A NOVEL STATISTICAL FUSION RULE FOR IMAGE FUSION AND ITS COMPARISON IN NON SUBSAMPLED CONTOURLET TRANSFORM DOMAIN AND WAVELET DOMAIN

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1 A NOVEL STATISTIAL FUSION RULE FOR IMAGE FUSION AND ITS OMPARISON IN NON SUSAMPLED ONTOURLET TRANSFORM DOMAIN AND WAVELET DOMAIN Manu V T and Phlomna Smon Department of omputer Scence Unverty of Kerala Karavattom ampu Thruvananthapuram Kerala Inda manuvt.ntc@gmal.com Department of omputer Scence Unverty of Kerala Karavattom ampu Thruvananthapuram Kerala Inda phlomna.mon@gmal.com ASTRAT Image fuon produce a ngle fued mage from a et of nput mage. A new method for mage fuon propoed baed on Weghted Average Mergng Method (WAMM n the Non Subampled ontourlet Tranform (NST doman. A performance analy on varou tattcal fuon rule are alo analyed both n NST and Wavelet doman. Analy ha been made on medcal mage remote enng mage and mult focu mage. Expermental reult how that the propoed method WAMM obtaned better reult n NST doman than the wavelet doman a t preerve more edge and keep the vual qualty ntact n the fued mage. KEYWORDS Non Subampled ontourlet Tranform Weghted Average Mergng Method Stattcal Fuon Rule Wavelet Pella Metrc. INTRODUTION Image fuon provde an effcent way to merge the vual nformaton from dfferent mage. The fued mage contan complete nformaton for better human or machne percepton and computer-proceng tak uch a egmentaton feature extracton and obect recognton. Image fuon can be done n pxel level gnal level and feature baed. The tradtonal mage fuon cheme performed the fuon rght on the ource mage whch often have erou de effect uch a reducng the contrat. Later reearcher realzed the necety to perform the fuon n the tranform doman a mathematcal tranformaton provde further nformaton from the gnal that not readly avalable n the raw gnal. Wth the advent of wavelet theory the concept of wavelet mult-cale decompoton ued n mage fuon [9]. The wavelet tranform ha been ued n many mage proceng applcaton uch a retoraton noe removal mage edge enhancement and feature extracton; wavelet are not very effcent n capturng the two-dmenonal data found n mage[5]. Several tranform have been propoed for mage gnal that have ncorporated drectonalty and multreoluton and hence thoe method could not effcently capture edge n natural mage. Do and Vetterl DOI : 0.5/ma

2 propoed contourlet tranform[8] an effcent drectonal mult reoluton mage repreentaton. The contourlet tranform acheve better reult than dcrete wavelet tranform n mage proceng n geometrc tranformaton. The contourlet tranform hft-varant baed on amplng. However hft nvarance a neceary condton n mage proceng applcaton. The NST a fully hft-nvarant multcale and multdrecton expanon that ha a fat mplementaton[]. It acheve a mlar ub band decompoton a that of contourlet but wthout downampler and upampler n t thu overcomng the problem of hft varance[].. NON SUSAMPLED ONTOURLET TRANSFORM The Non Subampled ontourlet Tranform (NST contructed by combnng the Non ubampled Pyramd (NSP and the Non ubampled Drectonal Flter ank (NSDF[]. The former provde multcale decompoton and the later provde drectonal decompoton[3]. A Non ubampled Pyramd plt the nput nto a low-pa ubband and a hgh-pa ubband. Then a Non ubampled Drectonal Flter ank decompoe the hgh-pa ubband nto everal drectonal ubband. The cheme terated repeatedly on the low-pa ubband []. Fgure. lock Dagram of NST Fgure. lock Dagram Frequency dvon 3. IMAGE FUSION SHEME AND STATISTIAL FUSION RULES Image fuon cheme n two ource mage can be condered a a tep by tep proce. Frt the ource mage are dvded nto coare cale and fne cale. oare cale repreent the hgh frequency component and fne cale repreent low frequency component n the ource mage. Low frequency component contan overall detal of the mage whle the hgh frequency component contan detal about edge and texture. Then the coeffcent of the ource mage 70

