Multi-focus Image Fusion Using Spatial Frequency and Genetic Algorithm

Transcription

1 0 IJCSNS Internatonal Journal of Computer Scence and Network Securty, VOL.8 No., February 008 Mult-focus Image Fuson Usng Spatal Frequency and Genetc Algorthm Jun Kong,, Kayuan Zheng,, Jngbo Zhang,,*,, Xue Feng Computer school, Northeast Normal Unversty, Changchun, Chna Key Laboratory for Appled Statstcs of MOE, Chna College of Humantes and Scences of Northeast Normal Unversty, Changchun, Chna Summary We ntroduce n ths paper a regon based mult-focus mage fuson algorthm usng spatal frequency and genetc algorthm. The basc dea s to dvde the source mages nto blocks, and then select the correspondng blocks wth hgher spatal frequency value to construct the resultant fused mage. GA s brought forward to determne the sutable szes of the block. Key words: Mult-focus mage fuson, genetc algorth spatal frequency.. Introducton A wde varety of data acquston devces are avalable at present, and hence mage fuson has become an mportant There are a number of technques for mult-focus mage fuson. Smple technques n whch the fuson operaton s performed drectly on the source mages (e.g. weghted average method), often have serous sde effects lke reducton n the contrast of the fused mage. Other approaches nclude, mage fuson usng controllable camera [], probablstc methods [3], mage gradent method wth majorty flterng [4], mult-scale methods [5] and mult-resoluton approaches [6] [9]. Methods descrbed n [] depend on controlled camera moton and do not work for arbtrary set of mages. Probablstc technques nvolve huge computaton usng floatng pont arthmetc and thus requre a lot of tme and memory-space. Image gradent method wth majorty flterng has the drawback that the defocused zone of one mage s enhanced at the expense of focused zone of others. We ntroduce n ths paper a regon based mult-focus mage fuson algorthm usng spatal frequency and genetc algorthm (GA), whch combnes pxel-level and feature-level fuson. The basc dea s to dvde the source mages nto blocks, and then select the correspondng blocks wth hgher spatal frequency value to construct the resultant fused mage. GA s brought forward to determne the sutable szes of the block. The advantages of our method are the smplcty of computaton and the automaton of selectng the block szes. And the resultant fused mages are both qualtatvely and vsually superor to those produced by the Haar wavelet method and morphologcal wavelet approach, partcularly when there * s movement n the objects or ms-regstraton of the source mages. The rest of ths paper s organzed as follows. Secton gves the bref ntroducton of the spatal frequency. Secton ntroducton of the GA The proposed fuson scheme s descrbed n Secton4. Expermental results and dscusson are presented n Secton 5.. Spatal Frequency Spatal frequency [0] measures the overall actvty level n an mage. For an M N mage block F, wth gray value F( at poston (, the spatal frequency s defned as SF + Where RF and CF are the row frequency M N RF = MN And column frequency m= n= = RF CF () [ F( n )] N M CF = [ F( m, ] (3) MN n= m= Fg. shows a mage block extracted from the Lab mage. Fg. - show the degraded versons after blurrng wth a Gaussan of radus 0.5,,, respectvely. It can be seen from TABLE that when the mage becomes more blurred, the spatal frequency value dmnshes accordngly. Ths demonstrates that the spatal frequency can be used to reflect the clarty of an mage. Correspondng author Ths work s support by Scence Foundaton for Young Teachers of Northeast Normal Unversty, NO , and Tranng Fund of NENU S Scentfc Innovaton Project, No. NENU-STC0708, Chna. ()

2 IJCSNS Internatonal Journal of Computer Scence and Network Securty, VOL.8 No., February 008 ( Fg.. Orgnal and blurred versons of an mage block from the Lab mage. orgnal mage; radus=0.5; ( radus=; radus=. Table. Spatal Frequences of the mage block n Fg. Fg. Fg. Fg.( Fg. 4. Mult-focus mage fuson The problem to be solved here s as follows: Gven two (or more) mages of a statonary camera, t s requred to combne the mages nto a sngle one that has all objects n focus wthout producng detals that are non-exstent n the gven mages. Although the fuson algorthm can be extended straghtforwardly to handle more than two source mages, we only consder the fusng of two source mages for smplcty. The algorthm conssts of the followng steps: () Decompose the source mages A and B nto blocks of sze M N. Denote the th blocks of A and B by A and B, respectvely. SF Fundamental concepts of genetc algorthm Assumng that we employ GA to search for the largest ftness value wth a gven ftness functon. In GA, as shown n Fg., the core components are depcted as follows [][]. () Select mate: A large porton of the low ftness ndvduals s dscarded through ths natural selecton step. Of the N ndvduals n one teraton, only the top N ndvduals survve for matng, and the bottom N bad = N N ones are dscarded to make room for the new of sprngs n the next teraton. Therefore, the selecton rate s N / N. () Crossover: Crossover s the frst way that a GA explores a ftness surface. Two ndvduals are chosen from N ndvduals to produce two new offsprng. A crossover pont s selected between the frst and the last chromosomes of each ndvdual after the crossover pont are exchanged, and two new offsprng are produced. (3) Mutate: Mutaton s the second way that a GA explores a ftness surface. It ntroduces trats not n the orgnal ndvduals, and keeps GA from convergng too fast. The pre-determned mutaton rate should be low. Most mutatons deterorate the ftness of an ndvdual, howeve the occasonal mprovement of the ftness adds dversty and strengthens the ndvdual. After obtanng the fundamental concepts n GA, we are able to desgn an optmzed fuson system wth the ad of GA. Fg.. The flow chart of genetc algorthm. () Compute the spatal frequency of each block, and denote the spatal frequences of A and B by A SF and B SF, respectvely.

