m A s T o tal Sen sitivity False Positive
Zuker
Sobel
OptDer
Zuker
Sobel
OptDer
100 9 55% 55% 44.44% 1 1 1
40 9 33.33% 33.33% 44.44% 2 1 1
30 9 44.44% 44.44% 55% 0 2 2
20 9 1 1 .1 1 % 33.33% 44.44% 2 2 2
13 9 22.22% 22.22% 44.44% 2 2 3
T able A-4: S en sitivity for p olyps > =
5mm
in real patient stan dard dose (lOOmAs) data. ._____ ______________________________ ____________________m A s T otal S en sitivity False Positive
Zuker
Sobel
OptDer
Zuker
Sobel
OptDer
100 18 88.89% 88.89% 88.89% 4.32 4.69 4.71
doses in the range 100-13m As where the Zucker-H um m el and Sobel operators shows 92.85% sen sitivity at 30m As and 13m A s radiation doses (see T able A - l) . Figure A- 2(a) illustrates the 3D surface extractio n for a 12m m polyp when the Zucker-Hummel operator was applied to com pute the surface norm al vectors and Figure A-2(b) shows the surface extraction using the O ptD er operator. Figure A-3 illustrates the surface extractio n for an 8 m m phantom polyp from a dataset scanned w ith 13m As. It can be noted th a t in both cases the
CAD-CTC
system achieved a more accurate surface extraction w hen th e O p tD er operator was employed. Due to incom plete surface segm entation th e developedCAD-CTC
system missed the polyp illustrated in Figure 2 when th e Zucker-Hum m el operator was used to extract the surface norm al vectors (see T ab le A - l) , whereas the p olyp was correctly detected when the O p tD er operator was applied. In Figures 2 and 3 it can be also observed th at the O p tD er operator generates b etter surface norm al concentration than the Zucker- H um m el operator. T h e application of the O p tD er operator to extract the surface norm al vectors offers b etter detection for polyps in the range 5-10mm than theT able A-5: S en sitivity for p olyps < 5
m m
in real p atien t’s standard and low dosedata. _____________ ________________________
m A s T otal Sensitivity
Zuker
Sobel
OptDer
100 48 60.41% 60.41% 68.75%
Sobel operator (see T ab le A-2). It also provides a b etter detection of flat polyps when com pared to the perform ance of the Zucker-H um m el and Sobel operators (see T able A-3). W h en the Zuker-Hum m el, Sobel and O p tD er operators were used to calculate the surface norm als of th e colon w all for stan dard dose real patient datasets, the sensitivities for the detection of polyps > = 5mm were 88.89% (see T able A-4) for all operators, b u t the O p tD er operator provides higher sensitivity (see T able A -5) in the detection of sm all polyps (< 5mm) than the Zucker-Hummel and Sobel operators. T ab le A -5 indicates th a t the overall sen sitivity for polyp detection was highest when the O p tD er operator was used and the experim ental d a ta indicates th a t this operator outperform ed th e Zucker-Hum m el and the Sobel operators especially w hen the system is applied to low-dose datasets.
(a) (b)
F igu re A-2: 3D surface extractio n of a 12m m phantom polyp (radiation dose 13m A s). (a) T h e 3D surface extracted b y the C A D - C T C system using the Zucker- Hum m el operator, (b) T h e 3D surface extracted b y the C A D - C T C system using th e O p tD er operator.
A - 3
C o n c l u s i o n s
T h e m ain ob jective of this A p p en d ix was to address th e problem of robust calcula tion of the surface cu rvature in 3D C T data. A s numerous autom ated C A D - C T C
system s identify the colorectal polyps based on analysing the local convexity of the colon surface, one of th e m ost im portant steps in this analysis is the precise calcula tion of the norm al vectors. In th is regard, a num ber of 3D gradient operators were investigated and the experim ents were conducted on a large number of synthetic and real patient datasets. E xp erim en tal d a ta indicated th a t the com m only used 3D
(a) (b)
Figu re A-3: 3D surface extractio n of a 12mm phantom polyp (radiation dose 13m As). (a) T h e 3D surface extracted b y the C A D - C T C system using the Zucker- Hum m el operator, (b) T h e 3D surface extracted b y the C A D - C T C system using the O p tD er operator.
gradient operators such as Zucker-Hum m el and Sobel fail to accu rately determ ine the norm al vector w hen dealing w ith datasets characterized b y a low signal to noise ratio. To address this problem a new gradient operator was proposed th at was able to retu rn b etter perform ance when applied to C T d a ta th a t is acquired w ith different radiation dose levels.
