NORGES TEKNISK-NATURVITENSKAPELIGE UNIVERSITETFAKULTET FOR INFORMASJONSTEKNOLOGI, MATEMATIKK OG

ELEKTROTEKNIKK

MASTEROPPGAVE

Kandidatens navn: Magdalena Jenner Stepaniak

Fag: Datateknikk, bildebehandling

Oppgavens tittel (norsk): Instabilitet i cervical columna

Oppgavens tittel (engelsk): Instability in the cervical columna

Oppgavens tekst:En rekke lidelser i ryggraden gir opphav til unormale bevegelsesmnster mel-lom ryggvirvler nar ryggraden beveges. Dette er et kjent fenomen for eksempeli forbindelse med revmatiske lidelser og ved slitasjeforandringer. I mange til-feller ma de unormale bevegelsene stabiliseres kirurgisk nar sykdommen nar etstadium der de unormale bevegelsene gir store smerter for pasienten eller derdet er fare for nevrologisk skade. Tidspunktet for slik stabilisering har hittil værtvalgt pa bakgrunn av kliniske kriterier uten at det alltid har vært mulig a fa godnok billedmessig kvantisering av graden av utslagene.Ved Intervensjonssenteret ved Rikshospitalet kan slike pasienter undersøkes ien apen MR. Den apne MR-maskinen er den eneste av sitt slag i Nord-Europaog tillater at pasienter undersøkes sittende. Dermed kan ryggen og nakken un-dersøkes med normale belastninger og bevegelsesutslag.I dette prosjektet vil vi pa bakgrunn av bildedata fra Intervensjonssenterets apneMR, samt ordinære CT-data forsøke segmentere ut nakkevirvlene og visualis-ere/kvantisere disses bevegelse. Et viktig fokus i denne oppgaven er a gjen-nomføre en klinisk studie der resultater fra visualiseringer basert pa MR og CT-bilder sammenholdes med kliniske funn.Prosjektet er en del av et allerede etablert samarbeide mellom Intervensjonssen-teret og Reumatologisk avdeling ved Rikshospitalet.

Oppgaven gitt: 19. januar 2004Besvarelsen leveres innen: 14. juni 2004Besvarelsen levert: 14. juni 2004Utført ved: Institutt for datateknikk og informasjonsvitenskapVeileder: Lars Aurdal og Per Kristian Hol

Oslo, 14. juni 2004

Lars AurdalFaglærer

Acknowledgments

I would like to thank Lars Aurdal for tutoring me during this project.

I would also like to thank Per Kristian Hol and Terje Tillung at Rikshospitalet for pro-viding me with medical images and for helping me to understand the medical side ofthe project.

Finally, I would like to thank the Interventional Centre at Rikshospitalet UniversityHospital in Oslo for providing me with a working place and good working environ-ment.

Abstract

Spinal instability is the cause to a variety of health problems, including rheumatic pain.This report deals with the problem of segmenting the cervical vertebrae, primarily theatlas and axis, using images from the open MR-scanner at the Interventional Centreat Rikshospitalet together with CT images, and visualize their movement. The visual-ization is compared with clinical discoveries to investigate if it may help physicians tobetter understand the complex anatomy present in the images.

A short overview of possible segmentation algorithms is given. Very few papers di-rectly address the problem of segmenting the spinal column. This may be due to thedifficulties related to segmenting spinal vertebrae. Magnetic Resonance Imaging (MRor MRI), which is the preferred image acquisition technique because it is believed tocause no side effects for the patient, relies on proton spin and favors soft tissue. Thisleads to poor bone contrast. Which in turn may cause segmentation problems whensegmenting the cervical vertebrae. On the contrary Computed Tomography (CT) pro-vide high bone contrast, but also ill side effects.

A manual segmentation solution to the segmentation problem is proposed. This so-lution is then used to generate a visualization of the cervical vertebrae. One healthyand one cervical vertebrae suffering from spinal instability is visualized to test if thevisualization gives reliable results. Ergo to see if it is possible to compare the behaviorof the vertebrae from the healthy subject with the vertebrae from the patient sufferingfrom spinal instability.