3 are decompoed. Second the coare cale and the fne cale n the ource mage are eparately fued baed on tattcal fuon rule ung NST [][5][6][7]. Separate fuon rule are appled on thee fne cale and coare cale to obtan the fuon coeffcent. The fued mage obtaned by nvere NST from thee fuon coeffcent. In th ecton two dfferent tattcal fuon rule are dcued. Thee rule are analyzed expermentally thereby examnng the performance of the mage fuon n both wavelet and NST doman. 3.. Method - Fuon baed on Entropy Entropy the meaure of nformaton content n the mage. A hgh value of entropy denote more nformaton content and vce vera. So th tattcal meaure could be ued n makng a decon to elect the fuon coeffcent. H( S P( X log P( X Entropy calculated on the low frequency component of the nput mage wthn a 3-by-3 wndow and whchever havng hgher value of entropy were elected a the fuon coeffcent among the low frequency component For the hgh frequency component regonal energy calculated over a 5-by-5 wndow ung the formula where E k d } K the mage k. S D m n d W( m+ 3 n+ 3 ( ( + m + n K the NST coeffcent correpondng to cale and drecton d at poton ( for W a flter that gve more weghtage to the central coeffcent and defned a W Then the coeffcent choen a the fue coeffcent when the regon energy of t larger hown a formula 3 ( A F d } E E A otherwe 7

4 Fnally the fued mage recontructed ung the fued coeffcent NST tranform. 3.. Method - Fuon baed on Mean F ung the nvere Mean the repreentatve value of a large dataet that decrbe the center or mddle value. Mean the meaure of the group contrbuton per contrbutor whch conceved to be the ame a the amount contrbuted by each n contrbutor f each were to contrbute equal amount w x n n x Mean calculated on the low frequency component of the nput mage wthn a 3-by-3 wndow and whchever havng hgher value of mean were elected a the fuon coeffcent among the low frequency component. For the hgh frequency component regonal energy calculated over a 5-by-5 wndow ung the formula E k m n d S D W ( m + 3 n + 3 ( d } K ( + m + n d } where K the NST coeffcent correpondng to cale and drecton d at poton ( for the mage k. W a flter that gve more weghtage to the central coeffcent and defned a W Then the coeffcent choen a the fue coeffcent when the regon energy of t larger hown a formula ( A F d } E E A otherwe; ; Fnally the fued mage recontructed ung the fued coeffcent NST tranform Method 3- Fuon baed on Standard Devaton F ung the nvere Standard Devaton provde a way to determne regon whch are clear and vague. It calculated by the formula 7

5 where w x n w ( x x n n n x Standard Devaton calculated on the low frequency component of the nput mage wthn a 3- by-3 wndow and whchever havng hgher value of mean were elected a the fuon coeffcent among the low frequency component. For the hgh frequency component regonal energy calculated over a 5-by-5 wndow ung the formula E k S D m n d W( m + 3 n + 3 ( d } K ( + m + n d } where K the NST coeffcent correpondng to cale and drecton d at poton ( for the mage k. W a flter that gve more weghtage to the central coeffcent and defned a W Then the coeffcent choen a the fue coeffcent when the regon energy of t larger hown a formula ( A F d } E E A otherwe Fnally the fued mage recontructed ung the fued coeffcent NST tranform. F ung the nvere.image FUSION ASED ON WEIGHTED AVERAGE MERGING METHOD (WAMM PROPOSED APPROAH In th ecton we dcu the fuon baed on WAMM n NST Doman. WAMM ued n the hgh frequency component to obtan the fuon coeffcent wherea Standard Devaton calculated on the low frequency component of the nput mage wthn a 3-by-3 wndow. An average of the low frequency component calculated. Whchever obtan the hgher value of average are elected a the fuon coeffcent among the low frequency component. 73

6 7 The man feature of th new method are that t preerve the mage qualty and the edge detal of the fued mage. The vual qualty of the fued mage better n NST doman. The Weghted Average Mergng Method (WAMM formulated a < + + ; ; } max } mn } } mn } max } E E w w E E w w A d d A d F A d d A d F The weght are etmated a: < other W W T M W T p M W W A A ; ( 0 mn max mn max mn 5 Where T denote the threhold and T (00.5. When the weght zero th mean the ubttuton of an mage by another. ( p M A called the match meaure whch defned a ( ( ( ( ( ( } } p E p E t n m t n m t w p M A T t S A d d A Fgure 3: Schematc Dagram of WAMM

