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rage volume metric surfaceund truth mode

eywords: Segingements; Hip

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varez, Baumer contour extrd speed, our mo subdivide fe-processing stbdivision and

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is a follows: ection 3 deson 4 containscontains clos

t exists betwef two bones; ones are soft t

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pe differencefrom hip illnel solution to frum of shapeg of patient s

nto two, parfemur-head ans, we extract

as they appe. While weela, Henríqueaction methodmain contribuemur segmentteps we apply d the preproceatient variabil

pelvic scan billing its spaceel’s resolutionemphasize vpplying a floen of soft tissuSection 2 con

scribes our fs some resultssing remarks

een the pelvithe femur an

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e the smooth,

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number of no

1

ensity

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s are esses, femur s and scans. rtially nd the t the

ear on use

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s and

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(blue)

otable

2

The femur head is the rounded end of the femur. Its surface comes in the closest contact with the pelvic bones and can generally be approximated with the shape of a sphere or conchoid

The pit (or fovea) for the ligament of the head of the femur is an indentation in the otherwise spherical surface of the femur-head

The femur body is the tubular shaft which makes up the majority of the femur

The greater trochanter is a large bony-bump at the top of the body, opposite to the femur head

CT images of the femur-head’s subchondral bone composition show large density variations, like a very thin compact shell compared to the much thicker one found in the femur body. Comparatively, regions of the acetabular rim covering the femur head are also noticibly denser.

The hip-joint’s task in the human body is to support upper-body weight- both while standing still and during movement. Hip movement is enabled by the hip functioning as a ball-and-socket (Field & Hutchinson, 2008) where the femur head constitutes the ball and the acetabulum provides the retaining socket.

2.2 Femoral Acetabular Impingement

Hip impingement, or Femoral-Acetabular Impingment (FAI), is a pathological condition where there is a deformity on either of the hip-joint’s bones. This deformity usually manifests itself as a bony-bump on the acetabular rim (Pincer impingements) or the femur’s head-neck junction (Cam impingements) or both. As a result, the hip joint will lose its ideal ball-and-socket shape which causes abnormal contact (impingement) between the femur and acetabulum during normal hip-rotation. In turn, this abnormal contact causes chaffing of the soft-tissue protecting the two bones, deteriorating the integrity of the joint over time. FAI is most often associated with pain during hip flexion, adduction, and the internal rotation of the femur. If left untreated, a FAI can lead to cartilage damage, labral tears, early hip arthritis, hyperlaxity, sports hernias, chronic lower back pain (Hossain & Andrew, 2008) and an eventual hip replacement surgery.

2.3 Medical Segmentation Methods

Medical images are a popular proving ground for segmentation methods as the images are usually full of complex shapes, noise and the extracted shapes have obvious, life-changing uses.

The original energy minimizing curves, or “snakes” (Kass, Witkin, & Terzopoulos, 1987), are perhaps the best known segmentation scheme. Since their introduction in 1987, a number of modifications/enhancements have been proposed. These include the addition of a balloon force operator (Cohen L. , 1991), 3D generalizations of the snake model (Cohen & Cohen, 1993), likening snakes to level-set methods with geodesic active-contours (Caselles, Kimmel, & Sapiro, 1997), increasing the a snake’s capture range & ability to evolve into concavities (Xu & Prince, 1998) and add topological flexibility (McInerney & Terzopoulos, 2000).Model-based segmentation schemes are useful in cases where part of an object’s information is missing. Early cases include Active shape models (Cootes, Taylor, Cooper, & Graham, 1995) and active appearance models (Cootes, Edwards, & Taylor, Active Appearance Models, 1998) based around point distribution models.

Similar to energy-minimizing curves are methods which are region-based rather than boundary-based. A prime example of this is the Chan-Vese method (Chan & Vese, 2001) (Vese & Chan, 2002) which seeks to minimize the energy inside a curve through the Mumford-Shaw functional. At roughly the same time, Diffusion Snakes (Cremers, Schnörr, Weickert, & Schellewald, 2000) were detailed, which used prior shapes along with the Mumford Shaw functional. As an aside, a model-based method which originally used the kernel density information of shape-priors (Cremers, Osher, & Soatto, Kernel Density Estimation and Intrinsic Alignment for Shape Priors in Level Set Segmentation, 2006) was modified to also include intensity-priors or regions inside the boundary (Chen & Radke, 2009).