An alternative segmentation solution based on semi-automatic segmentation is dis-cussed briefly.

Contents

1 Introduction 11.1 Medical background . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.1 Spinal anatomy . . . . . . . . . . . . . . . . . . . . . . . . . 11.1.2 Back pain . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.1.3 Image acquisition . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2 Document organization . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Methods 72.1 Segmentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.1.1 Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.1.2 Segmentation approaches . . . . . . . . . . . . . . . . . . . . 10

2.2 Visualization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3 Results and Discussion 133.1 Segmentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.1.1 Choice of segmentation approach . . . . . . . . . . . . . . . 143.2 Visualization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.2.1 Final results . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

4 Conclusion 19

5 Future work 215.1 Segmentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215.2 Visualization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

A Glossary 24

Chapter 1

Introduction

1.1 Medical background

1.1.1 Spinal anatomy

The following section is based on [BRID-01],[SPINEH-04],[BACK-02],[BURC-00],[BJAL-98] and [RODT-03].

As seen in Figure 1.1 the spinal column is made up of individual bones called vertebraewhich are divided into five regions.

Figure 1.1: Illustration of the spinal column. Copyright SpineUniverse.com

The cervical spine has seven vertebral segments, C1-C7. It is further divided into the

2 Introduction

upper cervical region, consisting of C1 and C2, and the lower cervical region, consist-ing of C3-C7. C1 and C2 are also known as the atlas and axis and are unique comparedto C3-C7 which have identical anatomical features and are more uniform in appear-ance.

The thoracic spine has 12 vertebral segments, T1-T12, that increase in size from T1through T12.

The lumbar spine has five vertebral segments, L1-L5, which graduate in size from L1through L5.

The vertebral segments are the weight bearing structures of the spinal column. Eachvertebra consists of a large vertebral body made of dense cortical bone, two bony areascalled pedicles made of thick comical bone and the laminae, an arch of bony structuresextending from the pedicles to form the posterior wall. The laminae is connected bythe ligamentum flavum which also serves to stabilize the spine.

Located between each vertebra, and connecting the vertebra in the front of the spine,are intervertebral discs that act as shock absorbers for the spine. In combination withpaired facet joints,found in the back of the vertebra, the discs create a three joint com-plex at each vertebral segment. It is this complex that allows for motion in flexion,extension, rotation and lateral bending of the spine.

The bones and ligaments of the spinal column protect the spinal cord which can beseen encapsulated by the vertebra in Figure 1.2.

Figure 1.2: Illustration of a vertebra. Copyright SpineUniverse.com

In this report we will primary concentrate on the atlas and the axis of the cervical spine.The atlas does not have a vertebral body and its main structures are the lateral masses.It is a ring of bone attached to the axis, and it protects the skull. The axis is morecomplex with the toot-like odontoid process, also referred to as the dens, as its most

1.1 Medical background 3

distinguishing feature. The dens acts as a post which the atlas rotates around. Unlikeall the other vertebrae the atlas and axis do not have discs between them. Most ofthe rotation in the neck is located here and the two segments also house the importantlower portion of the brainstem, the medulla oblongata, in their center.

Figure 1.3: Illustration of the atlas and axis. Copyright SpineUniverse.com

1.1.2 Back pain

Back pain is a common health problem in the world. As much as 80-90% of the adultpopulation will experience some kind of back pain. It is also one of the most expensivehealth problems for the society [HENR-02].

As mentioned in 1.1.1 Spinal anatomy, the spinal cord is protected by the spinal col-umn. Unfortunately to much movement, due to instability, by the column may resultin pressure on the cord. This will cause a lot of pain and can cause paralysis.

1.1.3 Image acquisition

This report will focus on the use of CT and MR for image acquisition.

CT

Computed tomography obtains a three-dimensional image with the use of two-dimensionalx-ray axial images. A x-ray tube rotates around the patient as the patient is graduallypassed trough a gantry. The data from the sweeps are then processed by a computer,and a single cross-section is produced.[WIKI-04a]

CT provides a high contrast of bone. Unfortunately is also has dangerous side effects,exposing the patient to ionizing radiation.

