Honours Year Project Report Detection of Fractures in Digital X-Ray Images

Transcription

1 Honours Year Project eort Detecton of Fractures n Dgtal X-ay Images By Vneta Lum La Fun Deartment of Comuter Scence School of Comutng Natonal Unversty of Sngaore 2004/2005

2 Honours Year Project eort Detecton of Fractures n Dgtal X-ay Images By Vneta Lum La Fun Deartment of Comuter Scence School of Comutng Natonal Unversty of Sngaore 2004/2005 Project No: Advsor: Delverables: H A/Prof. Leow Wee Kheng eort: Volume 2

3 Abstract Many eole n the world suffer from bone fractures. In Unted States alone, 6,800,000 eole wll fracture a bone n one year. Doctors use X-ray mages to determne the fracture oston, tye etc. Doctors have to nsect numerous x-ray mages everyday. However, wth only a low ercentage of % of the mages actually showng fractures, the task s very tedous and exhaustng, ossbly resultng n naccurate dagnoss by the doctors. Automated fracture detecton can releve the doctors' workload by screenng out the easer cases, leavng a few dffcult cases and the second confrmaton for the doctors' closer examnaton. There are already exstng classfers to detecton bone fracture but the ndvdual classfers have rather low fracture detecton rate. Each of the classfer s caable n detectng dfferent tye of fracture on the bones. So, by combnng the classfers both the fracture detecton rate and classfcaton accuracy wll then mrove sgnfcantly. We are takng two aroaches n combnng the classfers namely by combnng the aosteror robabllty P healthy samle and P fracture samle and combnng the classfcaton decson, n ths case t s ether fractured or healthy. Combnatons of feature tyes Intensty Gradent drecton, Gabor orentaton and Markov andom Feld wth the three classfers Bayesan, Probablstc Suort Vector Machne SVM, GnSVM roduces the aosteror robabllty as well as the classfcaton decson. These robabltes and classfcatons are then combned usng the varous combnaton rules to yeld better classfcaton accuracy and fracture detecton rate. Subject descrtors: I.5.2 Classfer desgn and evaluaton I.5.4 Alcatons J.3 Lfe and Medcal Scences Keywords: Fracture detecton, classfcaton, combnng classfers, suort vector machne Imlementaton software and hardware: Intel Pentum IV PC, Wndows XP Professonal, Lnux Fedora 2, Mcrosoft Excel, Matlab 6.5 r3, Matlab 7 3

4 Acknowledgements Frst and foremost, I would lke to thank my suervsor, A/Prof Leow Wee Kheng, for hs suort and hel throughout the course of the roject. He has been very atent wth me when I encountered roblems whle dong ths roject. Hs sound advce and excellent suggestons allowed me to get through qute a few tght atches. Hs knowledge of the subject at hand and nnovatve deas on how to tackle roblems are truly astoundng. I have learnt so much from hm throughout the duraton of a year. Next, I would lke to thank my mentors, Chen Yng and Denns Lm for ther gudance and hel on matters of mlementaton. They sent a huge amount of tme tryng to exlan to me about the ast work done n fracture detecton. I have troubled them numerous tmes wth my roblems, and they have always been atent and always tred to hel to the best of ther abltes. They are excellent mentor n gudng me n the feld of fracture detecton. Next on the lst are my frends n SoC. Some I have known for years, others for just a few months. The fun and laughter that we shared has heled me ths stressful erod. I dd enjoy the comanon of workng together Honours Year Lab 7.I had memorable moments whle workng wth my fellow lab mates. 4

5 Lst of Fgures:. The femur bone and a close u of the uer extremty.8.2 Neck-Shaft Angle Sde vew and front vew of the wrst bone X-ray mage of a bone wth dstal radus fracture.9 3. Feature extracton flow chart Classfcaton and combnaton flow chart Adatve samlng done on the radus.8 Lst of Tables:. Statstc of wrst fracture tye esults of tranng and testng when the left and rght femur mages are n two searate sets esults of tranng and testng the combned set of left and rght femur mages esults on the revous work done on radus Testng results of the dfferent feature tyes on radus mages esults of the alcaton of varous combnaton rules on the left and rght femur mages n searate sets esults of the alcaton of varous combnaton rules on the combned set of left and rght mages esults of votng method on femur mages esults of the alcaton of combnaton rule on the results on wrst bone esults of the votng methods on the wrst bone.46 5

6 Chater Introducton. MOTIVATION Many eole n the world suffer from bone fractures resultng from varous knds of njures. In Unted States alone, 6,800,000 eole wll fracture a bone n one day. As one s age ncreases, the chance for a erson to suffer an osteoorotc fracture wll also ncrease. In fact, the number of h fractures resultng from osteooross s set to soar, from.7 mllon worldwde n 990 to 6.3 mllon by 2050, wth Asans accountng for most of the ncrease. These stunnng fgures from the Internatonal Osteooross Foundaton are erhas surrsng, but defntely sgnfcant Internatonal Osteooross Foundaton, Osteooross s an alment whch s rated by the World Health Organzaton as the second greatest healthcare roblem n the world. That makes the doctors burden even heaver. Everyday, doctors vsually nsect numerous h x-ray mages for sgns of fracture. In Sngaore tself, there are some 800 annual cases of h fractures n Sngaore from osteooross alone, of whch 350 cases are seen by the Sngaore General Hostal SGH.Statstcs show that the bulk of h radograms x-rays examned by doctors are, n fact, healthy. For examle, among the samles of x-ray mages used for ths roject, only about % of the femur mages and 30% of the radus mages are fractured cases. In SGH, doctors vsually examne each x-ray twce before a dagnoss s made. After makng ther observatons of the geometry, texture and shae of the bone, they make a dagnoss based on certan rules. Ths s a tedous and tme-consumng rocess that s erformed twce over all x-rays. It has been found that a doctor workng under fatgue may fal to correctly dagnose a fracture. Ths wll lead to a serous mlcaton on the doctor s erformance as well as the mact on the atent. Wth ncreasng lfe exectancy and oulaton ncrease, the doctors job can only become more dauntng. However, comuters never feel trng n dong such knd of tedous, reeated, tme consumng job. Why not use comuters to assst the doctors? Comuters are unaffected by fatgue and can thus mantan a hgh level of effcency ndefntely. They can also erform the fracture detecton rocess faster, thus savng tme. Moreover, storng X-ray 6

