Morphological and Median Adaptive Filters Based on LCBP Rank Filter

Transcription

1 Telfor Journal Vol 5 No Morphologcal and Medan Adaptve Flters Based on LCBP ank Flter Dragana Prokn Member IEEE and Mlan Prokn Member IEEE Abstract The presented medan and morphologcal (mn and ma) flters based on low complet bt-ppelne (LCBP) rank flter provde reduced complet of requred processng hardware due to smlar ppelne stages and the complete absence of sortng networks n comparson wth other solutons FPGA realzaton of bt-ppelne medan and morphologcal flter and adaptve bt-ppelne rank flter accordng to ths paper provdes sgnfcantl hgher mamum operatng frequenc and much smaller used chp resources n comparson wth state-of-the-art sortng methods Kewords Medan flters morphologcal flters adaptve flters ppelne processng FPGA mplementaton I INTODUCTION ANK flterng s a nonlnear flterng operaton wdel used n sgnal processng performed b selectng a sample wth a specfed rank from a one-dmensonal (1D) or multdmensonal wndow of samples [1] ank flterng of 1D sgnal s performed b sldng a wndow of length N nput samples over an nput sgnal The output result (rank sample) of order from N nput samples has nput samples less or equal to the output result as well as N- nput samples greater or equal to the output result (Fg 1) nput ma medan mn wndow Sortng network output Fg 1 ank flterng Medan and morphologcal flters (mnmum and mamum flters) are the most popular specfc cases of rank flters n whch the rank s fed to =k=n/2 (nteger dvson) =0 or =N-1 of the sorted N wndow elements respectvel Medan flters remove mpulse nose wthout blurrng the edges n mages Mnmum and mamum Ths work was partal supported b the Mnstr of Educaton and Scence of the epublc of Serba under grant no T32039 and T32043 Correspondng Dragana Prokn s wth the School of Electrcal and Computer Engneerng of Professonal Studes Vojvode Stepe Belgrade Serba (tel: e-mal: dprokn@vseredurs) Mlan Prokn s wth the Unverst of Belgrade School of Electrcal Engneerng Kng Aleander s Boulevard Belgrade Serba (tel: e-mal: proka@eletfrs) flters are used for growng and contractng regons and lnes n mages durng pattern recognton [2] [3] Algorthms and methods for rank flterng can be classfed nto two categores: bt-level and word-level In most cases onl hardware mplementatons are feasble for real tme sgnal processng applcatons [4] The hardware archtectures for mplementng medan and morphologcal flters are based on dfferent methods: threshold decomposton [5] [6] bt seral [7]-[10] hstogram [11] nsert-delete approach [12] and sortng network based algorthms [13]-[18] Most embodments of medan and morphologcal flters are based on a sortng network Estng sortng algorthms are based on arrangng the elements n ascendng or descendng order and then selectng the output based on a desred rank of the flter Sortng networks are ver smple devces that onl perform compare-echange operatons (Fg 2) Archtectures that use bubble sort approach [16] requre N (2N+1) dual nput sorters Ths method s hghl regular but the hardware requrements ncrease n proporton to the wndow sze The odd-even transposton sortng network [12] s a ppelned structure consstng of N stages wth (N-1)/2 compare and swap unts n each stage (Fg 3) X1 X2 X3 X4 X5 X6 X7 X8 X9 comparator out out ( ) out out ( ) Fg 2 Compare block Fg 3 Odd-even transposton sortng network Each unt operates alternatel on both odd and even pars of W-bt wndow elements At the output of the last stage nput elements wll be sorted n such a manner that the largest element wll be at the top and the medan at the mddle The propagaton dela ncreases wth W Merge sortng algorthms repeatedl merge the pars of sorted X(1) X(2) X(3) X(4) X(5) X(6) X(7) X(8) X(9)