T h is section describes a m ethod for the accurate segm entation of polyp candidate surface using a level-set segm entation m ethod. T h e level set is a deform able surface th a t evolves under a force th a t includes gradient and curvature. T he curvature p rop erty was exploited in the evolution to extract only the surface of the candidate p olyp to avoid over segm entation of the colon wall.
B - l
L e v e l - S e t I n i t i a l i s a t i o n . F a s t - M a r c h i n g A l g o
r i t h m
T h e form ulation of th e level-set form ulation is co n cep tu ally simple. T h e evolving curve or front T, evolves as the zero levelset of a higher dim ensional function (fi. This function deforms w ith a force F th at is dependent on b o th curvature of th e front and external forces in the im age. T h e force acts in the direction of the norm al to th e front.
(fit + F \V 0| = 0
cf)(x,y,t
= 0) = given ( B - l.l) T h e proposed im plem entation is a standard two step approach which includes a fast-m arching in itial step to speed up the segm entation. Fast m arching is a special case of the above equation w here F (x ,y ) > 0. L et T ( x , y) be the tim e when the front T crosses the point (x , y). T h e function T(x, y) then satisfies the equation;|V T |F = 1
(B-l.2)
w hich sim ply says th a t the gradient of the arrival tim e is inversely proportional to the speed o f th e surface. T h e T function is evaluated using the diffusion and a ttractio n to pixels w ithin the front. T his forces the front to grow out from its in itial position to points w ith th e sm allest value of T{x,y). T h e T ( x , y) function is then updated until th e front converges to a stab le state.
B - 2 L e v e l - S e t A n a l y s i s
T h e theory behind level-set segm entation is largely based on w ork in partial dif ferential equations and the propagation of fronts under intrinsic properties such as curvature [145, 146]. Representing the boun dary as the zero level set instance of a higher d imensional function (f>, the effects of curvature can be easily incorporated.
<j> is represented by the continuous Lipschitz function <p(s,t = 0) = FzLd, where d is th e signed distance from position s to th e initial interface TO (see Equation B -2.1). T h e distance is given a p ositive sign outside the initial boundary (DQ), a negative sign inside th e boundary (|fi \ <9i2|) and zero on the boun dary (<9£1).
/ —d
Vs e \ <9fA
¿ ( s ) = | 0 V s e d t t . (B-2.1)
\ + d Vs e R n \ d t t )
From this definition of 0, intrinsic properties of the front can be easily deter mined, like the norm al n = ± |^ [ ■
Since curvature of the p olyp is an im portant factor in the segm entation evolution, particular em phasis is given to this measure. T h e m ean curvature (H), is connected to the physical evolution of soap bubbles and the heat equation as follows:
" = V W
( B - 2 - 2 )G aussian curvature (K ), has also being used to m odel physical problem s and can be calculated using the following expression:
r„
V<pTAdj(HW)V<p
K = --- w w --- ( ’
where is the Hessian m atrix of <j), and Adj(H) is the adjoint of the m atrix H. T h e proposed m ethod used the Neskovic and K im ias [147] m easure of curvature which involves b o th m ean and G aussian. In this approach, the direction of flow is obtained from the M ean cu rvature w hile the m agnitude of the flow is d ictated by th e G aussian curvature. T h is is appropriate as the M ean curvature alone can cause singularities and extracts the strictly convex surface of the p olyp candidate.
k = sign(H)y/K + \K\ (B-2.4) Using this value for k, the level set is iteratively u p d ated w ithin a defined narrow band around the segm ented b o u n d ary to increase the com putational efficiency. T he
& + ! = (f>t + K t { 1 - £K)\V| + /3 V /.V 0 (B-2.5) w here £ and b eta are user defined param eters (see T ab le 1), k is the curvature term defined in E quation B-2.4and K j is the gradient dependent speed term and is given b y i +v j ■ T h e third term , V / .V 0 represents the attraction force vector normal to the front.