7 mages n dgtal format s also a trend n hostals and makes our automated system more feasble. However, the comuter can only act as an ade because we stll need the exerence and rofessonal knowledge of the doctors to erform the second examnaton on some of the less obvous cases whch the rogram cannot classfy accurately. However, the comuter can re-screen all the mages and classfy the more obvous cases to ease the doctors burden. Sngaore General Hostal and School of Comutng, Natonal Unversty of Sngaore are cooeratng n the medcal comutng research. That s also an actve research area worldwde. It s really my honor to be nvolved n ths research. I hoe that ths thess could extend the ast works and fnally one day a mature, robust and accurate human body automated X-ray fracture detecton system wll be used among the hostals. Comuter technques that can detect fractures from x-rays are now avalable, but we would lke to further mrove on the erformance by alyng the technques to combne the classfers as the ndvdual classfers have dfferent caabltes n detectng varous forms of bone fractures. We are hong to combne the strength of these classfers to obtan a more accurate classfcaton. Ths roject s also an nterestng alcaton of usng the exstng technques to extract the Intensty Gradent drecton, Gabor orentaton and Markov andom Feld from the X-ray mages. The features are then classfed usng Bayesan, Probablstc SVM or the GnSVM whch return aosteror robablty and the classfcaton decson. We aly varous combnaton strateges on the aosteror robabltes and the classfcaton decsons. Besdes that, we beleve that by alyng the nose removal and texture enhancement n the extracton stage and usng a more effcent classfer wll further refne the ntal rocesses of the system and hence lead to a more accurate classfcaton. Before we go nto more detal about them, we shall frst have an overvew of the structures of the femur and radus, whch are the bones on whch the fracture detecton technques have been focusng on..2 Structure of Femur Lm et al The femur s the longest and strongest bone n the skeleton. It s almost cylndrcal n the greater art of ts extent. The femur, lke other long bones, s dvsble nto a body and two extremtes. For our research, we shall focus on the uer extremty. 7

8 .2. The Uer Extremty roxmal extremty. The uer extremty resents for examnaton a head, a neck, a greater and a lesser trochanter. See fgure. for an llustraton.2.. The Head caut femors The head s globular and forms a hemshere. It s drected uward and a lttle forward, wth the greater art of ts convexty beng above and n front. Its surface s smooth, coated wth cartlage n the fresh state, excet over an ovod deresson, the fovea cats femors, whch s stuated a lttle below and behnd the center of the head. Ths s where the lgament s attached to The Neck collum femors The neck s a flattened yramdal rocess of bone, whch connects the head wth the body.in an adult, the neck forms an angle of about 25 wth the body. Ths angle s known as the neck-shaft angle. In fgure.2, the neck-shaft angle s reresented by θ. 8

9 .2..3 The Trochanters The trochanters are romnent rocesses whch afford leverage to the muscles that rotate the thgh on ts axs. There are two of them, the greater and the lesser. The Greater Trochanter trochanter major s a large, rregular, quadrlateral rojecton whch s stuated at the juncton of the neck wth the uer art of the body. It s drected a lttle lateralward and backward, and, n the adult, s about cm. lower than the head. It has two surfaces and four borders. The Lesser Trochanter trochanter mnor s a concal rojecton whch vares n sze n dfferent subjects; t rojects from the lower and back art of the base of the neck..3 Structure of the radus and the Common Fractures adus s one of the most common arts of the bone whch suffers from fracture. Ths s because the radus are not as strong comared to the other bones for examle the femur. When a atent falls down or ht on a hard object, the art whch s mostly lkely to suffer from fractures s the wrst bone. Let us look take a quck look at the structure of the radus and the common fractures on Fgure.3: Sde vew and front vew of the hand bone Comare the healthy samle above wth the fractured one below. Fgure.4: X-ray mage of a bone wth dstal radus fracture 9

10 We can observe n the x-ray mages of the healthy and fractured samle that the texture atch and the ntensty of the fractured art of the bone s dfferent from the healthy ones. Fracture Tye Number of Images Percentage In Total Percentage In Fractured.adus.% 2.7% Fracture Only 2.Ulna 0 0.0% 0.0% Fracture Only 3.Both 3 3.3% 8.% adus & Ulna Fracture 4.Dstal % 59.5% adus Fracture Only 5.Dstal 6 6.7% 6.2% adus & Ulna Stylod Fracture 6.Dstal 3 3.3% 8.% adus &Ulna Fracture 7.Ulna.% 2.7% Stylod Fracture Only 8.Frst.% 2.7% Metacaral Fracture Subtotal 37 4.% 00% No Fractures % Total 90 00% Table.: Statstc of wrst fracture tye Just a bref nterretaton on the table above, we can see that 8/0 of the fractures on wrst bones are dstal radus fracture. Hence n ths art of the roject, we are gong to concentrate only on the dstal radus fracture..4 esearch Objectves The man objectve of ths roject s to mrove the classfcaton accuracy and fracture detecton rate of the femur and radus mages by combnng classfers. For the femurs, much effort has been contrbuted searately n ths area esecally n the alcaton of dfferent extracton algorthms. On the other hand, varous classfers were also used n 0

11 revous researches. As for the radus, only lmted research work was done on t. We am to gather the strength n each extracton algorthm and select the best avalable classfers. By makng mrovements n the extracton, classfcaton and combnaton rocess, ths wll lead us to acheve better erformance n terms of classfcaton accuracy and fracture detecton rate. The mroved system s gong to be aled to the radus to rove that the system s ndeed better than the exstng ones. Ths slts the roject nto the followng sub-objectves: Before we combne the classfers, we need to fnd the ossble ways to mrove on the feature extracton as well as the classfcaton. We need to fnd a method to combne the results of the varous classfers n order to acheve the best ossble classfcaton accuracy and fracture detecton rate. We need to conclude on the best derved methods to erform extracton, classfcaton and combnaton and aly t to the radus. We also attemt to adat the derved methods to be aled on other arts of the body..5 Contrbuton to esearch In our roject we have managed to make the followng useful contrbuton n the area of medcal magng artcularly n bone fracture detecton: We ntegrated the varous feature extracton algorthm for more effcent extracton. We exlored the varous classfers to select the most effcent classfer avalable. We comared the erformance of robablstc SVM versus standard SVM. We aled varous combnaton rules to mrove on the classfcaton and fracture detecton results. We develoed a method to comlement the exstng way of classfcaton. We used robablty nstead of just the classfcaton decson n the combnaton of classfer. We modfed the extracton and classfcaton algorthm to aly t on the radus. We have sgnfcantly mroved the femur and radus classfcaton accuracy and fracture detecton rate