2 124 Telfor Journal Vol 5 No subset untl the entre nput set s sorted Btonc mergesort [17] s a parallel algorthm for sortng It s also used for buldng a sortng network (Fg 4) Fg 4 Merge sortng network The fast algorthm BMSN [18] s based on the mnmum-mamum rank range mergng of the sorted subset whch reduces the number of nput elements at each stage of the sortng network The computatonal complet s further reduced b elmnatng comparators whch do not contrbute to computaton of the partcular desred output rank The throughput of the algorthm s further optmzed b ppelnng Ppelnng s acheved b ntroducng regsters for data storage n order to overlap processng The throughput of ppelned realzaton s lmted b nput/output bandwdth and clock of the sstem Unlke most sortng algorthms where the number of comparators s data dependent BMSN bulds a sortng network that s range dependent The number of elements contendng for the output place s reduced after each consecutve stage of sortng thus a reducton n the number of requred comparators s acheved compared to the conventonal methods The optmzaton n terms of area and speed due to a reducton n the number of comparators also depends on the desred rank of the output Snce the medan s the (N+1)/2 largest value ts search b merge sortng method usuall requres 3(N 2-1)/8 comparsons [1] whle BMSN algorthm requres onl N/2log 2 N comparsons The purpose of ths paper s to descrbe the advantages of usng a LCBP rank flter presented n [8] and [9] n morpholog and adaptve flters LCBP of N nput samples wth W bts each s producng a sngle bt of the output result n each ppelne stage and accumulatng them n order to produce the output result per each clock ccle ndependentl of the number N of nput samples LCBP works wthout sortng networks and maskng regsters contrar to all state-of-the-art methods II ALGOITHM DESCIPTION The sldng wndow comprses N unsgned nteger nput samples X[j] W bts each such as one-dmensonal dgtal sgnal samples: W 1 X [ j] b ( j) 2 (1) 0 b {10} where j = 0N-1 MSBs of all N nput samples X[j] are eamned frst The number of bts wth a zero value n each nput data sample s counted b the N-bt adder of zeros The result of ths adder s compared wth the desred rank and f t s greater than the rank the output of the comparator (the result bt) becomes zero In the net stage bts (MSB-1) wll be eamned and so on untl LSBs After passng through W delang deskew regsters the result bt wll become the MSB of the output result equal to the rank sample (selected nput sample) Table 1 shows an eample where fve unsgned 8-bt words (wth values of and 68 respectvel) are rank ordered The wndow sze s N = 5 and the rank value s =3 The result Y=156= s the thrd smallest among these fve numbers TABLE 1: AN EXAMPLE OF ODEING ALGOITHM Word (X) b 7 b 6 b 5 b 4 b 3 b 2 b 1 b esult (Y) Steps n the algorthm descrbed n [8] [9] are repeated for ever stage n order to generate the output result: Step 1: Get W-bt data samples X[j] j=0n-1 and the nput Step 2: Get the MSBs from k-th stage Count number of zeros If number of zeros >= then Output result bt of the k-th stage Y[k]=0 All other bts n an nput data sample wll be kept n case that MSB s zero All other bts n an nput data sample wll be set n case that MSB s one Else f number of zeros < then Output result bt of the k-th stage Y[k]=1 All other bts n an nput data sample wll be kept n case that MSB s one All other bts n an nput data sample wll be reset n case that MSB s zero Step 3: If k > 0 then k = k-1 epeat Step 2 Step 4: Output Y[W-1:0] III HADWAE IMPLEMENTATION Each control logc block n ppelne stage (Fg 5) passes through or modfes nput sample bts accordng to the aforementoned algorthm SAMPLE SAMPLE Fg 5 One ppelne stage Each control logc block (Fg 6) conssts of control elements (CE) feedng sample regsters n the net stage

3 Prokn and Prokn: Morphologcal and Medan Adaptve Flters Based on LCBP ank Flter 125 (Fg 7) Inputs j are the MSBs of the prevous sample regster and s the approprate output result bt In case that these two bts are dentcal the output j -1 s j -1 Otherwse MSB-1 bt of the net sample regster wll become j e the MSB of the prevous sample regster j W 1 j W 2 j 1 j 0 W 1 j W 2 j 1 j j1 j 1 ( j ) Fg 6 One control logc block j0 The selecton of one of multpleer nputs s provded b the output of XO crcut based on MSB of the prevous sample regster (n a general case j or n ths case jw-1 ) and the comparator output (n a general case or n ths case W-1 ) In case that these two bts are dentcal the multpleer output j-1 s the net bt j-1 (MSB-1) of the prevous sample regster (EG) Otherwse the