Possible p olyp candidate centres are determ ined over the entire d ata set by cal cu latin g the norm al vectors at each voxel on the colon wall. P olyp candidates are defined as regions of high convexity, therefore the centres for possible polyp candi dates are located at points th at contain high concentration o f norm al intersections (see C h ap ter 3).
T h e level set is initialised at the p olyp candidate centres and grows outwards until a stable boundary is encountered. T h e convex surface is m aintained b y placing a high influence on the curvature param eter. O nce the level-set has converged the surface of the p olyp candidate is taken as all boundary points th at have an associated gradient in order to ensure th a t on ly th e colon surface is extracted.
Tab le B -l: Control p aram eters used in the level-set segm entation [148],
following equation details the update parameters
Index C on trol Param eters Values
1 Fast-M arching Iterations 3
2 Level-set Iterations 10
3 Level-set £ 0.5
4 Level-set (3 0.08
5 Level-set N arrow bandw idth 10
O nce the tru e surface of th e p olyp candidates has being extracted, th ey are passed to a classifier to determ ine w hether th ey are p olyps or folds. T h e statistical features th a t are discussed in C h ap ter 3 are used to classify the candidate polyp surfaces into polyps or folds using the F N N N classifier.
B - 3
R e s u l t s
In to tal 181 polyp candidates were tested through the volum e. V isu al representa tions o f the segm entation p olyp are shown in Figure B - l. Table B - l lists the user defined param eters used in the level-set algorithm . From this tab le it can be seen
th at curvature is given a large influence to preserve the convexity of the polyp can didate surface. T h e narrow bandw idth is given a sm all value of 10 to increase the efficiency of the update.
(a) (b) (c)
.
lì
Haft
(d) (e) (f)
Figu re B -l: Im ages above show the p olyp candidate renderings of the extracted surface. Figures (a)-(c) show co rrectly classified polyps, where Figures (d)-(f) show correctly classified folds.
T able B-2 shows th e m easured point-to-curve error between the autom atic seg m entation results against those found from a m anual segm entation of the small num ber of p olyp candidates. Indicated in the tab le are the average error, standard d eviation of the error and the rootm ean - square (R M S) of the error. This error is m easured in voxels.
T ab le B-2: C on trol param eters used in the level-set segm entation. A verage Standard D eviation R M S
0.298 0.587 0.661
T able B-3 gives the results on two real patient supine d a ta sets. From the high num ber of p olyp surface candidates( 181 and 191), a relatively low number are de tected (6 and 3). T h e results show a sen sitivity of 100% for all polyps larger than
5mm. In current clinical studies th e p olyps below 5mm are discarded in the classifi cation. One cause th at generated the low sen sitivity for detection of polyps smaller th an 5mm is the low curvature difference between the p olyp and th e colon wall, therefore parts of th e colon w all is taken into the candidate surface (see Figure B-2). One p articu lar advantage of this surface extraction technique is the low num ber of false positives present in th e analysed data.
T a ale B-3: P erform ance analysis for autom atic polyp detection
D a ta Size D etected T P F P M issed
D a ta 1 Supine > 5 mm 6 3 3 0
(181 surf.) < 5 mm 0 0 0 2
D a ta 2 Supine > 5 mm 3 2 1 0
(191 surf.) < 5 mm 0 0 0 2
T o tal 9 5 4 4
Figu re B-2: O ne of th e < 5mm p olyps m isclassified due to the inclusion of colon w all in the surface extraction.
In conclusion, th e accurate segm entation described in this A p p en d ix is the first im p ortant step in th e classification of p olyp candidates into p olyp and fold. This A p p en d ix describes a m ethod for th e extractio n of accurate p olyp candidate surfaces using a level-set segm entation. T h e level-set is initialised using the distribution of surface norm al vectors and th e resulting surfaces are classified into polyp and non polyp. T h e level-set evolution is constrained b y the im age gradients and by the curvature of th e bo u n d ary and is able to perform robust p olyp segm entation when applied to stan dard and low dose datasets.