A number of segmentation strategies have been proposed focusing on the segmentation of femurs from MRI and CT scans, although none of these address the much more difficult task of segmenting hips suffering from FAIs. One such method required assigning a scan into one of four groups depending on the anticipated difficulty of segmentation, and in the worst case, separating the femur and acetabulum using a combination of the Hueckel operator and orthogonal line detection (Zoroofi, et al., 2003). Unfortunately, their techniques returned many moderate and poor results. Another method involved a significant amount of user-input, requiring the user to manually surround the femur head with contour points for a snake method and making manual correction whenever the snake failed due to soft edges (Magnenat-Thalmann, Yahia-Cherif, Gilles, & Molet, 2003).

In regards to model-based segmentation methods for femur bones, coarse-to-fine methods have been used with 3D meshes (Gilles, Moccozet, & Magnenat-Thalmann, 2006) for anatomical modeling, MRI scans with low resolutions or fields of view (Schmid, Kim, & Magnenat-Thalman, 2011), and statistical shape models (Yokota, Okada, Takao, Sugano, Tada, & Sato, 2009) have been used to segment diseased hips. In addition, 2D point-distribution models for ASMs (Song, Li, Ou, Han, Zhao, & Wang, 2007) have been tested against healthy hips. Generalized models of hip-bones can lead to complications when the object of segmentation has a FAI. This is due to the bony bump being outside the model’s expected distribution. Conversely, models specifically tailored for bones with impingements require a very large set of prior shapes as the location of the bony bumps can be highly irregular. To return the best segmentation results, a method which is elastic to the pronounced differences between bones is required.

2.4 Morphological Snakes

Our segmentation solution selected a 2D implementation of Morphological Snakes (Álvarez, Baumela, Henríquez, & Márquez-Neila, 2010) to extract our desired contours. This method is a recent modification of the well-known Geodesic Active Contours. The major difference between the two models is how each method solves the partial differential equations (PDEs) responsible for curve evolution. While Geodesic Active Contours expresses these PDEs with a set of differential operators, Morphological Snakes instead takes the approach of approximating these terms as the composition of morphological operators. Specifically, the inf (infimum) and sup (supremum) operators. This substitution claims three advantages: 1. Simplicity of Implementation – The level-set is

expressed as a binary piecewise constant function

2.

3.

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Once the primquentially sege queued for simer slice. If tces to be segmZp-2, Zp+3 &

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final contour i

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segmentation

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ontour (c) Slice Zi

dilat

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he femur, like ompact osseouhyses (Rizzo,ur body beinur head, on ac the soft tissu

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ns to obtainingr to the morphe “fine” conto

ing the Fem

most long bous tissue arou, 2001). This

ng easier to sccount of the ue that surrouve adjacent bomity, once aga

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sequential segth the super

p-most and bod.

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nitial contour: ch slice on then un-segmentif it is abovemer slice. Housed as an in

s used to sa between neian be viewed

(b

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g a final conthological snakur extraction p

mur Body RO

ones, has as mund its shaft t

results in thesegment thancompact bon

unds it. In addones which neain unlike the

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d. or the femur eps: (a) a pricted (b) the

gmentations awrior and infeottom-most sli

ices is similartage. They diwe have deci

e final contouted slice Zi w

e the primer sowever, befor

nitial contour, afeguard agaighboring femin Figure 3.7

b)

d) Slice Zi+1 with finlice Zi using Zi+1’our

tour is to supke algorithm parameters.

OI

much thicker shthan it does ate slices from those from

ne’s high contdition, the femeed to be isola

femur head w

ular in shapece segmentatfact, the conty follows closith a few mibeing that R

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way erior ices

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3.5

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5.1 Primer

For the ROIB, ce, which wrrespond to thd contain a tub

Finding the rOnce again, tea for the fines stage is the

OIB’s area. Oake algorithmough” parametGiven the thicnal contour shose to the rentour extractintours are likntour, and eve

gure 3.8 (left) Init

Finding the fiThe fine contr the femur he primer slicection of the femt employ a Hontour to extrae rough stepquential slicesstanced from t9). We use thisThe final contorphological sntour. Corregmentation pa

gure 3.9 (left) Ini

5.2 Subse

With final continue with t

es, where thward segmenta

r Slice Segm

the primer sliwe refer to ahe bottom-mosbular cross-se

ough contourthe rough cone contour ext

e largest circlnce this has

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tial contour for ros

ine contour our serves th

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itial contour for thfin

quent Slice S

ontour of the the segmenta

he primer sliation cascade.