4 Introduction

MR

Magnetic resonance imaging is an imaging technique based on the principles of nu-clear magnetic resonance. The spins of atomic nuclei of the tissue molecules arealigned in a powerful magnetic field. To cause some of the hydrogen nuclei to change,alignment radio frequency pulses are applied in a plane perpendicular to the magneticfield lines. Thereafter the radio frequency is turned of causing the nuclei to go back totheir original state, while releasing radio frequency energy which is picked up by coilswrapped around the patient. Recording and processing of these signals generates animage of the tissue.[WIKI-04b]

MR has no known hazardous side effects, but in contrast to CT, bone appears as lowintensity shadows having low contrast with surrounding tissue.

Open MR is a unique kind of MR in which the patient can sit upright. This allows thespine to be examined in a more natural position.The MR-images used in this study are acquired with the open MR-scanner at the In-verventional Centre at Riskhospitalet.

Figure 1.4: The open MR-scanner used at the Interventional Centre at Rikshospitalet.

1.2 Document organization

The next chapter gives a very short overview of general image segmentation meth-ods, as well as techniques considering the segmentation of bone, that can be used tosegment cervical vertebrae. It also considers different segmentation approaches andvisualization of segmented images.

1.2 Document organization 5

Chapter 3 presents and discusses the achieved results.

In chapter 4 we draw conclusions. Finally, in chapter 5 a plan for future work issummarized.

6 Introduction

Chapter 2

Methods

2.1 Segmentation

The classification of each image pixel to one of the image parts, in such a way thatpixels sharing a common property are grouped together, is called segmentation of animage. Segmentation is an important part of image analysis, since this is where oneextracts the interesting objects from the image, for further processing. [BOCK-98]

2.1.1 Algorithms

There exists a wide range of different image segmentation algorithms. Most of themare designed to solve a specific problem, although very few are concerned with thesegmentation of the cervical spine. The general ideas of other methods may still be ofinterest when solving this segmentation problem. Since a summary of this large fieldof techniques is not possible within the scope of this report we concentrate on twosegmentation techniques, which can be of interest to the problem of segmenting thecervical spine. Namely general, well renowned, image segmentation techniques andtechniques considering the segmentation of bones, of which techniques consideringsegmentation of the vertebrae are preferred.

The segmentation algorithms considered may be separated into two groups, namelydeformable model based and statistical model based. Since both groups are modelbased they both use a priori information to perform the segmentation. To performa segmentation without prior information about the object is in this case unlikely tosucceed. This is due to noise, gaps, lack of contrast and other irregularities in thestructure boundaries in the images. [MAIN] and [MONT-00]

8 Methods

Deformable model based algorithms

Deformable model based algorithms are one of the most common and popular meth-ods for model based segmentation. The reason for this comes from their ability tosegment, match and track objects by exploiting constraints derived from the imagedata together with the use of apriori knowledge about the object. In deformable modelbased algorithms a template model defined in one image is deformed to fit a secondimage by elastic modeling constraints. The algorithm is always locally defined andcomputed. The deformation process is always done iteratively, small deformations ata time. [MCIN-96], [MCIN-00] and [MAIN]

Deformable model based methods are also known as active contour models or snakes.The term snake was first introduced by [KASS-88], and refers to an energy minimiz-ing spline controlled by external and internal energy forces. The internal forces keepsthe snake well shaped and smooth, thus forming a counterbalance to the external con-straint forces. The snake lock onto nearby edges, localizing them fairly accurately.

Unfortunately the internal forces may shrink the model, while the external forces maycluster the vertices in corners of the model. [LOBR-95] develops an alternative model,which avoids these problems by using alternative functions for the internal energy.The suggested method handles and processes a contour as one topologically consistentunit. At the same time the deformation process is based on local operations on thevertices of the model.