3 IJCSNS Internatonal Journal of Computer Scence and Network Securty, VOL.8 No., February 008 (3) Compare the spatal frequences of two correspondng blocks A and B, and construct the th block F of the fused mage as A B A, SF > SF + th, A B F = B, SF < SF th, (4) A + B, otherwse. Here, th s a user-defned threshold. (4) Verfy and correct the fuson result n step (3): specfcally, f the center block comes from A, whle the majorty of ts surroundng blocks are from B, then ths center block wll be changed to be from B, and vce versa. In the mplementaton, we use a majorty flter together wth a 3 3 wndow. (5) Snce dfferent szes of block can lead to dfferent qualty of resultant mages, GA s employed to search for the optmzed szes of block. 5.Expermental results and dscusson We have compared our results wth those obtaned usng Haar wavelet transform fuson and morphologcal wavelet fuson proposed by Ishta De and Bhabatosh Chanda []. The expermental results are shown n Fg. 3 and Fg. 4. In each fgure, the reference mage (all n focus) and source mult-focus mages are gven frst, followed by resultant fused mages produced by Haar wavelet, morphologcal wavelet and our proposed method. A clearer comparson can be made by examng the dfferences between the reference mage and resultant mage. The Haar wavelet transform and morphologcal wavelet are decomposed up to the thrd level. (e) (g) () Fg. 3 The Dsk source mages (sze = ) and fuson results: reference mage. focus on the rght. ( focus on the left. Haar wavelet result. (e) morphologcal wavelet result. (f) the result of the proposed algorthm. (g) - ( are the local magnfcatons of,, (e) and (f), respectvely. A..Performance Analyss Careful nspecton of Fg. 3 and Fg. 4 reveals that the results obtaned by the proposed method are better than that of Haar wavelet transform method and morphologcal wavelet method, partcularly when there s a slght movement of the student s head n Fg. 4 and (. Howeve ths s a subjectve measure of qualty and may not be unversally acceptable. Hence root mean squared error (RMSE) measure and smlarty measure [] are also adopted. (f) (h) ( ( (

4 IJCSNS Internatonal Journal of Computer Scence and Network Securty, VOL.8 No., February Fg. 4 (Lab) (e) (g) () Fg. 4 The Lab source mages (sze = ) and fuson results: reference mage. focus on the rght. ( focus on the left. Haar wavelet result. (e) morphologcal wavelet result. (f) the result of the proposed algorthm. (g) - ( are the local magnfcatons of,, (e) and (f), respectvely. ) RMSE measure When there s a reference mage, the RMSE measure s more sutable for performance evaluaton. For reference mage R and fused mage F (both of sze I J ), the RMSE s defned as follows. I J = j= = (f) (h) ( [ R(,, ] RMSE I J (5) where R (, j ) and F (, are the pxel values at poston (, j ) of R and F, respectvely. Smaller the value s, better s the fused performance. Table shows the RMSE s of fused mages n Fgs Fgure Fg. 3 (Dsk) Table RMSEs of fused mages Proposed Algorthm / Block sze Haar wavelet Morphologcal wavelet [] ) Smlarty measure Gradent or dervatve operators are useful tools to measure the varaton of ntensty wth respect to mmedate neghborng ponts or pxels of an mage. It s observed that a pxel possesses hgh gradent value when t s sharply focused. An objectve crteron based on ths knowledge s suggested to measure the qualty of the results. Magntude of gradent G at a pont ( r, of mage X s obtaned by G( = { X X ( r +, c + ) + X c + ) X ( r +, }. (6) G for the mage wth all parts properly focused may be obtaned from varous partally focused mages as follows. For a set of n mult-focus mages X, =,..., n, the gradent mages G, =,..., n are obtaned frst. Then, G, =,..., n are combned nto G by takng the maxmum gradent value at each poston,.e. G = max{ G, G,..., Gn } (7) for all ( r, c ) Thus only the sharply focused regons from the consttuent mages have ther contrbuton n the maxmum gradent mage G. Let G denote the gradent mage obtaned from the reconstructed mage X. It s referred to as the gradent of fused mage. Then, more smlar G and G are, better s the fuson algorthm. The smlarty S between two mages s calculated as follows: S( G, G ) = ( G( ( G( G ) ) + ( G ) (8) Hence, for an deal fused mage S approaches the value. Smlarty between maxmum gradent and fused gradent mages are lst n Table 3. Table 3 Smlarty between maxmum gradent and fused gradent mages Fgure Fg. 3 (Dsk) Fg. 4 (Lab) Proposed Algorthm / Block sze Haar wavelet Morphologcal wavelet [] Then we can get the concluson from above that the results obtaned by our method are superor to Haar wavelet

