed on a rotating platform, between the x-ray

source and the sensor, and then 450 radiographs,

with a size of 1024×1024 pixels, were acquired on

360 degrees. Examples of the ex vivo proximal

femur radiographs are shown in Figure 1. Thanks to

these radiographs, and with the help of modern

computed tomography, the 3D mode allowed the

reconstruction of complete volumetric model of

911×806×711 voxels. Figure 2 shows the 3D model

of the reconstructed proximal femur. This model

serves as a ground truth to compare the

performances of the proposed algorithm.

In this study, eighteen 3D contours were

computed to reconstruct the 3D femur shape. Each

3D contour was estimated using 2 successive X-ray

images spaced by an angle of 8°. The step 8° was

chosen to realize the trade-off between the precision

and the matching process. In fact, if the two

projections are too close, this will generate more

errors for 3D coordinates estimation. And if the

projections are too far, a good matching between the

two contours will not be possible.

The next pair of X-ray radiographs was spaced

from the precedent one by an angle of 20°. This

way, we ensure including in the reconstruction a

minimum of information reflecting the different

forms of the proximal femur. The step 20

° between

two pairs of projections was chosen based on the

number of radiographs we wanted to use and to

improve the quality of the reconstruction.

0° 44°

92° 136°

220° 264°

292° 336°

Figure 1: X-ray images of the ex vivo proximal femur at

different angles.

3 METHOD AND EXPERIMENTS

Given few 2D X-ray images, our task is to establish

correspondence between the two input images. For a

given point of the edge identified in the first X-ray

image, the goal is to associate it to a point of the

edge identified in the second X-ray image. This

matching between points, on two different contours,

is realized using two criteria:

- The spatial distance: both associated points have to

be as close as possible to each other.

- Normals to the contours: the normals for both

associated points have to be in the same direction.

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Figure 2: 3D ground truth of proximal femur used for the

test and reconstructed from 450 radiographs using X-ray

tomography reconstruction.

3.1 Bone Edge Extraction

The edge extraction is the first step of the 3D

reconstruction procedure. Despite that the good

contrast between the background and the femur in

the X-ray images, the accurate edge extraction is not

always a simple task. The nature of the x-ray

imaging makes the border fuzzy difficult to define

the real position of the edges. Whereas, the edge

localization determines the precision of the 3D

coordinates estimation. For that, various authors

have proposed semi-automatic or interactive

solutions to solve this problem (Laporte et al., 2003;

Le Bras et al., 2004).

To accurately detect the contour of a given

proximal femur, a morphology method is applied on

binarized X-ray images. The binarization step aims

at separating bone tissue (lighter) from pore and

background (darker) pixels. A standard binarization

method is applied (Chappard et al., 2008). This

method consists in determining a threshold based on

the local minimum between the two modes of the

histogram of each image.

Figure 3: Extracted edge corresponding to the image of

Figure 1.(0°) before applying the closing operation and a

zoom on the squared area in blue.

A morphological closing operation is then applied to

eliminate small contours considered as noise of the

segmentation step. The structuring element is a disk-

shaped of radius of 3 pixels. Figure 4 depicts an

example of the edge extraction.

Figure 4: Extracted edge corresponding to the image of

Figure 1.(0°) after applying the closing operation.

3.2 2D Matching Process

Let us denote the detected edge pixels in image1

(red edge, see Figure 5) as I1= {I

, i=0, 1... M-1}

and the detected edge pixels in image2 (green edge,

see Figure 5) as I2= {I

, j=0, 1, ..., N-1}, where M

and N are the number of the edge points detected in

image1 and in image2, respectively. Each point has

two features: the 2D coordinates (x, y) and the

normal vector at that position. The matching process

consists first in finding for each point in I1= {I

i=0, 1... M-1}, the closest one in I2, by computing

the Euclidean distance d as (1).



 

),(

jiji

yyxxyxd 

(1)

The matching result is shown in Figure 5.

Figure 5: Matched points using the spatial distance and the

points coordinates.

As can be seen on Figure 5, many pairs of associated

points on the two contours have been found. To

improve the detection process, we propose to use an

additional criteria. For each retained pair of points,

the normals are estimated. If the normals are in the

same direction, these two points are retained,

otherwise they are rejected.

Figure 6 shows that using the distance and the

normals enable reducing the number of outliers

candidates pairs for the 3D reconstruction.

A2DMatchingMethodforReconstructionof3DProximalFemurusingX-rayImages

355

Figure 6: Matched points using the spatial distances and

the normals.

As mentioned in the introduction, since we are

dealing with binary images, the detected

corresponding points using the matching may differ

depending on the way of using the contours towards

each other. The matching is not symmetric.

Therefore, there are three cases of matching

directions:

(i) contour I1 toward contour I2,

(ii) contour I2 toward contour I1,

(iii) the intersection between the two directions.

Complete matching of all points Zoom

Figure 7: Matching after calculation of the distance and

the normals for the three cases. (i) edge I1 toward edge I2,

(ii) edge I2 toward edge I1, (iii) Intersection between (i)

and (ii).