J o u r n a l P u b l i c a t i o n
• T arik A . Chow dhury, P au l F. W h elan , O vid iu G hita, N icholas Sezille, Shane Foley, D evelopm ent of a syn th etic phantom for the selection of optim al scan ning param eters in C A D - C T colonography, Journal o f M edical physics and Engineering, (A ccep ted for publication).
• T arik A . Chowdhury, P au l F. W h elan and O vid iu G hita, T h e use of 3D sur face fittin g for robust p olyp detection and classification in C T colonography, Journal of Com puterized M edical Im aging and G raphics (In P ress).
P e e r R e v i e w e d C o n f e r e n c e P a p e r s
• T arik Chow dhury, O vid iu G h ita, P au l W helan, E valuation of 3D gradient filters for estim ation o f th e surface orientation in C T C , Irish M achine Vision and Im age Processing Conference, 30th august - 1st Septem ber, 2006, Dublin, Ireland.
• T arik A . Chow dhury, O vid iu G h ita, Paul F. W helan and A b hilash M iranda, A N ote on Feature Selection for P o lyp D etection in C T Colonography, T he 18th International Conference on P a ttern Recognition, Hong K on g , 20-24 August, 2006.
• T arik A . Chowdhury, P a u l F. W helan, and O vid iu G hita, A M ethod for A u to m atic Segm entation o f C ollapsed Colons at C T Colonography, 2nd Indian In tern ation al Conference on A rtificial Intelligence, Decem ber 20-22, 2005, Pune, India.
• T arik A . Chow dhury, O vid iu G h ita and P au l F. W helan, A statistical approach for robust p olyp detection in C T colonography, 27th A n n u al International
Conference of th e IE E E E ngineering in M edicine and B iology Society, 1-4 Septem ber 2005, Shanghai, China.
• M ichael Lynch, T arik Chow dhury, O vid iu G h ita and P au l F. W helan (2005), D eterm ining C an d id ate P olyp M orphology from C T C olonography using a Level-Set M ethod, European M edical and Biological Engineering Conference E M B E C 2005, N ovem ber 2005, P ragu e, C zech Republic.
A b s t r a c t s a n d P o s t e r s
• T .A . Chow dhury, P.F. W helan, H. Fenlon, P. M acM athuna, E valuation of radiation dose on autom atic p olyp detection at C T colonography: Experim ents w ith a syn th etic phantom , A ssociation of P hysical Scientists in M edicine, 2005 A n n u al Scientific M eeting, G alw ay, 25-26February, 2005 (Poster Presentation).
• T .A . Chow dhury, R .J .T . Sadleir, P .F . W helan, N. Sezille, A . Moss, A . O Hare, S. Foley, H. Fenlon, P. M acM athu n a (2004), A u to m atic D etection of Colon at C T Colonography, Irish Society o f G astroenterology, W inter M eeting 2004 (A b stract / Presentation).
• R .J .T . Sadleir P .F . W helan, N. Sezille, T .A . Chowdhury, J. B ruzzi, A . Moss, P. M cM athuna, H. Fenlon (2004), A u to m a tic detection of colorectal polyps at C T colonography using shape inform ation, A ssociation of P hysical Scientists in M edicine, 2004 A nnual Scientific M eeting, D u b lin ,11th June 2004, (Presen tation ) .
• T .A . Chow dhury, R .J .T . Sadleir, P .F . W helan, A . Moss, J. Varden, M. Short, H. Fenlon, P. M acM athu n a (2004), T h e im pact of radiation dose on im aged polyp characteristics at C T colonography: E xperim ents w ith a syn th etic phan tom , A sso ciation of P hysical Scientists in M edicine, 2004 A n nual Scientific M eeting, D u b lin ,11th June 2004, (Presentation).
• R .J .T . Sadleir, P .F . W helan, N. Sezille, T .A . Chowdhury, A . M oss, J. Bruzzi, H. Fenlon, P. M acM athuna, C om pu ter-A id ed D etection of C olorectal Polyps at C T Colonography, Irish S o ciety of G astroen terology W inter 2003. (Poster Presentation).
U n d e r r e v i e w
• T arik A . Chowdhury, P aul F. W h elan and O vid iu G hita, A M ethod for A u to m atic Segm entation of C ollapsed Colons in C T D ata, International Journal of T om ography and Statistics, under review.