mentation

ice is chosen aas Zb. This st slice of the ection of the fe

r ntour extractiotraction. The e whose entirbeen fitted, contours usin

he femur-headrast shell of thually free of ll be obtaineee Figure 3.8nly visible fl

be reset using

ough step (right) step

e same purpong the decisivfemur-head h

not near-circulmation on thetting circle. Intour much ais a curve whidy at the primehe fine step’s rimer slice is hm is applied

we use thnsure the best

he fine step (rightne step

Segmentatio

primer slice ation of all th

ce’s segment

as the bottom-slice should whole pelvic

emur body.

on finds a stainitial contourety fits insidthe morpholong the same sd’s primer sliche femur body

defects and d during the

8). Slightly jalaws on the rthe fine step.

final contour for

ose here that ive segmentatiohowever, the clar, meaning we rough step’snstead, we ex

as we do forich is near ever slice (see Finitial contourobtained wheto the new i

e “fine” se results.

t) Final contour f

on

well definedhe other slic

6

tation

-most also

scan,

arting ur for de the ogical set of ce. y, the quite

e fine agged rough

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en the initial et of

for the

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FiguFin

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wever, the prime, so we can onhus, an un-segour on Zi+1. H

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femur head hahe initial conmentation of smentation of sr to the set oflice Zs+1 for Rin the final cracting the setd estimation oe Zs. Thus we– VH to provid).

(a)

(c)

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ROIH subtracte

o matter howal contour, it irithm along wl curve providmentation for R

dure for doinentations awmer slice for nly iterate upwgmented slice However, priontour, we expa

femur body aexists a singl

lization. That femur-head foccurs at the hrochanter crowocus on segmeas already beenntour for Zs slice Zs+1 in Rlice Zs+1 in R

f voxels contaROIH as VH ancontours of slt of voxels inof the greater

e use the largede and initial c

contour for slice ice Zs+1 in ROIH (ed from ROIB (f)

w one of the is used as inpu

with the set ofded by the alROIB.

ng so is famiway from th

the ROIB is wards.

Zi will alwayor to using Zi+

and the contoare outside its e slice in ROIslice is Zs; w

first become height of interwns shortly thenting the grean segmented fis based not

ROIB, but alsROIH. For shorained within thnd the set of lice Zs+1 for

n VH from VB,r trochanter’s est set of concontour for sli

(b)

(d)

(f) Zs+1 in ROIB (b)

(d) Voxels of set slice Zs with its i

subsequent sut for the morf “fine” snakegorithm beco

iliar: performhe primer sl

the bottom-m

ys base its ini+1’s final cont

our, ensuring tdomain. IB which requwhere the gre

two, disjoirtrochanteric lhereafter. Of ater trochantefrom ROIH. t only the fiso from the firthand’s sake,he final contovoxels contaiROIB as VB. , we can obtai

cross-sectionnnected voxelsice Zs (See Fig

Voxels of set VB

VH (e) Volume foinitial contour

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ming lice.

most

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Segmentation sults for ROIH

Figure 3.11 Sampl

Results

In order to asategy, we cotomatic metho

he manual segm-slice, voxelogram. It cgmentation. Osults which aound truth.

1 Hospita

We have collenducted by th

were fromilateral) and tient we alsodiograph. In cowed us to stu

2 Testing

From these 20sampling as pomurs for validese patients ca

Table 4.1 Clinica

atient ID #

1

2

3

4

5

6

Other than feAIs, our sampriations whicgmentation st

rocessing

in our segmenfor the segmeunion between

with voxel’s inallow us to c

y one of the Figure 3.11.

ative collectiopresentation.

SegmeResults

le union of the 3Dfrom

and Disc

ssess the quampare the vood to the volumentation’s v-by-voxel bacan be con

Our goal in tesare identical,

al Database

ected 20 pelvihe Ottawa Ge

CAM type 3 were part

o have one aconjunction, tudy the variati

Database

0 scans we selossible and m

dation purposean be seen in T

al characteristics omanually

Age

39

47

29

33

22

54

emur size, orle set shows ch would tetrategy. The

ntation procesented femur. Tn the voxels enside for ROIconsolidate thROIs versus

. From here, on of voxels

entation for ROIB

D model from ROm ROIB

ussion

ality of our feolume segmenume of a man

volume was labasis using ansidered the sting is to obtaor within hu

ic scans fromeneral Hospita

patients (7 of the contro

antero-posteriothe scans andions between

lected 6 that pmanually segmes. The clinicaTable 4.1.

