A Statistical Method for Comparing Chest Radiograph Images of MTB Patients

Transcription

1 tattcal Method for Comparng Chet adograph Image of MT Patent Norlza Mohd. Noor, Omar Mohd. jal*, hee Lee Teng* Dploma Program tude, Unvert Teknolog Malaa * Inttute of Mathematcal cence, Unvert Malaa norlza@ctcampu.utm.m, omarrja@um.edu.m, heeleeteng@ahoo.co.uk btract :- Dgtal mage of chet radograph taken at dfferent tme pont ma be compared to nvetgate the effect of treatment on mcobacterum tuberculo (MT) patent. One method of comparon that of vuall locatng now-flake whch hould decreae n area or ze wth each ubequent mage. Th paper propoe a more objectve method; the comparon of mage htogram whereb a leftward hft of the htogram ndcate a potve effect of treatment. The comparon of two htogram equvalent to ether comparng the correpondng box-plot or the correpondng et of percentle. However, before the comparon made the mage need to be regtered and rezed. The reult of th tud how that the proporton of percentle (from htogram) can be ued a an ndcator of treatment effect (or patent progre). urther the correlaton hown to be the bet mlart meaure to ndcate the qualt of mage regtraton. nall, th tud alo how that a combnaton of regtraton and rezng can mprove the par-we comparon. Ke Word:- Chet adograph, Mcobacterum Tuberculo, Image egtraton, ezng, Correlaton, oxplot. 1 Introducton Two mllon death are due to MT [1] annuall. Global T ncdence tll growng at 1% a ear. To elmnate the problem of T the WHO [1] make everal uggeton, n partcular Gvng acce to qualt T dagno and treatment for all. n mportant ngredent [], [3], [4] for dagno of T the comparon of a ere of chet X-ra. If treatment ucceful, the preence of nowflake wll decreae or dmnh wth each ubequent (new) mage. In other word t mportant that we have a relable method of comparng X-ra mage. everal problem have to be faced before an comparon ma be made. rtl, the deaed area or nowflake do not ubcrbe to an fxed dmenon (hape, ze, or orentaton), [4]. uch two mage ma onl be compared b ther drect dfference nce no obvou feature ma be condered. In partcular f treatment ucceful, the ncdence of nowflake how a reducton n the econd mage. n meaure of th reducton wll ndcate ucce of treatment. To meaure the drect dfference between mage, the mage mut be regtered [5], [6], [7]. In ome cae the mage ma alo have to be rezed, ee g. 1(a), g. 1(b) and g. 1(c). In th tud mage at three tme pont wll be condered; namel the frt vt, econd vt and the lat vt. The varou tage for comparon nvolve; () Image regtraton ung CP (ee ecton). () Croppng the lung area. () ezng ubet mage from (), (ee ecton3). (v) electng the regon of nteret that the affected area ndcated b the preence of now-flake (under expert advce [4]). (v) Obtanng mage htogram and hence box-plot of mage n (v). (v) Comparng box-plot or equvalentl percentle from mage htogram. To enure the qualt of regtraton, mlart meaure and, ME and PN wll be ued. ecton 6 a hort tud howng that the bet choce of mlart meaure, whch n turn an approprate ndcator of qualt regtraton..