12 .6 Organzaton of eort After ntroducton we are gong to look at the related works of ths roject n chater 2. It wll be followed by the major hases of ths roject whch are namely the feature extracton n chater 3, classfcaton n chater 4 and combnng classfers n chater 5. The exermental tests carred out n ths roject and ts results wll then be dscussed n chater 6. The suggeston for future works wll be ncluded n chater 7. 2

13 Chater 2 elated Works 2. Fracture Detecton Tan T. P. et al s robably the frst to successfully erform automated fracture detecton n femur by usng vsual method. They used comuter vson methods to measure the angle between the neck and the shaft axes of the femur. For certan tye of the femur fracture, such as large dstorton of the neck-shaft angle, ther method s roved to be robust and relable. Ya W. H. et al attemted femur fracture detecton by another aroach that s the texture analyss. They used the gabor flters to extract the drecton ma accordng to the trabecular lnes on femur bone surface and use the ma to detect the fractures. The method works only on certan tye of fractures bascally fractures wth obvous cracks, but ts combnaton wth Tan s work was very successful to ncrease the classfcaton accuracy and fracture detecton rate. Sze W. K. et al used the nformaton of shae of the femur to detect the fractures. He detects the fracture bascally by frstly landmark the femur bone contour and then classfy t. 2.2 Suort Vector Machne SVM Suort vector machne s an ncreasng oular learnng theory whch s aled n the machne learnng feld. It has been aled n varous categorzatons for examle the euter s text-categorzaton and face detecton roblem. An advantage of SVM over other learnng theory s that t can be analyzed theoretcally usng comutatonal theory and also yeld good erformance when t s aled to real world roblem. There are two common grous of SVMs, namely the standard SVM and the robablstc SVM. Most of the SVMs aly smlar algorthms for classfcatons but the robablstc SVM takes extra stes to derve the robablty on to of just ure classfcaton. Examles of the ways to derve the robablty are comutng the dstance of the samle from the hyer lane whch searates the samles nto grous and fttng the SVM outut to a sgmod functon. The robablstc SVM has advantages over the standard SVM because the derved robablty can be used as a confdence measure to show that how strongly the SVM suort the classfcaton of a artcular samle. 3

14 Chater 3 Feature Extracton 3. Overvew of the algorthm Fgure 3.: Feature extracton flow chart The two flow charts n Fgure 3. and Fgure 3.2 llustrate the algorthm aled n ths roject. The frst chart llustrates the adated algorthms whle the second charts llustrate the new algorthms. For the frst chart, the boxes n lght urle are our raw data. The nk boxes are the modfcaton of adated algorthm to rerocess the mages before the feature extracton s done. The boxes n hot nk are the mlement exstng algorthm to extract the varous features namely the Gabor orentaton, Intensty Gradent drecton and 4

15 Markov andom feld. At the end of the extracton stage we get a ma for each feature extracton. The average of all the healthy samle mas s comled nto a mean ma. As for the second chart, the dfference ma s the ma whch contans the dfference between a samle s ma and the mean ma. There are three tyes of dfference mas corresondng to the three feature tyes. The red arrow leads to classfcaton usng three dfferent classfers. The yellow arrow takes the outut of classfcaton and combnes them usng fve combnaton rules. Fgure 3.2: Classfcaton and combnaton flow chart 5

16 3.2 Nose emoval Lm 2004 The frst ste n the feature extracton rocess s nose removal.as we know, we are dealng wth dgtal mages and t s bound to have some form of nose. In order to ncrease the accuracy for feature extracton we would lke to have as lttle nose as ossble n the mages. Ths s artcularly mortant n ntensty gradent as the ntensty based method s very suscetble to nose. Nose can cause the algorthm to wrongly calculate the ntensty gradent drecton. If the feature extracton ste nvolves some error, ths s ultmately dmnshng the accuracy of our classfcaton as the error wll be carred through the whole rocess of detectng bone fracture. Another otental source of error s the trabeculae whch wll be shown as lght and dark rdges n the x-ray mages. The soluton aled to solve ths roblem s to aly medan flterng to the mages. Medan flterng serves the urose of smoothng the lnes caused by trabeculae and also remove most nose. 3.3 Contrast Enhancement Ya 2003 Dgtzed x-ray mages are stored as Dgtal Imagng and Communcatons n Medcne DICOM format. These are grayscale mages whereby each xel s reresented as an ntensty level. The ntensty level ranges from 0 ure black to ure whte. The wder the ga s between the ntensty levels of the xels, the greater contrast we can see n the mage. However, the ranges for the ntensty levels of most bone mages are rather narrow. In Gabor Flterng, we need to extract the texture orentaton. The accuracy of the extracton deends a lot on the clarty of orented texture. The bgger the contrast, the clearer the orented texture wll be. In order to acheve ths, we frst buld an ntensty hstogram or the orgnal mage I and t s then adjusted so that the ntenstes n the range [ mn, max ] s sread through the entre range of [0,] n the texture contrast enhanced mage I. 6