5 4 IJCSNS Internatonal Journal of Computer Scence and Network Securty, VOL.8 No., February 008 transform method and morphologcal wavelet method n both objectve and vsual evaluatons. 6. Concluson In ths paper we have presented a block based mult-focus mage fuson algorthm usng spatal frequency and GA, whch combnes pxel-level and feature-level fuson. The basc dea s to dvde the source mages nto blocks, and then select the correspondng blocks wth hgher spatal frequency value to construct the resultant fused mage. GA s brought forward to search for the optmzed szes of the block. Performance analyss reveals that our method outperforms the fuson by Haar wavelet and morphologcal wavelet method [], partcularly when there s movement n the objects or ms-regstraton of the source mages. References [] Ishta De, Bhabatosh Chanda: A smple and effcent algorthm for multfocus mage fuson usng morphologcal wavelets. Sgnal Processng 86 (006) [] W. Seales, S. Dutta, Everywhere-n-focus mage fuson usng controllable cameras, Proceedngs of SPIE 905, 996, pp [3] I. Bloch, Informaton combnaton operators for data fuson: a revew wth classfcaton, IEEE Trans. SMC: Part A 6 (996) [4] H.A. Eltoukhy, S. Kavus, A computatonally effcent algorthm for mult-focus mage reconstructon, Proceedngs of SPIE Electronc Imagng, June 003. [5] S. Mukhopadhyay, B. Chanda, Fuson of d gray scale mages usng multscale morphology, Pattern Recognton 34 (00) [6] P.J. Burt, R.J. Lolezynsk, Enhanced mage capture through fuson, n: Proceedngs of the Fourth Internatonal Conference on Computer Vson, Berln, Germany, 993, pp [7] H. L, B. Manjunath, S. Mtra, Multsensor mage fuson usng the wavelet transfor Graph. Models Image Process. 57 (3) (995) [8] X. Yang, W. Yang, J. Pe, Dfferent focus ponts mages fuson based on wavelet decomposton, Proceedngs of Thrd Internatonal Conference on Informaton Fuson, vol., 000, pp [9] Z. Zhang, R.S. Blu Image fuson for a dgtal camera applcaton, Conference Record of the Thrty-Second Aslomar Conference on Sgnals, Systems and Computers, vol., 998, pp [0] Shutao L, James T. Kwok, Yaonan Wang: Combnaton of mages wth dverse focuses usng the spatal frequency. Informaton Fuson (00) [] D.E. Goldberg, Genetc Algorthms n Search, Optmzaton and Machne Learnng, Addson-Wesley, Readng, MA, 99. [] Chn-Shuh Sheha, Hsang-Cheh Huangb, Feng-Hsng Wangc, Jeng-Shyang Pana, Genetc watermarkng based on transform doman technques, Pattern Recognton 37 (004) Jun Kong was born n Jln, Chna. He receved the B.S and M.S degrees from the Department of Mathematcs of Northeast Normal Unversty, Chna, n 99 and 997, respectvely. In 00, he receved the Ph.D. degree from College of Mathematcs of Jln Unversty. From 003 to 004, he worked at Edth Cowan Unversty, Perth, WA, Australa, as a vstng scholar. He s an assocate professor and vce Dean of Computer School of Northeast Normal Unversty. Hs research nterests nclude artfcal ntellgence, dgtal mage processng, pattern recognton, machne learnng, bometrcs and nformaton securty. Kayuan Zheng was born n Jln, Chna. He receved hs B.S degrees from Computer School of Northeast Normal Unversty, Chna, n 003. Now he s also pursung hs M.S degree n Computer School of Northeast Normal Unversty. Hs man research nterests are dgtal mage processng, neural networks and pattern recognton. Jngbo Zhang receved her B.S and M.S degrees from Computer School of Northeast Normal Unversty, Chna, n 993 and 004, respectvely. Her man research nterests are dgtal mage processng, neural networks and pattern recognton. Xue Feng was born n Jln, Chna. She receved her B.S degrees from Computer School of Northeast Normal Unversty, Chna n 005. Now she s also pursung her M.S degree n Computer School of Northeast Normal Unversty. Her man research nterests are dgtal mage processng, pattern recognton and nformaton fuson.