2 In th tud, let {I(,j); 1,, M, j 1,, N} repreent the dgtal X-ra mage of a patent on h frt vt to the hoptal. Let {K(,j); 1,, M, j 1,, N} repreent the ame patent mage at a later precrbed tme pont. (a) (b) (c) g. 1 Three orgnal mage of the ame patent taken at three dfferent tme pont. (a) 1 t vt, mage ze: (b) nd vt, mage ze: (c) 3 rd vt, mage ze: even control pont regtraton (CP) ( x, ) ( x, ) G x G, ) Let,,, ( G be 7 elected pont on the lung area. Gven two mage (two tme pont) we have, 1 t mage {,, C, D,..., G ) nd mage {,, C, D,..., G }. The followng dtance were calculated: D D,... D where for example D,, GG ( x x ) + ( ) Hence each par of mage were regtered a follow; calculate, T x x T M x x ( ) ( x x ) TxG ( xg x ) G and let T medan{ T, T,..., T } x mlarl calculate. x x xg T T M ( ) ( ) TG ( G ) G and let T medan{ T, T,..., T }. Treatng the 1 t mage a a reference mage, then the nd and 3 rd mage were ubject to a vertcal dplacement T and a horzontal dplacement T. The mage are ad to be properl regtered f the dtance D D,... D are reduced or mnmzed. It can be hown (ee Table 1) that D (for 1 t and nd mage) whlt D 35 after CP. mlar reult hold for all other 7 pont. G,, GG Table 1 Dtance between 7 control pont for CP for 1 t and nd mage gven n g. 1. (efore (fter tranlaton) tranlaton) (1 t and nd ) (1 t and nd ) ( T x, T ) D D D CC D DD D EE D D GG x (-33,175) 3 ezng vew of the orgnal mage how that a gnfcant area of the mage taken up b the rrelevant background. urther gure 1 how that the three mage are of dfferent ze, and th ma have a gnfcant effect on comparon of mage.

3 Th tud propoe that the mage be rezed a follow; ) The mage cropped uch that the remanng mage eentall the lung area. ) Then an affne tranformaton carred out ung the MTL command Cx 0 0 MKETOM [ affne, 0 C 0 ] where for example n gure 1, C x and C 1. Cx and C the requred 048 percentage for rezng. The program wll then nterpolate the new pxel value ung the blnear nterpolaton. 4 ref evew of UL and e-label the obervaton (or expermental value) of {I(,j); 1,, M, j 1,, N} a 1,,, MN, the obervaton of {K(,j); 1,, M, j 1,, N} a x 1, x,, x MN, and the true I(,j) and K(,j) value wll be denoted b Y 1, Y,, Y MN and X 1, X,, X MN, repectvel. We look at two regreon model to tud the relatonhp between and x. We frt look at the ordnar mple lnear regreon (L) model [8] of the dependent varable, and explanator varable, x : α + β x + ε, 1,,,MN (1) where the maxmum lkelhood etmator (MLE) and COD are gven a follow: x ˆ α ˆ β x, ˆ β βˆ x and () where the the proporton of varaton explaned b explanator varable x and x, x, MN MN ( ), ( x x) and ( x x)( ) x. However, a ponted out b [9], the aumpton that the explanator varable can be meaured exactl ma not be realtc n man tuaton. The etmate of explanator varable ma contan meaurement error arng from the technque or ntrument ued or trng to quantf a varable that ha no phcal dmenon. In thee cae, the explanator varable ubject to error. uppoe that now the X and Y are two lnearl related unobervable varable (ee [10] and [11]) Y α + β (3) X and the two correpondng random varable x and are oberved wth error δ and ε repectvel x X + δ 1,, K, MN (4) Y + ε where δ and ε are mutuall ndependent and normall dtrbuted random varable. Equaton (3) and (4) are known a the UL model when there onl one relatonhp between the two varable X and Y. It can be hown that the maxmum lkelhood etmator when the rato of the error varance σ ε equal to one, λ 1, are gven a follow: σ δ ˆ α ˆ β x (5) 1 ( ) + {( ) 4 x} ˆ + β (6) x 1 1 ˆ σ ( ˆ ) + ( ˆ ˆ ˆ δ x X α βx ) MN λ (7) and ˆ x + ˆ( β ˆ) α X (8) ˆ λ + β The equaton n (3) and (4) can be wrtten a α + β x + ε β δ ) ( α + β x + V for 1,., MN (9) where the error of the model, normall dtrbuted. The redual um of quare and the regreon um of quare are gven a follow: ˆ ˆ β x + β E ˆ 1+ β and V