Another drawback of deformable models is poor convergence. The initial model mustbe initiated relatively close to the object in order to properly converge. And the snakealso has difficulties progressing into boundary concavities. Xu and Price propose a so-lution to these problems by introducing the gradient vector flow field, as a new externalforce, in [XU-98] and [XU-00]. The field is calculated as a diffusion of the gradientvectors of a gray-level or binary edge map derived from the image. The gradient vectorflow snake differs from other snake formulations in that the snake is specified directlyfrom a force balance condition. This is due to that the snakes external forces cannot bewritten as the negative gradient of a potential function.

The local deformation of the template can be erratic if the target structure differs suffi-ciently from the template structure. McInerney and Terzopoulos suggest improvementsto the original algorithm to make the snake adopt to different topologies.In [MCIN-95] a 2D model is made by superposing a simplical grid over the image.The snake is reparameterized using the points of interaction between the snake and thegrid.This snake is extended to 3D in [MCIN-99] where the deformable surfaces are de-scribed in terms of an affine cell image decomposition.

2.1 Segmentation 9

Cohen and Cohen suggest another method to eliminate the initialization problem ex-perienced by the original snake algorithm. By making the curve behave like a balloon,which is inflated by a additional force, the initial curve need no longer be close to thesolution to converge. The curve passes over weak edges, attracting toward detectededges by means of an attraction potential [COHE-91]. The method is further extendedto 3D in [COHE-93].

In [BOOT-01] Booth and Clausi use active contour models, to achive a completeboundary edge, for segmentation of the spinal cord. By using a deformable templateBooth and Clausi develope a method to construct a 3D spinal image from axial MRIcross sections.

Statistical model based algorithms

Statistical model based algorithms are trained to only deform to fit the data in waysconsistent with the training set.

Statistical models may also be known as active shape models. Active shape modelshave some similarities with the original snake method introduced by [KASS-88], butdiffers by applying global shape constraints. Active shape models combine models ofobject contures and grey level appearance surrounding the contures. The active shapemodel is an iterative algorithm based upon a point distribution model. The point distri-bution model is generated form a set of training examples of the object to be modelled.The active shape model locates an instance of the point distribution model in an image.In each iteration the active shape model proposes a new instance of the model in theimage, and approximates the proposed shape as closely as possible, whilst applyingshape constraints captured by the point distribution model.The point distribution model is presented in [COOT-92a] leading to the introduc-tion of active shape models in [COOT-92b]. Cootes further improves his methodsin [COOT-94] and [COOT-95].

There have emerged quite a few different solutions and improvements to the originalactive shape model algorithms by other authors. [HILL-96] use directional constraintsto improve shape approximation. Directional constraints allow the points, in the pointdistribution model, more freedom of movement in specified directions during search.The directional weighting results in an active shape model which require fewer itera-tions and generate more accurate interpretations.

Significantly influenced by [COOT-94] and [COOT-95], [KELE-98] extends the origi-nal 2D method to a true 3D voumetric segmentation technique. The new technique uses

10 Methods

elastic deformation of surface models. Just as Cootes et al. found out in [COOT-94],Kelemen et al. realizes that the modeling of gray level information near the objectboundaries provides valuable information and makes the algorithm more robust.Based on the above mentioned experience Kelemen et al. introduce a new 3D volu-metric segmentation technique based on a hierarchical parametric object descriptioninstead of a point distribution method in [KELE-99].

Instead of using the normalized first derivative profile for the gray level variationsaround the border of the object [GINN-02] presentes a segmentation scheme that issteered by optimal local features.

[SMYT-96] use active shape models to automatically analyze vertebrae in lateral dualenergy xray absorptiometry images of the spine. The method prove to be quite accu-rate and robust.

In [BENA-01] Benameur et al. use a statistical model based method for 3D recon-struction of scoliotic vertebrae.

2.1.2 Segmentation approaches

There are three ways to approach the segmentation problem, namely manual-, automatic-and semi-automatic segmentation. This section gives a short description of each ap-proach, and mentions their main advantages and disadvantages.

Manual segmentation

Manual segmentation refers to the process whereby a skilled operator uses slice trac-ing, region painting, etc., to define regions of interest. The use of this technique isoften necessitated by the complex structures present in medical images.