of the six patientsy segmented

Sex 

M 

F 

F 

M 

M 

M 

rientation anda number of

est the rigoumost import

ss is the creatiThis is resolveencased by ROIB’s final conthe slices whic

those coverethe results caor be polygo

Final FemModel

OIH and the 3D m

emur segmentnted by our nual segmentabeled on in aan image ed

“ground tain semi-automuman error of

m a study into al. Of these s

bilateral anol group. For or and one ld radiograph patients.

provided as dimented both ofal characteristi

s whose femurs w

FAI Diagn

Bilater

Left

Left

Left

Right

Contro

d the presencother inter-pa

ur of any ftant dissimila

7

ion of ed by OIH’s tours.

ch are ed by an be nized

mur l

model

tation semi-ation. slice-diting truth” matic f this

FAIs scans, d 10 each

ateral have

iverse f their ics of

were

nosis

al

t

ol

ce of atient femur arities

betwheadimpaconc

Figu

Asbounclosestrate

Figu

Strcontofromwhichead

Fig

Ditrochof thcurvprevconc

ween patients ad. The femuract of inter-pacerned.

ure 4.1 Femur and

s an examplndaries of thee due to blurregy will need

ure 4.2 Cross-sect

rict model-basours from the

m the averagech seeks to end will especial

gure 4.3 Concavity

Figure 4.4

ifferential gahanter can be he two is expee evolution pralence of com

cavity.

are innevitablr body’s thicatient differen

d acetabulum app

poin

e, Figure 4.e femur-head red edges andto separate th

tions where the fe

(right) de

sed metthods e right image e femur shapenforce a spherily have difficu

y between femur

wide (righ

4 Various shapes

aps betweenseen in Figurcted cause somrematurely. Ampact bone

ly located at ock, tubular shnces as far as

pear (left) well-spnts

1 shows a and acetabul

d CT noise. Ahese two objec

emur head appeareformed

will have diffin Figure 4.2

e. Any segmicity constrainulty here.

head and greaterht) narrow

of the femur head

n femur heare 4.3, where me snake met

Also worth notin the slice

or near the femhape lessens s segmentation

paced (right) close

slice where lum appear qu

Any segmentatcts.

rs (left) near-circu

ficulty getting2 as it’s a far entation stratnt over the fem

r-trochanter is (lef

d’s fovea

ad and grethe more narr

thods to halt thting is the higwith the narr

mur the

n is

e at

the uite tion

ular

the cry

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ater row heir gher row

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Finally, Figurewhich are ne

hile others still

3 Testing

All of our scanr each one of2 voxels, whe

68 x 0.68 x 1.2As for paramearted off with sized-slices was better able eater trochantege to some of During the areshold value xels which be

six CT scamphasize the centuating thetabulum and We also applces in ROIB

tten the intensWe used a defsted femurs) dxels corresponperimentationreshold for thcasionally imreshold value ove the primethe whole femThe rough ano different set

he rough metterion whereased balloon rmer can be fo

Table 4.2 Test par

σ 0.0

Table 4.3 Test pa

σ 0.0

For these parntours are tryie Gaussian coe maximum nuI) during the

reshold for G(d DR is the ntral pixel val

4 Qualitat

The images fom our patien

e 4.4 ilustrateearly straightl appear as de

Conditions

ns were acquif them, the sliere each voxe25 mm. eters used duan upscale faere sufficientlto map the coer. In addition

f the sharp turnacetabular remof 316 HU (fo

elonged to the ans, we foun

acetabulum’he voxels femur head.

lied a floorinwith default

sities of musclfault value of during the ceinding to com

n, we discovehe top-most smprove result

of 144 HU er slice. This amur head ROI.nd the fine cots of procedurthod uses anas the fine mstopping crit

ound in Table

rameters for Morpballoon (Ro

N 100

arameters for mordifference-radiu

N 100

rameters, G(Iing to minimiz

onvolution appumber of iter

e speed propa(I) during the

difference mue that propag

tive Segmen

found in Tabnt #3’s left hip

es a wide arrayt, other are aeep dimples.