4 E ˆ ˆ β x + β ˆ 1+ β Therefore, the COD for UL can be defned a βˆ x (10) and t can be hown that ME and PN Two other ndcator of proper regtraton are the ME and PN defned a follow: ME mn m n 0 j 0 I(, j) K(, j) where I econd vt mage and K the frt vt mage, MX and PN 0 log10 ME where MX 1, bt. The dgtal mage coded ung 1bt DICOM format, therefore MX Table how that the bet mlart meaure (no rezng or regtraton). In th cae actuall the bet ndcator of dmlart. Table 3 (after regtraton wth 4 control pont and rezng, ee g. 3 and g. 4) agan how that a good ndcator of mlart for the ame mage n g. 4(a), g. 4(b) and g. 4(c). However ME and PN ma alo be ued. nce can ndcate both mlart and dmlart between mage, all future dcuon wll be confned to the ue of. (a) (b) (c) 6 blt of mlart Meaure to Compare Image Due to the complex dmenon of the nowflake, an ntal experment mulate the tuaton where the ame object (plaque hown n g. (a), g. (b) and g. (c)) captured on camera at dfferent dtance. Th equvalent to the ame patent at dfferent dtance or poton from the X-ra camera (pobl due to radographer error). g. (d), g. (e) and g. (f) are the cropped mage of g. (a), g. (b) and g. (c) repectvel. Thee cropped mage are equvalent to the correpondng lung area after removal of rrelevant background. To compare thee cropped mage, the mage dmenon mut be the ame. Clearl the mage are not dentcal pxelwe (pxel (, j ) mage hown n g. (d) and pxel (, j) m age hown n g. (e)). Henceforth an ndcator of mage mlart necear. (d) (e) (f) g. One object taken at three dfferent dtance ung the ame camera that produce the ame mage ze of , (a) Camera dtance:7 cm, (b) Camera dtance:6 cm, (c) Camera dtance:5 cm. (d), (e) and (f) the mage of regon of nteret cropped wth mage ze of (a) (b) (c) g. 3 ub mage from g. (a), g. (b) and g.(c) repectvel after 4 control pont regtraton. Note the dfferent mage ze though the regon of nteret captured.

5 (a) (b) (c) g. 4 The reultant mage from g. 3 after rezng wth ffne tranformaton. ll mage ha the ame ze of pxel. Table Comparon of mlart meaure (No rezng and no tranlaton) Image (g. ) mlart meaure (d)-(e) (d)-(f) ME PN Table 3 Comparon of mlart meaure (wth 4 control pont regtraton and ffne rezng method) mlart Image (g. 4) meaure (a)-(b) (a)-(c) ME PN Comparng Two Image nce onl a mall ecton of the orgnal mage to compared, the mage htogram a potental tool for comparon. However, a mpler wa of comparng two dtrbuton n fact the comparon of two box-plot [1] or t correpondng percentle. or clart, the p th percentle defned to be that value of a varable for whch p percent of the value of the dtrbuton are maller. 8 Decrpton of the Experment or each patent, h ere of vt to the hoptal and conequentl the chet x-ra mage obtaned are labeled, and C. The mnmum treatment perod for MT 6 month and the progre montored ever month va clncal tet (uuall the putum tet) and chet x-ra mage. In th tud the chet x-ra mage are compared par-we, for three tme pont, that frt and the econd chet x-ra (), frt and lat chet x-ra (C), ee g. 5(a), g. 5 (b), g. 5 (c). The X-ra flm were canned nto 1 bt DICOM fle ung Kodak L 75 X-ra flm canner. The experment were carred out a follow; (a) The mage were ubjected to CP wth the 1 t vt mage beng the reference mage (ee g. 5(d), g. 5 (e), g. 5 (f)). (b) The lung area wa cropped a beng the regon of nteret ee g. 5(g), g. 5 (h), g. 5 (). (c) ezng carred out ung ffne tranformaton. eultant mage hown n g. 5(j), g. 5 (k), g. 5 (l). (d) Hgh dent area of MT elected for comparon, g. 5(m), g. 5 (n), g. 5 (o). (e) The correpondng box-plot for (d) wa gven n g eult and Dcuon ecton 6 ha hown that a good ndcator of mlart (or dmlart) between a par of dgtal mage. urther, comparng value between Table and Table 3 clearl how that after CP and rezng the par of mage ma then be condered utable for comparon (b drect dfference). Nneteen patent were tuded and g. 5 llutrate the man tage of the experment. The crucal reult gven n g. 6 whch how a leftward hft of box-plot. Lookng multaneoul at g. 6 and g. 5(m), g. 5(n), g. 5(o), clearl how that a the whte area or nowflake decreae n ntent, we oberved the left-ward hft n the mage htogram. In other word, g. 6 ndcate that the patent makng a potve progre. However, comparng htogram for large number of patent ma prove to be nconvenent. uch eleven percentle (10, 0, 5, 30, 40, 50, 60, 70, 75, 80, 90) from the mage htogram calculated, and Table 4 how the number (total) of percentle wth the left-ward hft.