7 . Fuon aed on Propoed Method n NST Doman Standard Devaton calculated on the low frequency component of the nput mage wthn a 3- by-3 wndow and whchever ha the hgher value of Mean are elected a the fuon coeffcent among the low frequency component. Whle WAMM ued n the hgh frequency component to obtan the fuon coeffcent. The hgh frequency component ha the crucal nformaton wthn the mage lke the texture brghtne and contrat. The WAMM take care of preervng thee detal much more better than the fuon cheme that we dcued before. Fgure : Schematc Dagram of Propoed Method The ue of tandard devaton enhance the fuon cheme by preervng the edge n the mage whle WAMM help to preerve the texture and other detaled nformaton n the mage by provdng a way to combne the value wthout much ba e a low value compenated by gvng a proper weght to provde a conderable contrbuton wth repect to a hgh value. 5. PERFORMANE MEASURES The ue n the performance evaluaton of an mage fuon algorthm that the unavalablty of reference mage. In addton relevant reearch how that a ngle meaurement cannot be effectvely evaluate the performance of dfferent fuon algorthm or alway cannot be content wth human vual percepton. ( Qualtatve approache: nvolve vual comparon of the nput mage and the output mage. ( Quanttatve approache: nvolve a et of pre-defned qualty ndcator for meaurng the pectral and patal mlarte between the fued mage and the orgnal mage. 75

8 ecaue qualtatve approache and vual evaluaton may contan ubectve factor and may be nfluenced by peronal preference quanttatve approache are often requred to prove the correctne of the vual evaluaton. For quanttatve evaluaton a varety of fuon qualty aement method have been ntroduced by dfferent author. The qualty ndexe/ndcator ntroduced nclude for example Standard Devaton (SD Mean Abolute Error (MAE Root Mean Square Error (RMSE Sum Squared Error (SSE baed Index Agreement oeffcent baed on Sum Squared Error (SSE Mean Square Error (MSE and Root Mean Square Error Informaton Entropy Spatal Dtorton Index Mean a Error (ME a Index orrelaton oeffcent ( Warpng Degree (WDPella Metrc (P Spectral Dtorton Index (SDI Image Fuon Qualty Index (IFQI Spectral Angle Mapper (SAM Relatve Dmenonle Global Error (ERGASetc. However t alo not eay for a quanttatve method to provde convncng meaurement. In our work obectve analy of the propoed method done ung the performance metrc. Even though thee metrc do not provde a foolproof etmate of the performance of the method they can be ued n comparatve analy a a performance ndcator. Followng are the metrc ued for performance evaluaton n th reearch work. 5.. Entropy Entropy a meaure of nformaton content of an mage. It help to know the nformaton content of the ource mage and the output fued mage. An ncreaed value of entropy of the fued mage mple a better fuon cheme. H ( S P( X log P( X Smlarty Meaure The magntude of gradent G ( m n at a pont (m n of mage F obtaned by G ( m n F ( m n F ( m + n + + F ( m n F ( m + n } 8 '' where G G are the gradent mage of nput mage. Then G G are combned nto G by '' takng the maxmum gradent value at each poton. G can be een a the gradent mage of the deal fuon mage. The gradent of the actual fuon mage G are alo calculated. The mlarty S between the deal fuon mage and the actual fued mage calculated by formula S( G G ( G( m n ( G( m n G ( m n + ( G ( m n A hgher value of S would ndcate a better fuon cheme Pella Metrc Let xx N} and yy N} be the orgnal and the tet mage gnal repectvely. The Unveral Image Qualty ndex propoed by Zhou Wang [3] defned a 76

9 σ xy xy Q ( σ + σ [( x + ( y ] w x N y N x n x n x y 0 3 Th qualty ndex model any dtorton a a combnaton of three dfferent factor: Lo of orrelaton Lumnance Dtorton and ontrat Dtorton. In order to undertand th the defnton of Q can be rewrtten a a product of three component: 5 The frt component the correlaton coeffcent between x and y whch meaure the degree of lnear correlaton between x and y and t dynamc range [-]. The bet value obtaned when y ax +b for all N where a and b are contant and a>0. Even f x and y are lnearly related there tll mght be relatve dtorton between them whch are evaluated n econd and thrd component. The econd component wth a value range of [0] meaure how cloe the mean lumnance between x and y. It equal f and only f x y σ σ x and y can be vewed a etmate of the contrat of x and y o the thrd component meaure how mlar the contrat of the mage are. It range of value alo [0]where the bet value acheved f σ σ and only f x y. Pella Metrc[3] a qualty meaure whch derved from the above mentoned metrc and offer much more focu on the localty of reference of the mage. It take nto account regonbaed meaurement to etmate how well the mportant nformaton n the ource mage repreented by the fued mage. The evaluaton of Pella Metrc of the fued mage f of the nput mage a and b defned a 6 77