The aim of the intersection technique is to keep the

pairs of points that are common in both matching

directions.

Figure 7 summarizes the obtained results for the

three cases.

Meshed shapes Errors comparing to the

ground truth

Figure 8: Meshed shapes and corresponding errors to the

ground truth. (i) edge I1 toward edge I2, (ii) edge I2

toward edge I1, (iii) Intersection between (i) and (ii).

Figure 8 presents the meshed shapes of the proximal

femur obtained from the reconstructed contours for

the three cases presented in Figure 7.

The estimated errors obtained in comparison to

the ground truth are presented too. These errors were

evaluated using the Metro tool for measuring error

on simplified surfaces (Cignoni et al., 1998). The red

and blue colors in the 3D reconstructed shapes

represent respectively the high and the low error

values. Errors are minimal in the case (c) where the

matching is performed in the two directions. This

demonstrates that the filtering of the outliers helps to

reduce the errors and increase the reliability of the

3D reconstruction technique.

(i)

(ii)

(iii)

(%)

(i)

(ii)

(iii)

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4 CONCLUSIONS

This work shows that it is possible to recover the 3D

shape of the proximal femur from relatively small

number of X-ray projections. This was possible

thanks to x-ray stereo model, contour points

matching and combination of a round-trip scan to

exploit the different possibilities of estimating the

3D contours. As a prospect to this work, we would

like to reduce furthermore the number of the X-ray

images and improve the accuracy by exploring new

matching techniques as the Chamfer matching. The

incorporation of this whole system will help

providing enhanced 3D images for orthopedic

procedures and intra-operative assistance.

ACKNOWLEDGEMENTS

This work is part of the FRACTOS project

supported by the Region Centre (France). We

gratefully acknowledge the Region Centre for its

support.

REFERENCES

Baka, N., Kaptein, B. L., de Bruijne, M., van Walsum, T.,

Giphart, J. E., Niessen, W. J., Lelieveldt, B. P. F.,

2011. 2D-3D shape reconstruction of the distal femur

from stereo X-ray imaging using statistical shape

models. In Medical Image Analysis. 15(6):840-50.

Caponetti, L., Fanelli, A. M., 1993. Computed-aided

simulation for bone surgery. In IEEE Comput Graph

Appl. 13:86-92.

CGAL, Computational Geometry Algorithms Library.

http://www.cgal.org.

Chappard, C., Marchadier, A., Benhamou, C. L., 2008.

Side-to-side and within-side variability of 3d bone

microarchitecture by conventional micro-computed

tomography of paired iliac crest biopsies. Bone, Vol.

43, No. 1, Pages 203-208.

Cignoni, P., Rocchini, C., Scopigno, R., June 1998. Metro:

measuring error on simplified surfaces. In Computer

Graphics Forum, Blackwell Publishers, vol. 17(2), pp

167-174. Available at http://vcg.sf.net.

Cui, M., Femiani, J., Hu, J., Wonka, P., Razdan, A.,

January 2009. Curve matching for open 2D curves. In

Journal Pattern Recognition Letters. Volume 30 Issue

1, Pages 1-10.

Frenkel, M., Basri, R., 2003. Curve matching using the

fast marching method. Energy Minimization Methods

in Computer Vision and Pattern Recognition. Lecture

Notes in Computer Science Volume 2683, 2003, pp

35-51.

Gamage, P., Xie, S. Q., Delmas, P., Xu, W. L., 2011.

Diagnostic radiograph based 3D bone reconstruction

framework: Application to the femur. In Comput Med

Imaging Graph. 35(6):427-37.

Laporte, S., Skalli, W., De Guise, J.A., Lavaste, F.,

Mitton, D., 2003. A biplanar reconstruction method

based on 2D and 3D contours: application to the distal

femur. In Comput Methods Biomech Engin 6(1): 1-6.

Le Bras, A., Laporte, S., Bousson, V., Mitton, D., De

Guise, J.A., Laredo, J.D., Skalli, W., 2004. 3D

reconstruction of the proximal femur with low-dose

digital stereoradiography. In Comput Aided Surg 9(3):

51-7.

Park, J., S., Han J., H., 16 March 1998. Contour matching:

a curvature-based approach. In Image and Vision

Computing, Volume 16, Issue 3, Pages 181-189.

Whitmarsh, T., Humbert, L., De Craene, M., Del Rio

Barquero, L., M., Frangi, A., F., December 2011.

Reconstructing the 3D Shape and Bone Mineral

Density Distribution of the Proximal Femur From

Dual-Energy X-Ray Absorptiometry. In IEEE

Transactions on Medical Imaging, Vol. 30, No. 12.

Zheng, G., Gollmer, S., Schumann, S., Dong, X., Feilkas,

T., 2009. A 2D/3D correspondence building method

for reconstruction of a patient-specific 3D bone

surface model using point distribution models and

calibrated X-ray images. In Medical Image Analysis.

Volume 13, Issue 6, Pages 883–899.

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