17 3.4 Adatve Samlng Ya 2003 Bone mages come n dfferent shaes and szes deendng on the condton of the bone, age and gender of the atent. We must be able to determne the corresondng regons across dfferent mages before we can erform feature extracton on t. One of the standard methods s by normalzng the sze of the nut mages. Ths s not a feasble method as the mortant texture nformaton mght be removed or nose wll be ntroduced. Hence, adatve samlng method s used. The samled locaton n dfferent mages corresonds to consstent locatons n the normalzed samlng grd. From the set of contour onts P we obtaned usng the snake method, the bound of the regon of nterest OI s found. The to-left corner of the OI s x mn, y mn and bottom rght corner s x max, y max. The to-left corner u, v s ntalzed to x mn, y mn and and subsequent regons are obtaned by ncrementng u by u and v by v. The samled regons have a wdth of S x and S y. Where S x and S y are S SS x max x + / n + x 2 mn x S y 2 y max y mn+ / ny + 2 n x and n y are the number of samles horzontally and vertcally n the OI and they are set as constants for all bones. By settng the wdth and heght n ths way we can ensure that the samled regons have szes whch wll cover the whole OI. In order to maxmze the coverage and avodng the sace near the contour beng left out, the samled regons are made to overla by half ther dmensons horzontally and vertcally. Smlar extracton dea was aled to the femur and radus mages. In terms of adatve samlng we have to adjust the sze of the boundng box as now the radus whch we are dealng wth s smaller comared to the femur. Here we use the radus to 7

18 llustrate how adatve samlng s done. We must make sure that the ga between grds are small so that we do not mss out on any fractures and also the box has to be bg enough to cover most art of the radus bone. We have chosen the wdth of the box to be 8 and the heght to be 5. Each grd s 5 x 5 xels. After the extracton s done, we wll obtan a feature ma whch has the sze of 8 x 5.Ths ma s used n Markov andom Feld, Gabor Flter or Intensty Gradent. Then we wll end u wth a dfference ma by takng the dfference between the mean mas of healthy samle wth each of the feature ma. Fgure 3.3: Adatve samlng done on the radus. 3.5 Extracton based on feature tye Subsequent stes are determned by the feature tye we are nterested n. There are 3 feature tyes are namely Gabor orentaton, Intensty gradent drecton and Markov andom Feld Gabor Flter Ya 2003 In Gabor Flterng, each of the samled regons s convolved usng Gabor Flter whch s senstve to the orentaton of the bone texture. The most domnant orentaton for the samled regon s encoded n unt vector form based on the Gabor Flter resonses. The unt vector s drecton reflects the orentaton. A channel n the Gabor Flter Bank s obtaned by combnng the orented Gaussan h x,y h x,y g x,y ex2π j f x 3 8

19 2 x' / λ + y' g x,y ex 2 2 2πλσ 2σ 2 4 wth the real and magnary art of the comlex snusodal gratng whch s as follows. ex2π j f x cos 2π f x +j sn2 π f x 5 hc f, θ x, y g x', y'cos2πfx' 6 hs f, θ x, y g x', y'sn2πfx' 7 Where x ', y' x cosθ + y snθ, xsnθ + y cosθ θ s the orentaton of the Gaussan from x axs λ s the asect rato σ s the standard devaton of the Gaussan f s the frequency The frequency f s the most revalent frequency of the bone found through the analyss of bone texture. It s then used as the centre frequency n the Gabor Flter bank descrbed above. A Gabor Flter bank of frequency and 8 orentaton channels s used to extract the orentaton of the texture atterns n the femur. The detected orentaton of the samled regon s reresented usng two dmensonal unt vectors. These unt vectors are then comled nto orentaton mas Intensty Gradent Lm 2004 As for ntensty gradent, we extract the ntensty gradent from the samled regon n each femur mage and then comle them nto ntensty gradent mas. 9

20 We fnd the maxmum ntensty gradent magntude by lookng for the ont n the mage wth the greatest magntude dfference comared to the centre of the samled regon. The drecton of the ntensty gradent s determned by the oston of the ont and ts value comared to the value of the centre of the samled regon. Each samle s unquely reresented by ts own ntensty gradent ma wth the ntensty gradent drecton n each of the samled regon Markov andom Feld Xng 2004 In Markov andom Feld, Markov andom Feld model arameter θ for each samled regon of each mage. The model arameter values comose a feature ma for each mage. The model arameter θ s calculated usng the Least Squares Ft method. We frst wrte the square of error as: Where e f ntensty of the xel at θ q model arameter f q f + q + ε q q n θ ε q nose, usually a Gaussan random varable wth zero mean and varance N neghborhood centered at 2 For each xel, by ckng a sze of neghborhood N as 3 x 3 we get 9 f + q f + q2... f + q9 θ... θ T f 2 We then obtan over determned matrx multlcaton 20

21 f + q f + q2... f + q9 f + q f 2 + q f 2 + q2... f 2 + q9 T f 2 + q2 θ.... θ f n + q f n + q2... f n + q9 f n + q9 Ths s n the form of AX B We can then solve for X usng X A A T A T B Now we would have an orentaton ma Gabor orentaton, ntensty gradent ma Intensty Gradent drecton and feature ma Markov andom Feld for each of the samle. The mean ma s the average of all the healthy samles. For each of the samle, we buld a dfference ma whch reresents the dfference between the mean ma and the ma of that samle. The ma of a fractured samle wll most lkely dffer from the mean ma to a great extent. 2

22 Chater 4 Classfcaton 4. Bayesan Lm et al We are famlar wth the Bayes ule whch s x class class class x x x class s ether x healthy or x fracture.it s estmated by usng the sets of healthy and fracture tranng samles dfference mas whch are modeled by a multvarate Gaussan functon. x s the dfference ma of a artcular samle. The ror robablty for femur, fracture and healthy are 0.5 and 0.85 for the left and 0.08 and 0.92 for the rght whereas for radus, fracture and healthy are 0.3 and 0.7 for both left and rght. The denomnator x s the same for both healthy x and fracture x and so t can be gnored as we are comarng healthy x and fracture x to see whch one s bgger. The artcular samle s classfed as healthy f healthy x > fracture x and vce versa. One drawback n ths method s that we have too few fracture samles for accurate estmaton of the multvarate Gaussan. The fractured samles are unlkely to be well clustered n the feature sace. We would want to cluster the fracture samles n to several clusters based on ther smlarty and then model each cluster usng a dfferent multvarate Gaussan, unfortunately ths s unable to be acheve when we do not have enough fractured samle. 4.2 Probablstc Suort Vector Machne SVM Platt 999 In order to aly the varous combnaton rules, we need to have the outut of the classfer as aosteror robabltes. The aosteror robabltes reflect the confdence 22