The manual method is believed to be the most accurate. Also, the use of a humanexpert ensures that the segment boundaries are perceptually valid. Unfortunately themethod suffers form several drawbacks. It is extremely costly in time and effort, issubject to both inter- and intra-operator variability and human error. [HIGG-96]

Automatic segmentation

Automatic segmentation refers to the process whereby segment boundaries are as-signed automatically by a program.

2.2 Visualization 11

Some of the advantages are quickness and minimal user interaction. However au-tomatic segmentation algorithms are usually problem specific and therefore hard toadjust to different segmentation problems. [HIGG-96]

Semi-automatic segmentation

Semi-automatic segmentation combines manual interaction with automated process-ing, and can be viewed as the golden mean, to solve segmentation problems.

This method has many advantages over manual and strictly automated techniques. It isquicker, gives reproducible results, is minimally affected by human inconsistency anderror and the user does not have to be an image-processing expert. [HIGG-96]

2.2 Visualization

There are several ways to visualize medical images.

The visualization techniques can be classified in two broad groups, namely surfacevisualization and direct volume visualization. The first group typically use some kindof segmentation technique in advance. Examples of popular surface visualization al-gorithms are contour connecting [KEPP-75] and the marching cubes [BOUR-96] al-gorithms. The second group is based on a transfer function. The visualization of thestructure of interest is accomplished by visiting all voxels and applying the transferfunction to build the image. A popular direct volume visualization algorithm is raycasting [LEVO-88], [LEVO-90]. [MANS-00]

Subsequent to segmentation, surface reconstruction from voxel datasets generated byMRI usually use a variant of the marching cubes algorithm by Lorensen and Cline, andtherefore belong to the fist group [BOUR-96].

The marching cubes algorithm creates a polygonal representation of constant densitysurfaces from 3D medical data. The idea is to create a triangular mesh that will ap-proximate the isosurfaces and calculate the normals to the surface at each vertex ofthe triangle. The algorithm locate the surface in a cube of eight pixels, calculate thenormals using linear interpolation and march to the next cube repeating the process.[LORE-87]

12 Methods

Chapter 3

Results and Discussion

In this chapter we will present the achieved results and techniques, and discuss theoutcome of the choices made leading to the obtained results, as well as the resultsthemselves.

3.1 Segmentation

The segmentation of the cervical vertebrae was performed manually in Gimp v.1.2.3.The region of interest (ROI) was outlined and segmented, as seen in Figure 3.1 and3.2.

Figure 3.1: An outline of the region of interest (ROI). This is the first step in the manual segmen-tation procedure of an MR image of the cervical spine. The ROI, in this case the spinal cord, canbe seen outlined in red.

14 Results and Discussion

Figure 3.2: A segmented image of the spinal cord. The outline in figure 3.1 has now been filledwith white color while the rest of the MR image has been filled with black color. This is the finalmanual segmentation step, and the spinal cord can now be seen clearly segmented from the restof the image.

3.1.1 Choice of segmentation approach

Manual segmentation was the chosen segmentation approach. This approach can notbe said to be the best of the three segmentation approaches presented in subsection2.1.2. Nevertheless it was the best suitable for the problem at hand.

A important part of this project is to examine if the visualization results are collatedwith the clinical discoveries. In other words to investigate if visualization may help tosupport the theories made by the physicians based on medical examination. Segmen-tation accuracy was therefore more important than efficiency.

Although segmentation efficiency had a lower priority in this project, we hoped to beable to replace the manual segmentation approach with a semi-automatic algorithm,based on the algorithms in subsection 2.1.1, given satisfactory visualization resultsand time. Unfortunately time was not on our side. Semi-automatic segmentation willthus be dealt with in 5 Future work.

3.2 Visualization

The visualization was performed in Matlab v.6.5.1.199709 based on the segmentedimages.

3.2 Visualization 15

Two different visualizations where carried out. One of a patient suffering from spinalinstability and one of a healthy subject, making it possible to compare the instablespinal column with the healthy one. Informed consent was received for the MR im-ages of the healthy subject.

