Image Registration for a Series of Chest Radiograph Images

Transcription

1 Proceedng of the 5th WE Internatonal Conference on gnal Proceng, Itanbul, Turkey, May 7-9, 006 (pp ) Image Regtraton for a ere of Chet Radograph Image Omar Mohd. Rjal*, Norlza Mohd. Noor, hee Lee Teng* * Inttute of Mathematcal cence, Unverty Malaya Dploma Program tude, Unvert Teknolog Malaya btract :- To nvetgate the effect of treatment, a tudy on the progre of an MT patent carred out. One approach to compare a ere of chet radograph taken at three dfferent tme pont. or each radograph a ubet of the mage repreentng the deaed area derved, and henceforth montorng defned a the actvty n n of comparng the three correpondng ubet mage. The element of each ubet mage of dmenon ( ) treated a n number from whch, fve tattc are calculated (mn, frt quartle, medan, thrd quartle, max). In other word, the box plot of each ubet mage derved. The total number of tattc that how a left ward hft (decreae n magntude) an ndcaton of patent progre. However, before comparng a par of box plot, the correpondng par of mage need to be rezed and regtered. Th tudy how that a combnaton of rezng and regtraton can mprove the par we comparon. Key Word:- Chet Radograph, Mycobacterum Tuberculo, Image Regtraton, Correlaton, ox-plot 1 Introducton The common radograph flm tll an mportant tool n the dagnotc proce for lung alment depte rapd advance n medcal magng technology, ee Mddlem [1] and Moore []. In Malaya, government hoptal perform the major part of detecton ung radograph flm mply out of economc conderaton. Problem aocated wth the vual nterpretaton (and comparon) of tandard chet radograph flm are well known [3]. Thee remark motvate a need to create objectve method n partcular for comparng two or more dgtal radograph mage. efore a par of radograph mage may be compared they need to be regtered, and n ome cae rezed a well. Image regtraton and rezng neceary becaue condton vary when the ere of X-ray flm are taken. In th tudy the tep nvolved are () crop the regon of nteret that the lung area, () apply a method called 7-control pont regtraton (CPR) whch ue for mage regtraton, and () reze the mage ung affne tranformaton (a MTL functon). fter regtraton and rezng t tll neceary to check whether the mage are properly overlappng. Th done by etmatng correlaton R R ( and [4], [5]) a well a ME and PNR. In th tudy, let {I(,j); 1,, M, j 1,, N} repreent the dgtal X-ray 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. even control pont regtraton (CPR) Let ( x, y ) x, y G (, ), ( ),, x G y 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,, ( x x ) ( ) + y y It can be hown that D (for 1 t and nd mage) and D (for 1 t and 3 rd mage). Hence fore each par of mage wa regtered a follow; calculate

2 Proceedng of the 5th WE Internatonal Conference on gnal Proceng, Itanbul, Turkey, May 7-9, 006 (pp ) T T M x x ( x x ) ( x x ) TxG ( xg x ) G and let T medan{ T, T,..., T } x. mlarly calculate T y y T M y y x ( ) ( y y ) TyG ( yg y ) G and let T medan{ T, T,..., T } y y x y xg. Treatng the 1 t mage a a reference mage, then the nd and 3 rd mage were ubject to a vertcal and T,. horzontal tranlaton how by ( ) x T y The mage are ad to be properly regtered f the dtance D D,... D are mnmzed. yg,, 3 Rezng vew of the orgnal mage how that a gnfcant area of the mage taken up by the rrelevant background. urther gure 1 how that the three mage are of dfferent ze, and th may have a gnfcant effect on comparon of mage. Th tudy propoe that the mage be rezed a follow; ) The mage cropped uch that the remanng mage eentally the lung area. ) Then an affne tranformaton carred out ung the MTL command x 0 0 MKETORM [ affne, 0 y 0 ] where for example n gure 4, C x and C y Cx and Cy the requred 1844 percentage for rezng. The program wll then nterpolate the new pxel value ung the blnear nterpolaton. 4 ref Revew of ULR and R Re-label the obervaton (or expermental value) of {I(,j); 1,, M, j 1,, N} a y 1, y,, y 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 by Y 1, Y,, Y MN and X 1, X,, X MN, repectvely. We look at two regreon model to tudy the relatonhp between y and x. We frt look at the ordnary mple lnear regreon (L) model [6] of the dependent varable, y and explanatory varable, x : y α + β x + ε, 1,,,MN (1) where the maxmum lkelhood etmator (MLE) and COD are gven a follow: ˆ α y ˆ β x, ˆ β βˆ and R () where the R the proporton of varaton explaned by explanatory varable x and y x y, x, MN MN ( y y), ( x x) and ( x x)( y y). However, a ponted out by [5], the aumpton that the explanatory varable can be meaured exactly may not be realtc n many tuaton. The etmate of explanatory varable may contan meaurement error arng from the technque or ntrument ued or tryng to quantfy a varable that ha no phycal dmenon. In thee cae, the explanatory varable ubject to error. uppoe that now the X and Y are two lnearly related unobervable varable (ee [4] and [7]) Y α + β (3) X and the two correpondng random varable x and y are oberved wth error δ and ε repectvely x X + δ 1,, K, MN (4) y Y + ε