23 measure of the classfcaton. The standard SVMs ncludng those whch have been used by the revous students who were dong rojects n ths area do not rovde such robabltes, t only returns the classfcaton decson. In the robablstc SVM whch we are usng n ths roject as one of the classfers, we tran the SVM and then ma the SVM oututs to the robabltes usng a sgmod functon Standard SVM After tranng the SVM, we have a SVM model whch s a structure of the Lagrangans weght, bas, suort vectors and the number of suort vectors. We then make use of these arameters for classfcaton.let the unthresholded outut of the SVM be derved from the followng functons Where y s the class of the nut α s the Lagrangans weght k x, x s the kernel functon b s the bas f x h x + b h x yα k x, x 2 fx s known as the dscrmnant functon whch mas the nut samles to an outut value usng the kernel exanson. The samle s classfed as healthy f the outut of the dscrmnant functon s larger than 0 and vce versa. In ths roject, the kernel functon we used was adal Bass Functon 2 x x k x, x ex 3 2 nσ The arameter σ s chosen to be snce t gves the best classfcaton results out of those values whch were we tested on. In order to use as σ, we must set the arg to durng the tranng hase. 23

24 4.2.2 Fndng the sgmod arameters Wth the outut of the SVM usng the tranng set, the arameters for the sgmod are estmated usng the Maxmum-Lkelhood method on the tranng set n the sgmod model. f, y and stored We defne a new tranng set f, t, where the t are the target robabltes defned as y + t 4 2 The arameters A and B are found by mnmzng the negatve log lkelhood of the tranng data, whch s a cross- entroy error functon: mn t log + + tlog 5 Where + ex Af + B Fttng a Sgmod After the SVM The arameters of the model are adated to gve the best robablty oututs. We aly the followng equaton to evaluate the sgmod functon. y f 7 + ex Af + B We take the mnmum and maxmum outut value of fx and dvde the values between them nto 00. Ths gves us the f for the above equaton. y means the sgmod wll actually yeld the result as the aosteror robablty healthy samle.subsequently we can get fracture samle by - healthy samle. A and B are the sgmod model arameters. We then get a sgmod whch s used for the testng samles. 24

25 4.2.4 Obtan the Probabltes for Testng Samles The testng samles are then classfed usng the same SVM model we obtaned from the tranng. Each of the outut of the classfcaton s then used as f n the sgmod functon to obtan the aosteror healthy samle. 4.3 Gn Suort Vector Machne SVM Chakrabartty et al Gn SVM s used n ths roject because t roduces the aosteror robabltes whch are needed n order to aly the combnaton rules. Ths toolbox runs on Lnux. We can later see n the results art of ths reort that the Gn SVM s a very useful tool as t s classfcaton accuracy s by far the hghest comared wth the Bayesan and Probablstc SVM How to Tran and Test the Gn SVM The tranng and testng data are stored n.dat fles. The tranng and testng fles start wth the feature dmenson, number of classes 2 and the number of data onts number of tranng and testng samles, label only for tranng fle, the resence of label s ndcated by -flag, weght f alcable and featuresdfferences ma n a column vector. A scrt n Perl s then wrtten to read n the.dat fles, together wth several arameters to do the tranng and testng. Those arameters ncludes k kernel tye, - kernel arameter a, -2 kernel arameter band C the Global egularzaton constant. There are 2 kernel tyes namely the olynomal kernel a + b x. y c and the Gaussan kernel ex a x y 2.Both kernel tyes were tred but the olynomal kernel seems to gve very oor classfcaton accuracy. Attenton s then dverted n usng the Gaussan kernel and varous values for the arameter a were used to fnd the value whch gves the best accuracy because there s no secfc rules n choose the arameters. The values tred were 0.0, 0.,, 2, 5, 0, 00 and From the observaton, we can see that the accuracy of classfcaton s very senstve towards the arameter a. A slght dfference n the value mght cause the classfcaton rate to dro tremendously. The weght arameter 25

26 whch s C s assumed to be ncluded n the data when -cflag s resent n the command lne. The value C 5 s used for the healthy samle and C00 s used for the fractured samle because we have much fewer fracture samles than the healthy samles. Ths s just an examle of how to use the Gn SVM. Detals on the setu of each exermental test carred out n ths roject wll be ncluded n chater Theory on how Gn SVM works Gn SVM uses regresson n generatng the aosteror robablty. Same as the Probablstc SVM, t s a kernel based model as well. Estmaton of the condtonal robablty class samle from the tranng data x[n] and labels y [n] can be obtaned usng a regularzed form of kernel logstc regresson. For each outgong state j, one such robablstc model can be constructed for the ncomng state condtonal on x[n]: j ex f j x[ n] / S S 0 ex f x[ n] S s the number of classes and f sj x s the functon for kernel exanson over the tranng data x[m] by transformng the data to feature sace. The functon f s the same as the one n Probablstc SVM. However, besdes usng the adal Bass Functon and Polynomal we can also use the DTK Strng Kernel n the Gn SVM. sj 8 Gn SVM roduces a sarse soluton by otmzng a dual otmzaton functonal usng a lower bound of the dual logstc functonal. For the bnary class Gn SVM we are usng n ths roject, the margn s defned as the extent over whch data onts are asymtotcally normally dstrbuted. A lne s ftted to searate the data onts nto two, namely the healthy and fracture clusters. The dstrbuton dstance z from one sde of the margn for one data s then calculated n order to estmate the robablty. 26

27 Chater 5 Combnng Classfers 5. Motvaton The ultmate goal n detectng bone fracture detecton system s to acheve the hghest classfcaton accuracy and fracture detecton rate ossble. Ths objectve tradtonally led to the develoment of dfferent classfcaton schemes for the bone fracture detecton. Thus far, the most common classfers used n ths feld are Bayesan and SVM. Dfferent mlementaton of the SVM wll exhbt dfferent erformance deendng on the samles as well as the effcency of the tranng. The results of the exerment done usng the varous classfers wll be the bass for choosng one of the classfers as a fnal soluton used for that roblem. It has been observed that although one of the classfers mght out erform the others but the set of samles msclassfed by the dfferent classfers mght not necessarly overla. Ths shows us the otental that dfferent classfers are a comlment of each other. A samle whch s wrongly classfed usng a classfer mght be correctly classfed usng other classfers. The observaton has motvated the nterest n combnng the classfers n detectng bone fractures. Ths aroach does not conventonally rely on the decson of a sngle classfer. Instead, all the decsons of the classfers are taken nto consderaton. The ndvdual decson s combned to derve a consensus decson. It has been exermentally demonstrated that some of the combnaton scheme consstently outerforms a sngle best classfer. However, there sn t any convncng exlanaton on why some combnaton schemes are better than the others and n what crcumstances. As we can see n the results from the alcaton of the combnaton scheme, ts erformance vares wth the dfferent samles used. 27