10 Q α E ( a b f QW ( a b f Q ( a W b f 7 where a b f are the edge mage of a b and f repectvely. anny operator elected to detect the edge nformaton whch detect the edge by earchng the local maxmum of mage gradent. anny operator detect the trong edge and weak edge wth two threhold repectvely where the threhold are ytem automatc electon. The anny operator not entve to noe and can detect the true weak edge. In order to meaure the metrc a ldng wndow employed: tartng from the top-left corner of the two mage a ldng wndow of a fxed ze travere over the entre mage untl the bottomrght corner reached. For each wndow the local qualty ndex computed. Fnally the overall mage qualty ndex computed by averagng all local qualty ndce. Q W ( a b f the weghted fuon qualty ndex and defned a ( λ( w Q ( a f w + ( ( w Q ( b f w Q W ( a b f c( w 0 λ 0 w W 8 where λ(w a local weght gven by ( a w λ( w ( a w + ( b w ( a w where ome alency of mage a n wndow w. The energy elected a the alent feature and the ze of the wndow 3 by 3 and t moved tartng from the top-left corner of the two mage untl the bottom-rght corner reached 9 The overall alency of a wndow defned a ( w max ( a w ( b w c( w w / w ( ( w ( w 30 3 The Keyword ecton begn wth the word Keyword n 3 pt. Tme New Roman bold talc Small ap font wth a 6pt. pacng followng. There may be up to fve keyword (or hort phrae eparated by comma and x pace n 0 pt. Tme New Roman talc. An 8 pt. lne pacng follow. 6. RESULT ANALYSIS Image Fuon technque requre the regtered mage for tetng. Image Regtraton [] the determnaton of a geometrcal tranformaton that algn pont n one vew of an obect wth correpondng pont n another vew of that obect or another obect. The experment are carred out wth the regtered mage. The varou tattcal rule have been analyzed and the propoed tattcal fuon rule (WAMM teted n both wavelet doman and NST doman on Medcal mage Remote Senng mage and Mult Focu mage. 78

11 6.. Experment on Medcal Image Dfferent medcal magng technque may provde can wth complementary and occaonally conflctng nformaton. The combnaton of mage can often lead to addtonal clncal nformaton not apparent n the eparate mage. The goal of mage fuon to mpoe a tructural anatomcal framework n functonal mage. Often a ngle functonal mage may not contan enough anatomcal detal to determne the poton of a tumour or other leon Am: To fue two greycale medcal mageof whch one a T mage and the other a MR mage Expermental Setup: Input mage: 56 x 56 greycale T and MR mage of bran (Fgure 5. (a-b. (a (b 79

12 (c (d Fgure 5:(aT mage (bmr mage (cwavelet fued mage ung Entropy (d NST fued mage ung Entropy (e (f 80

13 (g (h Fgure 5:(e Wavelet fued mage ung Mean(f NST fued mage ung Mean (g Wavelet fued mage ung SD (h NST fued mage ung SD ( ( Fgure 5:( Wavelet fued mage ung WAMM (NST fued mage ung WAMM 8

14 6..3 omparatve Analy Table : The performance meaure obtaned for Medcal Image Fuon ung dfferent method Doman EN EN EN3 S PM Method (Entropy Method (Mean Method3 (S D WAMM Wavelet NST Wavelet NST Wavelet NST Wavelet NST Here EN and EN repreent the entropy of the orgnal mage to be fued n wavelet and NST doman repectvely. In the fued mage wth WAMM perform better than n NST than wavelet doman and t preerve more detal n the fued mage. The artfact and ncontence n wavelet doman removed n NST doman ung WAMM method. In the above table t een that the fuon wth SD Smlarty and PM gve better reult 6.. Experment on Multfocu mage Due to the lmted depth-of-focu of optcal lene (epecally thoe wth long focal length t often not poble to get an mage that contan all relevant obect n focu. One poblty to overcome th problem to take everal pcture wth dfferent focu pont and combne them together nto a ngle frame that fnally contan the focued regon of all nput mage Am: To fue two greycale multfocu mage ung the extng method and the propoed method Expermental Setup: Input mage: 56 x 56 greycale clock mage wth Fgure 5.:(aFocu on rght clock (bfocu on left clock. 8

15 6..3. Reult: (a (b (c (d Fgure 6:(aFocu on rght clock (bfocu on left clock (cwavelet fued mage ung Entropy (d NST fued mage ung Entropy 83

16 (e (f (g (h Fg 6 (e Wavelet fued mage ung Mean(f NST fued mage ung Mean(g Wavelet fued mage ung SD(h NST fued mage ung SD 8

17 ( ( Fg 6 ( Wavelet fued mage ung WAMM ( NST fued mage ung WAMM omparatve Analy: Table : The performance meaure obtaned for mult-focu mage fuon ung dfferent method Doman EN EN EN3 S PM Method (Entropy Method (Mean Method3 (SD WAMM Wavelet NST Wavelet NST Wavelet NST Wavelet NST Here EN and EN repreent the entropy of the orgnal mage to be fued n wavelet and NST doman repectvely In the fued mage wth WAMM perform better than n NST than wavelet doman and t preerve more detal n the fued mage. The artfact and ncontence n wavelet doman 85