3 Proceedng of the 5th WE Internatonal Conference on gnal Proceng, Itanbul, Turkey, May 7-9, 006 (pp ) where δ and ε are mutually ndependent and normally dtrbuted random varable. Equaton (3) and (4) are known a the ULR model when there only 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 y ˆ β x (5) 1 ( ) + {( ) 4 } ˆ + β (6) 1 1 ˆ σ ( ˆ ) + ( ˆ ˆ ˆ δ x X y α βx ) MN λ (7) and ˆ x + ˆ( β y ˆ) α X (8) ˆ λ + β The equaton n (3) and (4) can be wrtten a y α + β x + ε β δ ) ( α + β x + V for 1,., MN (9) where the error of the model, normally dtrbuted. The redual um of quare and the regreon um of quare are gven a follow: ˆ ˆ β + β E ˆ 1+ β and R E ˆ ˆ β + β ˆ 1+ β Therefore, the COD for ULR can be defned a βˆ R R (10) and t can be hown that 0 R R 1. 5 ME and PNR Two other ndcator of proper regtraton are the ME and PNR defned a follow: ME mn m n 0 j 0 V I(, j) K(, j) where I econd vt mage and K the frt vt mage, MX and PNR 0 log10 ME where MX 1, bt. The dgtal mage coded ung 1bt DICOM format, therefore MX Comparng Two Image nce only a mall ecton of the orgnal mage to compared, the mage htogram a potental tool for comparon. However, a mpler way of comparng two dtrbuton n fact the comparon of two box-plot [8]. 7 Decrpton of the Experment or each patent, h ere of vt to the hoptal and conequently the chet x-ray mage obtaned are labeled, and C. The mnmum treatment perod for MT 6 month and the progre montored every month va clncal tet (uually the putum tet) and chet x-ray mage. In th tudy the chet x-ray mage are compared par-we, for three tme pont, that frt and the econd chet x-ray (), frt and lat chet x-ray (C) The X-ray flm were canned nto 1 bt DICOM fle ung Kodak L 75 X-ray flm canner. Two major experment were carred out; (a) The mage were ubjected to CPR (ee g. ). Then the ubet mage were obtaned. g. 3 gve the relevant box-plot. (b) The mage were ubjected to both rezng and CPR, ee g 4 and g. 5 before the ubet mage were obtaned (ee g. 6). The correpondng box-plot wa gven n g Reult nd Dcuon g. 1 how mage of dfferent ze. The mage are regtered ung CPR and the ubet mage obtaned a gven n g.. The box-plot of g. 3 how a general hft to the left ndcatng a potve patent progre. The effect of rezng and CPR are llutrated n g. 5 and 6. gan the box-plot how mlar reult.

4 Proceedng of the 5th WE Internatonal Conference on gnal Proceng, Itanbul, Turkey, May 7-9, 006 (pp ) The effectvene of CPR clearly hown by comparng the frt two column of Table 1 whch how that D D,... D were reduced. R,, To how the effect of rezng, the ncreae R of and and the decreae n ME a hown n Table how that rezng mportant. nally Table how that the PNR not entve to the effect of rezng. In concluon mage regtraton and mage rezng hould both be carred out to acheve ome mprovement n the par-we comparon (compare g.3 and g. 7). (a) 1 t vt (b) nd vt (c) 3 rd vt gure : ubet mage wth regtraton only after CPR. g. 3 Lowet box-plot correpond to ubet mage from the 3 rd vt mlarly top-mot box-plot for the lat vt. The ubet mage mage after regtraton only. (a) 1 t vt (b) nd vt ze: ze: (a) 1 t vt (b) nd vt (c) 3 rd vt g. 4 Croppng the regon of nteret lung area. (c) 3 rd vt, ze: g. 1 Three orgnal mage of the ame patent taken at three dfferent tme pont. (a) 1 t vt (b) nd vt (c) 3 rd vt g. 5 Image after affne tranformaton.

5 Proceedng of the 5th WE Internatonal Conference on gnal Proceng, Itanbul, Turkey, May 7-9, 006 (pp ) (a)1 t vt (b) nd vt (c) 3 rd vt g. 6 ubet mage wth rezng and regtraton mage after CPR. [7] Chang, Y.., Rjal O. M. and Noor N. M., Image Qualty and Noe Evaluaton, The Proceedng of the 7 th Internatonal ympoum On gnal Proceng and It pplcaton (IP 003), Par, rance, 003. [8] reund, R. J. and Wlon, W. J., tattcal Method, cademc Pre, Table 1: Dtance etween 7 control pont for CPR for 1 t and nd mage. (efore (fter tranlaton) tranlaton) (1 t and nd ) (1 t and nd ) ( T x, T y ) gure 7 Lowet box-plot correpond to ubet mage from the 3 rd vt mlarly top-mot box-plot for the lat vt. The ubet mage the mage wth rezng and regtraton after CPR. Reference [1] Mddlem, H, Radology of the future n developng countre, rth Journal of Radology, 55, pp , 198. [] Moore,.M., Dgtal X-ray Imagng, IEE Proceedng, Vol. 134, part, Number, pecal Iue On Medcal Imagng, [3] haban, H, Medcal Conultant for Repratory Deae, Prvate Converaton, Inttute of Repratory Deae, Kuala Lumpur Hoptal. [4] Dolby, G. R., The Ultratructural Relaton; ynthe of the unctonal and tructural Relaton, IOMETRIK, 63, pp , [5] uller, W.., Meaurement Error Model, New York, John Wley, [6] Weberg,., ppled Lnear Regreon, New York, John Wley, D D D CC D DD D EE D D (8,-1)

6 Proceedng of the 5th WE Internatonal Conference on gnal Proceng, Itanbul, Turkey, May 7-9, 006 (pp ) Table : Comparon of the mlarty meaure between regtraton wthout rezng and regtraton wth rezng. R R PNR 4 ME ( 10 ) Patent 1 t and nd vt 1 t and nd vt 1 t and nd vt 1 t and nd vt Wthout Wth Wthout Wth Wthout Wth Wthout Wth rezng rezng rezng rezng rezng rezng rezng rezng