6 (a) 1 t vt (b) nd vt (c) fnal vt ze: 096 x x x 048 g. 6 Lowet box-plot correpond to ubet mage from the 1 t vt mlarl top-mot box-plot for the lat vt. (d) 1 t vt (e) nd vt (f) fnal vt ze: 096 x x x 048 Table 4 Percentle of 0 MT patent. 1t vt and nd 1 t and Lat vt vt Patent (+) (-) (+) (-) 1 (165500) (93400) (95600) (g) 1 t vt (h) nd vt () fnal vt ze: 1650 x x x (110800) (144400) (148700) (118600) (94100) (38300) (j) 1 t vt (k) nd vt (l) fnal vt ze: 1564 x x x (34000) (15701) (55601) (8601) (m) 1 t vt (n) nd vt (o) fnal vt ze: 35 x x x 644 g. 5 Decrpton of the experment. (a), (b), (c) Orgnal mage (d), (e), (f) eultant mage after CP. (g), (h), () Cropped out the regon of nteret (j), (k), (l) ezed mage ung ffne Tranformaton (m), (n), (o) elected rea: Hgh Dent MT Infected rea 14 (9910) (34140) (38410) (39000) (3960) (3930)

7 ourteen patent howed clear-cut recover wth ten or eleven negatve for frt and lat vt. Three patent (1, 3, 19) how the extreme revere tuaton wth eleven plu. Two ntermedate cae are () patent makng a lght recover and () patent 8 howng no change. In the cae of patent and patent 8, further treatment referred back to the medcal expert. 10 cknowledgement We would lke to acknowledge the contrbuton from Datn Dr. Hjh zah Mahuddn and Dr. zwaat ba, The eprator Unt, Kuala Lumpur General Hoptal, and Dr Hamdah haban, elangor Medcal Centre. Th reearch wa funded under an IP grant from the Mntr of cence, Technolog and the Envronment and Unvert Teknolog Malaa. eference: [1] WHO: The Global Plan To top T : cton or Lfe Toward World ree Of Tuberculo. Geneva; WHO, 006. [] Mddlem, H, adolog of the future n developng countre, rth Journal of adolog, 55, pp , 198. [3] Moore,.M., Dgtal X-ra Imagng, IEE Proceedng, Vol. 134, part, Number, pecal Iue On Medcal Imagng, [4] haban, H, Medcal Conultant for eprator Deae, Prvate Converaton, Inttute of eprator Deae, Kuala Lumpur Hoptal. [5] Hll, Derek L G, atchelor, Phlpp G., Holden, Mark, and Hawke, Davd Medcal Image egtraton. Phc n Medcne and olog. Vol. 46. [6] Gonzalez, afael C., Wood, chard E., Eddn, teven L Dgtal Image Proceng Ung MTL. Pearon Educaton, Inc. [7] arbara Ztova, Jan luer Image egtraton method: a urve. Image and Von Computng, vol [8] Weberg,., ppled Lnear egreon, New York, John Wle, [9] uller, W.., Meaurement Error Model, New York, John Wle, [10] Dolb, G.., The Ultratructural elaton; nthe of the unctonal and tructural elaton, IOMETIK, 63, pp , [11] Chang, Y.., jal O. M. and Noor N. M., Image Qualt and Noe Evaluaton, The Proceedng of the 7 th Internatonal mpoum On gnal Proceng and It pplcaton (IP 003), Par, rance, 003. [1] reund,. J. and Wlon, W. J., tattcal Method, cademc Pre, 1997