28 5.2 Values Obtaned from Classfers We made use of the Bayesan classfer, Probablstc SVM and the Gn SVM whch gve us the aosteror robabltes healthy samle and fracture samle as well as a classfcaton decson on whether the samle s classfed as healthy or fracture. Ths nformaton s used n varous combnaton schemes. We have 3 feature tyes Gabor orentaton, Markov andom Feld and Intensty gradent drecton and 3 classfers Bayesan, Probablstc SVM and Gn SVM. So we get 9 dfferent robabltes and classfcatons out of the combnaton of feature tyes and classfers. 5.3 Theoretcal Framework Kttler et al. 998 Consder any roblem where the attern Z s to be assgned to one of the m ossble classes {w,.w m }. Let us assume that we have classfers each reresentng the gven samle by a dstnct measurement. Denote the measurement of samle used by the -th classfer by x. In the samle sace, each class w k s modeled usng the robablty densty functon x w k and ts aror robablty of occurrence s denoted by w k. In ths case, we have Z as the feature ma of the samle, m s 2 namely healthy and fractured so we have w and w 2. s assgned to 3 because we are combnng 3 classfers. Accordng to the Bayesan theory, gven the samle measurement x,,.. the attern Z wll be assgned to the class w j.e θ f the aosteror robablty of he nterretaton s the maxmum. assgn θ f j θ j x,... x max θ k x,... x Ths would requre us to comuter the robabltes of the varous hyotheses by consderng all the measurements smultaneously n order to reach a decson. However, ths may not be a ractcal rooston. k 28

29 We attemt to smlfy the above rule by exressng t n terms of decson suort comutatons erformed by ndvdual classfer. Ths aroach wll lead to the ractcal combnaton rules namely the roduct rule and sum rule as well as a range of effcent classfer combnaton strateges. The aosteror robablty can be rewrtten as,...,...,... k k k x x x x x x θ θ 2 accordng to the Bayes Theorem. x, x s the uncondtonal measurement jont robablty densty and can be exressed n terms of the condtonal measurement dstrbutons and hence we can only concentrate on the numerator of the equaton Dervaton of Product ule We can exress the jont robablty dstrbuton of the measurements extracted by the classfers as k k x x x,... θ θ 3 By substtutng 3 nto 2 we get m j j j k k k x x x x,... θ θ θ 4 By usng ths equaton, we can exress the decson rule as 29

30 5 k k m k j j f j x x assgn max θ θ θ Dervaton of Sum ule We may assume that the aosteror robabltes comuted by the classfers wll not devate dramatcally from the ror robabltes. Under such assumton we may say that k k k x δ θ θ + 6 By substtutng ths nto the roduct rule and exandng the roduct the followng sum decson rule s yelded k k m k j j f j x x assgn ] max[ θ θ Wth the roduct rule and the sum rule, we can derve several combnaton strateges. 5.4 Classfer Combnaton Strateges The roduct and sum combnaton rule can be aroxmated by the uer or lower bounds based on the followng relatonsh max mn k k k k x x x x θ θ θ θ 8 The hardenng of the aosteror robabltes roduce the bnary valued functon as k max j m j k k x x θ θ 9 0 otherwse allows us to combne the decson outcome nstead of the aosteror robabltes. 30

31 These aroxmaton yelds the followng rules: Max rule max θ j max max θ k x m k 0 Mn rule mn θ j max mn θ k x m k Majorty ule j m max k k 2 These combnaton rules and strateges are aled to the values outut by the classfers to determne a good decson on whether the samle gven s healthy or fracture. The outut values used by the combnaton strateges can ether be aosteror robabltes or classfcaton decsons deendng on the ndvdual strategy. We also further attemt to mrove the classfcaton accuracy and fracture detecton rate by flng the rght mages to make u a bgger set of tranng and testng samle. Ths wll result n a more otmum tranng and hence lead to a further mrovement n the erformance when the combnaton rules are aled. 3

32 Chater 6 Exermental Tests 6. Test Setu We have managed to obtan 432 femur mages from a local ublc hostal. These mages are then randomly dvded nto 62 tranng and 54 testng samles each on the left and rght makng a total of 324 tranng and 08 testng samles. The ercentages of the fractured and healthy samle are ket almost the same n the tranng and testng samles. In the tranng set, 39 femurs are fractured 25 on the left and 4 on the rght and n the testng set 2 were fractured 8 on the left and 4 on the rght. The ercentage of fractured on the left s about 5% and 8% on the rght. As for the wrst mages, they were obtaned from the same hostal and dvded randomly nto 7 tranng 29 for the left and 42 on the rght and on the left and 4 on the rght testng mages. The ercentage of fractured cases n the tranng and testng sets were ket aroxmately the same 30%. In the tranng set, 2 8 on the left and 3 on the rght radus bones were fractured whereas 23 0 on the left and 3 on the rght were fractured n the testng set. We are not able to get balanced number of the wrst mages because out of all the mages whch we get only a small orton of them are usable. Some of them are too blur or there were already mlant n t. Ths s due to the fact that we are usng raw data from the hostal and the suly of mages s subjected to avalablty. There are 4 dfferent hases of the exermental tests carred out n ths roject. Phase Do a searate test on left and rght femur mages usng each of the classfers to evaluate the erformance of the ndvdual classfer. The 9 combnatons are Gabor flter Bayesan, Gabor flter- Probablstc SVM, Gabor flter Gn SVM, Intensty gradent Bayesan, Intensty gradent - Probablstc SVM, Intensty gradent Gn SVM, Markov 32