The visualization shows indeed differences between the healthy subject and the patient,as seen in Figure 3.3, 3.4, 3.5 and 3.6

Figure 3.3: Visualization of the cervical spine of the healthy subject, as seen from above. The ver-tebrae is seen in blue, while the spinal canal is in red and the spinal cord in yellow. No narrowingof the spinal canal and pinch of the spinal cord can be seen.

Figure 3.4: Visualization of the cervical spine of the patient, suffering from spinal instability, asseen from above. The vertebrae is seen in blue, while the spinal canal is in red and the spinal cordin yellow. A narrowing of the spinal canal and possible pinch off the cord can bee seen to the left.

16 Results and Discussion

Figure 3.5: A closer look at the spinal canal and cord of the healthy subject, as seen through thevertebrae. The color codes are the same as in the preceding figures. The cord is protected by thespinal column with enough space and fluid between itself and the canal.

Figure 3.6: A closer look at the spinal canal and cord of the patient, as seen through the vertebrae.The color codes are the same as in the preceding figures. The narrowing of the spinal canal andpossible pinch of the spinal cord can now be seen more clearly at the upper right side. The pinchmay induce pressure on the cord, which in turn cause pain for the patient.

3.2 Visualization 17

3.2.1 Final results

There are some differences between the two visualized cervical spines. This may bedue to the different size in image arrays used to segment these spines.Nevertheless the visualizations of the spinal cord and canal are quite satisfactory. Un-fortunately it is hard to see the movement of the vertebrae.

The reason for this may be the poor bone contrast in MR images which lead to seg-mentation problems. As well as the choice of segmentation approach. Manual seg-mentation is prone to human error and the quality of the segmentation process affectthe visualization results.

At this the results give an impression of the advantages a visualization may have as acomparison- and verification tool. But they also point out that both the segmentationand visualization processes needs to be improved before they actually can serve assuch a tool.

18 Results and Discussion

Chapter 4

Conclusion

A minor number of works dealing with segmentation of medical images have beeninvestigated.

A manual segmentation approach has been chosen, leading to a visualization of thecervical spine of two subjects. One that has a healthy spine and one that is sufferingfrom spinal instability.

The visualization shows a difference in the two patients cervical spine. The patientsuffering from spinal instability has a reduction of spinal fluid and the spinal cord ispinched at the top level of the cervical spine.

The visualization is, at this stadium, promising, but has trouble showing the vertebralmovement. It is hard to see what causes the pinch in the spinal cord and the reduc-tion of spinal fluids in the column. This may be due to the difficulties related to thesegmentation of the vertebrae. A semi-automatic segmentation approach is thereforeproposed, as well as other potential improvements.

20 Conclusion

Chapter 5

Future work

This chapter presents our suggestions for future improvements.

5.1 Segmentation

The quality of the visualization is heavily influenced by the quality of the segmenta-tion. The manual segmentation approach is very time consuming and prone to humanerror. A semi-automatic segmentation may thus improve the visualization as well asmake the system more efficient.

Deformable model based algorithms are best suited to find local curved transforma-tions between images, and less so for finding global rigid or affine transformations.

Statistical model based algorithms have therefore been the most popular technique formedical image segmentation. A improvement may be to use one one of the mentionedstatistical model based algorithms of section 2.1.1 Algorithms. Either as it is or withminor adjustments to better fit the problem of segmenting cervical vertebrae.

5.2 Visualization

User interaction, in order to allow the user to change parameters and obtain a dynamicnavigation process, during the visualization process will undoubtedly be a further im-provement to the present solution. If the operator can interactively change the point ofview, a better understanding of the vertebral movement may be possible.

Implementation of a GUI to make the system user friendly may be a good idea in thiscase.