18 removed n NST doman ung WAMM method. In the above table t een that the fuon wth SD Smlarty and PM gve better reult. 7. ONLUSIONS In th work a new tattcal fuon rule Weghted Average Mergng Method (WAMM propoed n NST doman. A revew of the dfferent tattcal fuon rule uch a Entropy Mean Standard Devaton and Weghted Arthmetc Mergng Method dcued. In the method fuon rule ung Standard Devaton the edge nformaton preerved uccefully wthn the mage but mage lacked vual qualty that we expected. So n order to overcome the lmtaton of the extng tattcal fuon rule the combnaton of Standard Devaton n the coare cale and Weghted Arthmetc Mergng Method (WAMM n the fne cale propoed. A new tattcal fuon rule WAMM propoed n NST doman. Expermental reult how that WAMM method for mage fuon obtaned better reult n NST doman when teted wth performance meaure SD Smlarty and Pella Metrc. It preerve the edge detal and the vual qualty of the fued mage. The analy obtaned how that the propoed WAMM yeld better reult n NST doman. Th propoed cheme teted both n NST and n wavelet doman and the reult were compared and obtaned better reult. A a future work an Adaptve Weghted Average Mergng Method can be uggeted. AKNOWLEDGEMENTS All author would lke to thank Dr. Olver Rocknger and the TNO Human Factor Reearch Inttute for provdng the ource IR and vble mage that are publcly avalable onlne at REFERENES [] A. L. unha J. Zhou and M. N. Do The Nonubampled ontourlet Tranform: Theory Degn and Applcaton" IEEE Tran. Image Proceng vol.5 no. 0 pp Oct. 006 [] J. Zhou A. L. da unha and M. N. Do Nonubampled contourlet tranform: ontructon and Applcaton n Enhancement" Proc. of IEEE Internatonal onference on Image Proceng Sep [3] J. Zhou A. L. da unha and M. N. Do Nonubampled contourlet tranform: Flter degn and applcaton n mage denong " Proc. of IEEE Internatonal onference on Image Proceng Sep [] n Yang Shutao L and Fengme Sun. Image Fuon Ung Nonubampled ontourlet Tranform " IEEE Internatonal onference on Image and Graphc 007. [5] Heng Ma huanyng Ja and Shuang Lu. Multource Image Fuon aed on Wavelet Tranform" Internatonal Journal of Informaton Technology Vol. No [6] Le Tang Feng Zhao Zong-Gu Zhao. The Nonubampled contourlet tranform for mage fuon" Proc. of the Internatonal onference on Wavelet Analy and Pattern Recognton Nov [7] Qang Fu Fenghua Ren Legeng hen. Mult-focu Image Fuon Algorthm aed on Nonubampled ontourlet Tranform" Proc. of IEEE Internatonal onference on Image Proceng 00. [8] Do M N Vetterl M. The contourlet tranform: an effcent drectonal amultreoluton mage repreentaton" IEEE Tranacton on Image Proceng

19 [9] M. J. Shena. The dcrete wavelet tranform: Weddng the trou and Mallat algorthm"ieee Tran. Sgnal Proce.vol. 0 no. 0 pp.68 Oct. 99. [0] R. Gonzalez and R. Wood. Dgtal Image Proceng 3rd Edton. Prentce Hall 009. [] R. H. amberger and M. J. T. Smth. A Flter bank for the drectonal decompoton of mage: Theory and degn"ieee Tran. Sgnal Proce. vol. 0 no. pp Apr. 99. [] G. Pella and H. Heman A new qualty metrc for mage fuon In Proc. Int. onf. Image Proceng arcelona Span pp World Academy of Scence Engneerng and Technology [3] Z. Wang and A.. ovk. A unveral mage qualty ndex IEEE Sgnal Proceng Letter Vol. 9 No. 3 pp [] arbara Ztova Jan Fluer Image regtraton method: a urvey.image and Von omputng ( Author Manu.V.T. wa born n Kerala Inda on June He graduated n omputer Scence & Engneerng from Natonal Inttute of Technology alcut Inda n 007. He dd h mater at Unverty of Kerala wth pecalzaton n Dgtal Image omputng. H area of nteret are mage proceng and operatng ytem. PhlomnaSmon dd her.tech(govt Engg ollege Thruvananthapuram and M.Tech SE from Pondcherry Unverty. Her area of nteret are artfcal ntellgencecomputer network and mage proceng 87