33 andom Feld Bayesan, Markov andom Feld - Probablstc SVM, Markov andom Feld Gn SVM. For the combnaton usng the GnSVM, each test s reeated usng the dfferent combnatons of kernel tyes and ate Dstorton Factor n order to fne tune the erformance of the classfer. Phase 2 Ths hase s the same as hase excet that now we are flng the rght mages and combng t wth the left mages n order to form a bgger set of tranng and testng samles. Phase 3 Aly the 5 combnaton rules to combne the results of classfcaton we obtaned from Phase and Phase 2. Phase 4 eeat hase 2 and hase 3 on the wrst mages usng the classfer and arameters whch has best erformance n hase n order to rove the concluson we draw n Phase. Combnaton s done on the results of classfcaton. The detals and results of each hase wll be llustrated n the subsectons below. 6.2 Classfer Parameters Tunng Gn SVM s traned wth dfferent arameters ate Dstorton factor and kernel tye on dfferent sets of samles. Every choce of these arameters wll drectly affect the classfcaton accuracy. Besdes that, the accuracy s also very senstve to the change n arameters. Just a slght change of 0.0 n the gamma value mght cause the classfcaton accuracy to dro substantally. In order to fne tune the classfer arameters, we have run elaborated tests n order to fnd the best ossble combnaton of arameters. In Phase, we use dfferent combnatons of arameters n the Gn SVM. We have use ether the adal Bass Functon or Polynomal Functon for the kernel tye and the ate Dstorton factor values whch are attemted for tranng and testng are 0.0, 0.,, 2, 5, 33

34 0, 00 and The classfcaton rate and fracture detecton rate n tranng and testng are tabulated when a dfferent combnaton of the arameters are used. All together we have 6 sets of results for Phase. The combnaton wth hghest classfcaton and fracture detecton rate wll be selected to classfy the samles to be used n Phase 2 and Phase 3. We have found that for the exermental tests carred out n hase, the olynomal functon s hoeless because the classfcaton rate s less than 0%. For the tests carred out usng the adal Bass Functon, we have concluded that for Intensty Gradent, the erformance s good for small ate Dstorton factor value whereas for Markov andom Feld large ate Dstorton factor value has better erformance. Gabor flter had reasonably well erformance for most values of ate Dstorton factor. For the tranng samles of the femur the best arameters are: Intensty gradent: 0.0 Markov andom Feld: 2 Gabor Flter: Snce the wrst mages wll be a totally dfferent set of samles, we wll reeat the arameter fne tunng rocess mentoned above. We have found that the adal Bass Functon stll outerformed the Polynomal functon. Small ate Dstorton Factor s sutable for Intensty gradent and Markov andom Feld whereas larger ate Dstorton factor values s good for the Gabor Flter. For the tranng samles of the wrst the best arameters are: Intensty gradent: 5 Markov andom Feld: 0. Gabor Flter: 0. 34

35 6.3 Indvdual Classfers' Performance Tranng Testng Classfcaton accuracy Fracture Detecton ate Classfcaton accuracy Fracture Detecton ate Intensty Gradent GINI Left 00.00% 00.00% 88.90% 7% Intensty Gradent GINI ght 00.00% 00.00% 92.60% 25% Intensty Gradent SVM Left 00.00% 00.00% 87.03% 25.00% Intensty Gradent SVM ght 00.00% 00.00% 94.40% 25.00% Intensty Gradent Bayesan Left 97.80% 00.00% 90.70% 50.00% Intensty Gradent Bayesan ght 99% 00.00% 87.03% 25.00% MF GINI Left 98.80% 00.00% 98.0% 00.00% MF GINI ght 00.00% 00.00% 98.0% 00.00% MF SVM Left 00.00% 00.00% 87.03% 6.70% MF SVM ght 00.00% 00.00% 94.40% 25.00% MF Bayesan Left 99.30% 00.00% 96.20% 25.00% MF Bayesan ght 00.00% 00.00% 98.0% 25.00% Garbov Flter GINI Left 00.00% 00.00% 87.00% 6.70% Garbov Flter GINI ght 00.00% 00.00% 98.0% 75.00% Garbov Flter SVM Left 93.20% 92.00% 79.60% 6.70% Garbov Flter SVM ght 98.0% 92.80% 94.40% 00.00% Garbov Flter Bayesan Left 94.40% 72.00% 96.20% 37.50% Garbov Flter Bayesan ght 97.50% 7.40% 94.40% 50.00% Table 6.: esults of tranng and testng when the left and rght femur mages are n two searate sets. 35

36 Table 6. shows the classfcaton accuracy and fracture detecton rate of Phase. For the tranng samles, the hghest classfcaton accuracy s 00% and the lowest classfcaton accuracy s 93.2%. Ths shows that the tranng s well done as the classfcaton accuracy s hgh n general. The hghest fracture detecton rate s 00% whle the lowest fracture detecton rate s 7.4 %. Among all the classfers used n ths roject, Gn SVM has the best erformance comared wth the Probablstc SVM and Bayesan n terms of ts hgh classfcaton accuracy and fracture detecton rate. The combnaton of Gabor Flter feature extracton and Bayesan classfer has the worst overall erformance. The classfcaton on Gabor orentaton s the least accurate comared to the other two feature tyes. As for the testng samles, the classfcaton accuracy ranges from 79.6 % to 98.0%. The fracture detecton rate ranges from 6.75% to 00%.It s low for all combnatons excet for the Markov andom Feld usng Gn SVM as classfer. Bayesan classfer has the hghest classfcaton accuracy and fracture detecton rate. The overall classfcaton accuracy and fracture detecton rate s hgher than when standard SVM and Bayesan were used. The classfcaton accuracy and fracture detecton rate was only on an average of 70% and 80%. For ths exerment and the one that we are gong to dscuss next, although we get hgh classfcaton accuracy and fracture detecton rate n MF usng Gn SVM but we could not just sto here and draw a naïve concluson that ths s the best method for classfcaton because ths close-to-erfect result mght be due to the tye of fracture that s n ths set of samle haens to be more easly detected usng the MF and Gn SVM. In order to deloy ths system n the real world, we have to derve a more general and robust method whch covers ossbly all the tyes of samle whch we mght encounter. Hence, there s a motvaton to derve other methods whch have hgh classfcaton accuracy and fracture detecton rate gven any tye of samle mage. 36