22 Future work

Annexes

Appendix A

Glossary of Spinal Terms andabbreviations

Atlas The first vertebra of the cervical spine. Also known as C1.Axis The second vertebra of the cervical spine. Also known as C2.Cervical Neck region of the spine containing the first seven vertebrae.CT Computerized Tomography.GUI Graphical User Interface.MR Magnetic Resonance. Also known as MRI.MRI Magnetic Resonance Imaging.ROI Region Of Interest.Spinal Canal Bony channel which contains the spinal cord and nerve roots.Spinal Column Flexible bone column extending from the base of the skull to the tailbone.Spinal Cord Longitudal cord of nerve tissue that is enclosed in the spinal canal.Vertebra One of the 33 bones of the spinal column.

Bibliography

[BACK-02] Anatomy - Lumbar spine. http://www.back.com/anatomy-lumbar.html, April 2002.

[BENA-01] S. Benemeur, M. Mignotte, S. Parent, H. Labelle, W. Skalli, and J. A. D.Guise, 3D Biplanar Reconstruction of Scoliotic Vertebrae Using Sta-tistical Models, 2001, pp. 577–582.

[BJAL-98] J. G. Bjalie, E. Haug, O. Sand, and Ø. V. Sjaastad, Menneskekroppen,Fysiologi og anatomi, Gykdendal Norsk Forlag AS, 1998.

[BOCK-98] R. Bock, Image Segmentation. http://rkb.home.cern.ch/rkb/AN16pp/node131.html,April 1998.

[BOOT-01] S. Booth and D. A. Clausi, Image Segmentation Using MRI VertebralCross-Sections, IEEE Canadian Conference on Electrical and Com-puter Engineering, May 2001, pp. 1303–1307.

[BOUR-96] P. Bourke, Approaches to Modelling the Surface of the Hu-man Cortex - Survey and Esamples of Current Techniques.http://www.astronomy.swin.edu.au/ pbourke/modelling/cortex/cortex2.html,Oct. 1996.

[BRID-01] K. Bridwell, Vertebral column. http://www.spineuniverse.com/displayarticle/php/article1286.html,June 2001.

[BURC-00] M. T. Burcon, Chiropractic Care: The Atlas and Axis.http://www.spineuniverse.com/displayarticle/php/article796.html,Feb. 2000.

[COHE-91] L. D. Cohen, On Active Contour Models and Balloons, ComputerVision, Graphics, and Image Processing: Image Understanding, 53(1991), pp. 211–218.

[COHE-93] L. D. Cohen and I. Cohen, Finite-Element Methods for Active ContourModels and Balloons for 2-D and 3-D Images, IEEE Transactions onPattern Analysis and Machine Intelligence, 15 (1993), pp. 1131–1147.

26 BIBLIOGRAPHY

[COOT-92a] T. F. Cootes, C. J. Taylor, D. H. Cooper, and J. Graham, Training Mod-els of Shape from Sets of Examples, British Machine Vision Confer-ence, Springer-Verlag, 1992, pp. 9–18.

[COOT-92b] T. F. Cootes and C. J. Taylor, Active Shape Models - ’Smart Snakes’,British Machine Vision Conference, Springer-Verlag, 1992, pp. 266–275.

[COOT-94] T. F. Cootes, A. Hill, C. J. Taylor, and J. Haslam, The Use of ActiveShape Models for Locating Structures in Medical Images, Image andVision Computing, 12 (1994), pp. 355–366.

[COOT-95] T. F. Cootes, C. J. Taylor, D. Cooper, and J. Graham, Active ShapeModels - Their Training and Application, Computer Vision and ImageUnderstanding, 61 (1995), pp. 38–59.

[GINN-02] B. van Ginneken, A. F. Frangi, J. J. Staal, B. M. ter Haar Romeny,and M. A. Viergever, Active Shape Model Segmentation With OptimalFeatures, IEEE Transactions on Medical Imaging, 21 (2002), pp. 924–933.

[HENR-02] T. E. Henriksen, Den darlige ryggen.http://www.uleval.no/default.asp?file=ryggnettverk.xml, May 2002.

[HIGG-96] W. E. Higgins, A. J. Wang, and J. M. Reinhardt, Semi-automatic 4danalysis of cardiac image sequences, in Medical Imaging 1996: Phys-iology and Function from Multidimensional Images, E. A. Hoffman,ed., SPIE, Sept. 1996, pp. 359–372.