s

red using a Gices have a reel had a phys

uring the prepctor of 2. Thely large that toncavities on n, the upscale ns in the femumoval step, wor all tested feacetabulum’sd that this vs bones witfor soft-tiss

ng threshold value of 12

le and fat voxf 201 HU (onciling threshold

mpact osseous ered that lowlices of the f

ts. For this for the top-maccounts for th. ontour extractres, as well asn edge-based

method uses anerion. The p4.2 and the la

phological snake ough Contours)

ETB 0.1

rphological snakeus (Fine Contour

DR 12

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magnitude wigates the ballo

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le 4.4 and Tp, which was

y of foveas. Sangular conca

GE Lightspeed esolution of 51sical dimensio

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ur head’s exterwe used a deemurs) to highs hard shell. Avalue did wethout acciden

sue between

exclusively to7 HU in ord

xels near the bce again, for ad step to hightissue. After

wering the cefemur head wreason we u

most 25% of he top-most 1

tions methods input param

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parameters foatter in Table 4

with edge-thresh

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e with snake-ballos)

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pagation proceith respect tooon.

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Table 4.5 origs diagnosed w

8

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all the hlight some eiling would use a slices 2.5%

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er h.

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of our segmentath those from a ma

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e compariso our methodtion can be se5 for the femu

son of our segmenwith those from a

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n contains theice. Volume hinside the akes. column conta

ground truhite was manuoxel basis withmn shows how

hown in blacns. Green vo

of the ground while red vox

can on whiches which spanoughly a 1cm

tion method resulanual segmentati

Ground Truth

on of segmd and those een in Table 4ur body.

ntation method rea manual segment

Ground Truth

e final contouhighlighted in final contou

ains the vouth segmentually segmenteh an image edi

w well these twck indicate ideoxels indicatetruth segmen

xels indicate th

h the images nned from the

below her mi

lts for the femur hon

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mentation resobtained thou4.4 for the fem

esults for the femutation

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ur of our methwhite represe

ur evolved

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wo segmentatientical results ed voxels whntation but nohe opposite.

are top

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ults ugh mur

ur

e

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for hich t of

ID1

2

3

ID4

5

6

Ihowgro

Table 4.6 Volum

D # O

Table 4.7Volu

D # O

In order to prw the models ound truth m

metric renderings

Our Method

umetric rendering

Our Method

rovide a moreobtained thro

models, 3D v

of the first tree p

G

gs of the last three

G

e complete visough our methvolume rend

patients’ left femu

Ground Truth

e patients’ femurs

Ground Truth

sual assessmehod compare terings have

9

urs

h

s

h

ent of to the been

10

obtained for each model. The left femurs from the first three patients can be found in Table 4.6 while the right femurs from the last three patients are in Table 4.7. The middle column of each table contains the renderings of femurs segmented with our method while the last row contains renderings from manually segmented femurs. All renderings were taken from an antero-posterior (AP) position.

The technique (Stegmaier, Strengert, Klein, & Ertl, 2005) used to produce these 2D projections is an example of a Digitally Reconstructed Radiograph (DRR) (Sherouse, Novins, & Chaney, 1990). DRRs are an approximation of a 2D x-ray image obtained from CT or MRI data. A DRR’s semi-transparent approach to volume rendering allowed us to present more depth compared to polygonized surface models.

4.5 Quantitative Segmentation Comparison

The accuracy of our segmentation method is measured numerically in terms of the intersection of voxels covered by both models and the distance from the bordering voxels in the ground truth model to the nearest bordering voxels in the model segmented through our method. The volumetric overlap errors (VOEs) of the models can be seen Table 4.8. This table displays the global error (VOEg), the average slice error (VOES Avg), the slice minimum error (VOES Min) and slice maximum error (VOES Max).

Table 4.8 Volumetric overlap error

ID # VOEg (%)

VOEs Avg. ± stdev (%)

VOEs Min (%)

VOEs Max (%)

1 L 2.51 3.36±6.57 0.80 58.80 R 2.84 3.88±8.21 0.84 71.30

2 L 2.90 3.79±5.84 1.11 48.61 R 3.14 3.99±5.60 1.23 48.17

3 L 2.22 2.42±1.75 0.86 9.89 R 2.18 2.51±2.42 0.62 19.38

4 L 3.26 3.38±1.77 0.68 9.94 R 3.54 3.92±1.91 1.75 16.59

5 L 2.41 3.59±8.94 0.74 77.38 R 2.27 3.12±6.00 0.87 52.47

6 L 2.62 2.76±1.85 1.24 13.41 R 2.67 2.88±2.18 1.28 16.06

Avg. 2.71±0.44 3.30±0.56 1.00±0.33 36.84±25.17

The precision of our extracted contours is displayed in

Table 4.9 with Symmetric Surface Distances (SSD). This table includes the global average (SSDg.avg), an average of slice averages (SSDs.avg Avg) and a maximal surface distance (SSDmax).