37 Tranng Testng Classfcaton accuracy Fracture Detecton ate Classfcaton accuracy Fracture Detecton ate Intensty Gradent GINI 00.00% 00.00% 92.60% 4% Intensty Gradent SVM 00.00% 00.00% 85.20% 33.00% Intensty Gradent Bayesan 95.0% 00.00% 77.80% 75.00% MF GINI 00.00% 00.00% 00.00% 00.00% MF SVM 99.70% 99.00% 93.50% 4.70% MF Bayesan 99.70% 00.00% 94.40% 58.30% Garbov Flter GINI 00.00% 00.00% 88.00% 4.70% Garbov Flter SVM 93.50% 97.20% 8.50% 4.70% Garbov Flter Bayesan 00.00% 00.00% 92.60% 58.30% Table 6.2: esults of tranng and testng the combned set of left and rght femur mages. 37

38 Table 6.2 shows the results of Phase 2. The motvaton behnd ths s because the larger the number the tranng samle the more accurate the tranng wll be. The classfcaton accuracy ranges from 93.5% to 00% whereas the fracture detecton rate ranges from 97.2% to 00% for the tranng samles. We can see a substantal mrovement on both the classfcaton accuracy and fracture detecton rate from Phase. Gn SVM has the best erformance followed by Bayesan and Probablstc SVM. There s an nterestng observaton whereby the classfcaton and fracture detecton usng Gn SVM s erfect regardless of the feature tye. Ths observaton s mortant as we can see Gn SVM also erforms the best when the left and rght mages are traned searately. We can focus on usng the Gn SVM n the future when we are tryng to mrove the bone fracture detecton rate. Gabor Flter traned wth Probablstc SVM has the worst erformance among all. We can see that ths set of results has dfferent trend comared to Phase. Ths s because wth a larger set of tranng and testng samles, the arameters we get out of the tranng wll be dfferent and hence we mght have an entrely dfferent observatons on the when we do testng on t. As for the testng samles, the hghest classfcaton accuracy s 00% and the lowest s 77.8%.The fracture detecton rate ranges from 4.7% to 00%. We can see an mrovement n both classfcaton accuracy and fracture detecton rate n general comared to Phase. Hence, combnng the mages to tran the classfer wth a larger samle set s another alternatve to mrovng the classfcaton accuracy and fracture detecton rate besdes alyng combnaton rules whch we are gong to dscuss n the next secton. The Markov andom Feld and Gn SVM combnaton stll have the best erformance. The Intensty Gradent classfed usng Bayesan has the lowest classfcaton rate but the fracture detecton rate s the second hghest. Intensty Gradent dd not erform as well comared to the Markov andom Feld and Gabor Flter. 38

39 MF Left ght Classfcaton Accuracy 78.80% 75.60% Fracture Detecton ate 80.00% 84.60% Table 6.3: esults on the revous work done on radus Prevous work on wrst bone fracture detecton has been done usng the Markov andom Feld feature extracton and classfed usng a standard SVM. The results show reasonable fracture detecton rate but the classfcaton accuracy s rather low. Ths mght be due to the hgh ercentage about /3 of fractured samle. Our am s to ncrease both the classfcaton accuracy and fracture detecton rate usng the methods we have derved from the work done on femur. Intensty Gradent MF Gabor Flter Left ght Combne Left ght Combne Left ght Combne Classfcaton Accuracy 87.90% 90.20% 96.00% 84.80% 70.70% 86.50% 84.80% 80.50% 90.50% Fracture Detecton ate 80.00% 92.30% 87.00% 80.00% 84.60% 9.30% 70% 76.90% 87.00% Table 6.4: Testng results of the dfferent feature tyes on radus mages All the tranngs have erfect erformance. The Gn SVM erformed the best n our roject. It has mroved the classfcaton accuracy and fracture detecton rate even before the varous combnaton rules were aled. The hghest classfcaton rate s 96% and fracture detecton rate s 87%. We susect art of the reason for the oor classfcaton rate n the revous work done was due to lack of tranng and testng samles, we hence combne the left and rght mages to form bgger tranng and testng sets n order to mrove on the tranng of the SVM. We combned the left and rght mages by flng the rght mages vertcally to orent t wth the left mages. 39

40 As we can see by comarng the two tables, by just usng the Gn SVM nstead of standard SVM on the Intensty gradent drecton, both the classfcaton accuracy and fracture detecton rate has mroved whereas for the MF and Gabor Flter only one of them has ncreased. When we combne the two sets of left and rght samles, we can see the overall mrovement n both the classfcaton accuracy and fracture detecton rate. Ths roves that our hyothess mght be correct. As we have more samles, the SVM wll be more well traned and hence roduce better classfcaton. Although there s already a sgnfcant mrovement but we would lke to further mrove on t by alyng the varous combnaton rules to fnd out whch rule works the best.besdes that we can see f t wll hel to boost the classfcaton accuracy as well as the fracture detecton rate. 6.4 Indvdual Classfers' Probablty Estmatons From what we have observed n Phase, the robabltes that we get from Bayesan, Probablstc SVM and Gn SVM has sgnfcant dfference n terms of the range. The values are all between 0 and as t s a robablty. The values for Bayesan are on the lower end of the range, values of Gn SVM are n the mddle range and the values from Probablstc SVM are on the hgher end. Ths makes t really dffcult for us to combne all of the 9 robablty values for each samle. We have attemted to comute a confdence value for each of these 3 classfers. The confdence value s comuted by havng takng the result of testng samles. The values searated nto 0 bns. Then we comute the confdence value for each bn by takng the number of correct classfcaton dvded by number of samles whch falls nto ths bn. We wll then combne the 9 robablty values for each samle usng a weght.the hgher weght wll be assgned to the robablty value wth hgher confdence. Theoretcally ths s a very ntutve method to combne the robablty values but the lmtaton s the dserson of the robablty values. The robablty values tend to ether cluster together and made t hard to be searated n to bns or too sarse and hence each bn ether has one or no samle. If the values were evenly sread over the 0 bns, ths method would be alcable. Fnally we have decded to do 3 searate combnatons on the 3 oututs of Bayesan Gabor Flter, Intensty Gradent and Markov andom Feld, Probablstc SVM and Gn SVM. 40