[HILL-96] A. Hill and T. F. C. C. J. Taylor, Active Shape Models and the ShapeApproximation Problem, Image and Vision Computing, (1996).

[KASS-88] M. Kass, A. Witkin, and D. Terzopoulos, Snakes: Active ContourModels, International Journal of Computer Vision, (1998), pp. 321–331.

[KELE-98] A. Kelemen, G. Szkely, and G. Gerig, Three-dimensional Model-basedSegmentation of Brain MRI, Workshop on Biomedical Image Analy-sis, 1998, pp. 4–13.

[KELE-99] , Elastic Model-Based Segmentation of 3-D NeuroradiologicalData Sets, IEEE Transactions on Medical Imaging, 18 (1999), pp. 828–839.

[KEPP-75] E. Keppel, Approximating Compex Surfaces by Triangulation of Con-tour Lines, IBM Journal of Research and Development, 19 (1975),pp. 2–11.

BIBLIOGRAPHY 27

[LEVO-88] M. Levoc, Display of Surfaces from Volume Data, IEEE ComputerGraphics and Applications, 8 (1988), pp. 29–37.

[LEVO-90] , Efficient Ray Tracing of Volume Data, ACM Transactions onGraphics, 9 (1990), pp. 245–261.

[LOBR-95] S. Lobregt and M. A. Viergever, A Discrete Dynamic Contour Model,IEEE Transactions on Medical Imaging, 14 (1995).

[LORE-87] W. E. Lorensen and H. E. Cline, Marching Cubes: A High Resolution3D Surface Construction Algorithm, in Computer Graphics, vol. 21,International Conference on Computer Graphics and Interactive Tech-niques, July 1987, pp. 163–169.

[MAIN] J. B. A. Main and M. A. Viergever, An Overview of Medical ImageRegistration Methods. Imaging Science Department, Imaging CenterUtrecht.

[MANS-00] I. H. Manssour and C. M. D. S. Freitas, Collaborative Visualization inMedicine, WSCG-2000 The Internation Conference in Central Europeon Computer Graphics, Feb. 2000.

[MCIN-00] T. McInerney and D. Tersopoulos, Deformable Models, AcademicPress, 2000, ch. 8, pp. 127–145.

[MCIN-95] , Topologically Adaptable Snakes, The fifth International Confer-ence on Computer Vision, June 1995, pp. 840–845.

[MCIN-96] , Deformable Models in Medical Image Analysis: A Survey,Medical Image Analysis, 1 (1996), pp. 91–108.

[MCIN-99] , Topology Adaptive Deformable Surfaces for Medical ImageVolume Segmentation, IEEE Transactions on Medical Imaging, 18(1999), pp. 840–850.

[MONT-00] J. Montaganat, H. Delingette, N. Scapel, and N. Ayache, Represen-tation, shape, topology and evolution of deformable surfaces. Appli-cation to 3D medical image segmentation., Tech. Rep. 3954, INRIA,May 2000.

[RODT-03] M. Rodts, Your healthy spine. http://www.spineuniverse.com/displayarticle/php/article1296.html,Nov. 2003.

[SMYT-96] P. P. Smyth, C. J. Taylor, and J. E. Adams, Automatic Measurement ofVertebral Shape Using Active Shape Models, British Machine VisionConference, 1996.

28 BIBLIOGRAPHY

[SPINEH-04] Vertebral bodies. http://www.spine-health.com/topics/anat/a002.html.

[WIKI-04a] Computed axial tomography. http://www.wikipedia.org/wiki/Computed axial tomography.

[WIKI-04b] Magnetic resonance imaging. http://wikipedia.org/wiki/Magnetic resonance imaging.

[XU-00] C. Xu and J. L. Price, Gradient Vector Flow Deformable Models, Aca-demic Press, 2000, ch. 10, pp. 159–169.

[XU-98] C. Xu and J. L. Prince, Snakes Sapes and Gradient Vector Flow, IEEETransactions on Image Processing, 7 (1998), pp. 359–369.