multpleer output j-1 s the j (MSB) of the prevous sample regster (EG) In the proposed LCBP soluton the rank logc block generatng the output result bt of the approprate weght n each ppelne stage conssts of an N-bt adder and a comparator provdng the least comple soluton n FPGA However ths part can be realzed n an other manner whch s more optmal consderng the utlzaton of hardware resources of the partcular chp After passng through delang deskew regsters n each ppelne stage (Fg 9) the result bt wll become the output result equal to the rank sample (selected nput sample) ESULT j 1 SEL j-1 0 CE ' j-1 DESKEW S Fg 7 One control logc element The operaton of the control logc block (CTL) s presented usng the modfcaton of bts from the prevous sample regster (EG) comprsng nput sample [j] bts j wheren = W-1 0 (Fg 8) After passng through the control block (CTL) modfed values are stored n the net sample regster (EG) as j wheren = W- 2 0 Fg 9 Deskew regsters In cases of mnmum or mamum flter the approprate rank logc block s further smplfed to: Ma: Mn: N N-1 X[ j ] MSB MSB-1 MSB-k LSB EG jw-1 jw-k j0 jw-2 CTL MSB-1 MSB-k LSB ' jw-2 ' jw-k ' j0 EG N-BIT ADDE OF ZEOS C O M P A A T O W-1 Fg 8 The eample of frst stage (W-1) control block LCBP rank/medan flter also benefts from the absence of comple bubble sort selecton sort merge sort quck sort and odd-even transposton sort networks n comparson wth [10]-[18] The decreased complet of LCBP rank/medan flter also provdes smpler routng of sgnals and avods the nserton of addtonal logc cells and logc epanders n sgnal paths IV LCABP MEDIAN FILTE An adaptve medan flter can be consdered as an teratve flter The teratve processng was ntroduced n order to detect and replace corrupted pels onl In each teraton flterng wndows of dfferent szes are utlzed The basc algorthm of the adaptve medan flter descrbed n [17] has four steps: Step 1: Intalze the smallest wndow sze W=3 and mamum wndow sze (W ma )

4 126 Telfor Journal Vol 5 No Step 2: Generate mnmum value mn medan value med and mamum value ma usng the selected rank flter (LCBP n our case) Step 3: Evaluate termnatng condtons If mn < pr < ma then the pel pr s not corrupted b nose and the output value pr s the value of the orgnal pel e pr = pr If mn < pr < ma s not satsfed then the output value pr s the medan of the wndow e pr = med and the processng contnues Step 4: Increase wndow sze W If man pels have the same value then t s mpossble to determne (wth the current wndow sze) whether the pels are corrupted wth hgh ntenst nose or whether t s the constant area wth all pels of the same color Ths s the reason wh wndow sze W has to be ncreased If wndow sze W s smaller than W ma ncrease wndow sze W b two e W=W+2 and repeat the computaton from step 2 If wndow sze W reaches the mamum value W ma the processng ends and the output value s defned as pr = med Although the adaptve medan flter s defned as an teratve flter t s possble to generate the result n a twostep process usng multple LCBP rank flters wth a dfferent number of nputs from 33 to W ma W ma operatng n parallel The mnmum value mn medan value med and mamum value ma are generated n each LCBP rank flter However as these LCBPs have dfferent latences t s necessar to dela outputs of LCBPs wth a smaller wndow sze W n order to have all outputs avalable at the same tme In the second step one output s selected b the selector usng the aforementoned algorthm (Fg 10) WINDOW N N SELECTO Fg 10 Hardware mplementaton of LCABP rank flter V TEST ESULTS LCBP flterng algorthm s relatvel smple allowng straghtforward hardware mplementaton VHDL desgn of LCBP medan mn and ma flters have been compled and smulated usng Xln ISE Desgn Sute v111 n Xln FPGA Vrte II E (Table 2) and Xln FPGA Vrte II Pro (Tables 3 and 4) Test results clearl demonstrate a sgnfcantl hgher mamum operatng frequenc and much smaller used chp resources n comparson wth bt-ppelne flters based on sortng methods [17] [18] Furthermore conventonal sortng algorthms are not practcal for larger wndow szes (55 77 and bgger) due to the growth of the sort network wth the square of the wndow sze as well as a sgnfcant decrease n mamum operatng