4.6 Discussion

Table 4.9 shows that our segmentation strategy returns average results which are quite close to the ground truth. The vast majority of our contours are within 0-1 voxels of the ground truth’s contour. This is within the expected variability typical for manual segmentations (1-2 voxels) (Kaus, Pekar, Lorenz, Truyen, Lobregt, & Weese, 2003).

The last column of Table 4.9 highlights a model’s least accurate contour. Across each one of our models, these least accurate contours could be counted to be in one of three locations on the femur (a) the crown of the femur head (b)

the slope of the femur neck directly below the head and (c) the narrow concavity between the greater trochanter and the femur neck.

Table 4.9 Symmetric Surface Distances

ID # SSDg.avg ± stdev (mm)

SSDs.avg Avg. ± stdev (mm)

SSDmax (mm)

1 L 0.26±0.42 0.29±0.27 4.83 R 0.29±0.46 0.33±0.44 6.30

2 L 0.28±0.41 0.31±0.25 3.49 R 0.30±0.44 0.32±0.22 4.32

3 L 0.23±0.38 0.22±0.11 2.76 R 0.22±0.37 0.22±0.11 2.76

4 L 0.31±0.43 0.30±0.12 3.42 R 0.37±0.40 0.37±0.09 3.16

5 L 0.26±0.45 0.31±0.51 7.36 R 0.25±0.42 0.28±0.33 4.93

6 L 0.29±0.38 0.29±0.13 2.16 R 0.29±0.39 0.29±0.14 2.50

Avg. 0.28±0.04 0.29±0.04 4.00±1.60 Errors in the first two locations can be visualized in the

profiles of femur models obtained through our method, seen in Table 4.6 and Table 4.7. We attribute errors in these two regions to blurred and noisy cross-sections of the bone surfaces.

Errors, in the gap between the greater trochanter and the femur neck usually occur when the gap is particularly narrow and deep. This issue is native to most snake segmentation schemes and can be attributed to the external forces acting on the evolving contour cancelling each other out when inside narrow concavities (Xu & Prince, 1998). Possible fixes to this shortcoming include increasing the upscale factor during the pre-processing phase or to alter the external force model to better carry the flow of gradients.

The most recent femur-segmentation strategy against which we can compare our quantitative results is (Schmid, Kim, & Magnenat-Thalman, 2011). Schmid et al. reported and an SSDg.avg of 1.21 ± 0.53mm, a SSDmax of 7.57 ± 2.46 and a VOEg of 18.02 ± 6.12 % with their high-resolution, low field-of-view, MRI scans of the human femurs. The high-field of view of our scans is a partial contributor to our improvement over these results.

Generally, our segmentation results for the femur body better matched the manual segmentation than the results from the femur head. This is especially true for the top-most slices of the femur head which are the leading location of our SSDmax. This is recognized as being due to the tubular regions of the femur having a much thicker shell of compact bone than can be found around the femur head’s. This supplies the snake algorithm with strong stopping criteria which halts the curve’s evolution.

5 Conclusion

In this paper, we described a method to segment a femur from a CT scan. We initiate the segmentation by having the user subdivide the femur into two regions (the near-spherical head and the vertically tubular body) and used two levels of segmentation (rough and fine). A number of pre-processing steps are employed on each ROI’s volume to improve the shape and accuracy of our methodology, such as replacing

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sections of the acetabulum with low-gradient fill. Afterwards, we segment the femur-head followed by the femur body using a sequential set of related morphological snake operations.

We find the qualitative results returned by our method to be extremely encouraging given the diverse set of bones on which we experimented. We were able to return results which were largely within the expected range of error for manual segmentations. The user initialization can take under a minute to perform while the segmentation process usually took roughly 5-10 minutes to complete on a modern desktop computer, which is a staggering improvement over the hours it might take a radiologist to manually segment a femur.

The next step in our research is to implement a 3D implementation of morphological snakes to see if we can improve results on error-prone locations on the femur.

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