frequenc [18] In addton to fve tmes less resource requrements of LCBP flter for the 33 wndow and seven tmes less for the 55 wndow than BMSN (Table 2) the mamum operatng frequenc of LCBP flter s almost fve tmes hgher for the 33 wndow and more than ten tmes hgher for the 55 wndow It should also be noted that the mamum operatng frequenc of LCBP flter s decreased about 2% for the 55 wndow n comparson wth the 33 wndow whle a decrease n the mamum operatng frequenc of BMSN the flter s greater than 50% The number of nput / output ports of LCBP flter ncreases proportonall wth the ncrease n wndow sze whle the requred number of nput / output ports for BMSN flter mplementaton wth the 55 wndow s almost doubled n comparson wth the 33 wndow due to the complet of the method Based on Table 3 t can be concluded that standard sortng algorthms used n the mplementaton of a medan flter [17] have resource requrements whch are hgher on the average 25 tmes (for the 55 wndow) to 67 tmes (for the 99 wndow) n comparson wth LCBP medan flter Smultaneousl LCBP flter has a hgher operatng frequenc for the 55 wndow appromatel the same frequenc for the 77 wndow and a 1% lower frequenc for the 99 wndow n comparson wth [17] LCBP medan flter used n the mplementaton of an adaptve flter based on the test results shown n Table 4 for all wndow szes has a mamum operatng frequenc whch s 10MHz hgher on the average than the methods descrbed n [17] Wndow sze TABLE 2: MEDIAN MIN AND MAX FILTES IN XILINX FPGA VITEX E FPGA VITEX-E ank LCBP rank flter BMSN [18] Flp flops SLICEs IOB f ma [MHz] Flp flops SLICEs IOB f ma [MHz] medan /12288 (4%) 81/ /12288 (21%) 89/ mn /12288 (4%) 81/ /12288 (20%) 89/ ma /12288 (4%) 81/ /12288 (20%) 89/ medan /12288 (6%) 209/ /12288 (46%) 393/ mn /12288 (6%) 209/ /12288 (42%) 393/ ma /12288 (6%) 209/ /12288 (42%) 393/

5 Prokn and Prokn: Morphologcal and Medan Adaptve Flters Based on LCBP ank Flter 127 Number N of nput samples n a wndow (WW) LCBP medan flter TABLE 3: MEDIAN FILTES IN XILINX FPGA VITEX II PO FPGA VITEX II Pro Odd-even merge sortng network Method [17] Btonc sortng network f ma [MHz] SLICEs f ma [MHz] SLICEs f ma [MHz] SLICEs 25 (55) /23616 (3%) /23616 (7%) /23616 (7%) 49 (77) /23616 (4%) /23616 (19%) /23616 (20%) 81 (99) /23616 (7%) /23616 (41%) /23616 (44%) Mamum number N of nput samples n a wndow (W ma W ma ) TABLE 4: ADAPTIVE MEDIAN FILTES IN XILINX FPGA VITEX II PO LCABP medan flter FPGA VITEX II Pro Odd-even merge sortng network Method [17] Btonc sortng network f ma [MHz] Slces f ma [MHz] Slces f ma [MHz] Slces 25 (55) /23616 (6%) /23616 (9%) /23616 (9%) 49 (77) /23616 (13%) /23616 (31%) /23616 (28%) 81 (99) /23616 (24%) /23616 (77%) /23616 (70%) VI CONCLUSION In ths paper the comparson of FPGA realzatons of varous rank flterng methods s presented For realzatons dfferent FPGA platforms are used The proposed LCBP method provdes not onl a smple ppelned archtecture but also a hghl regular structure wth repeated modules LCABP requres sgnfcantl less chp resources n comparson wth the best sortng networks used n state-of-the-art morphologcal and adaptve flters The hardware mplementaton of morphologcal and medan adaptve flters based on LCBP rank flter can easl ft nto modern FPGAs leavng enough resources to mplement other processng logc The mamum clock rate of the desgned flter meets the demands of real-tme applcatons [19] [20] EFEENCES [1] S Marshall Logc-based Nonlnear Image Processng Bellngham Washngton 2007 pp [2] T Chen and H Wu Space varant medan flters for the restoraton of mpulse nose corrupted mages IEEE Trans Crcuts Sst II vol 48 no 8 pp Aug 2001 [3] D S chards VLSI medan flters IEEE Trans Acoust Speech Sgnal Process vol 38 no 1 pp Jan 1990 [4] J Gl and M Werman Computng 2D mn medan and ma flters IEEE Trans Pattern Anal Mach Intell vol 15 no 5 pp [5] J Ftch E Cole N Gallagher C Jr Threshold decomposton of multdmensonal ranked order operatons IEEE Trans Crcuts Sst vol 32 no 5 pp [6] L W Chang and S S Yu A New Implementaton of Generalzed Order Statstcs Flter b Threshold Decomposton IEEE Trans Sgnal Proc vol 40 pp [7] C Chang and V Punam A real-tme bt-seral rank flter mplementaton usng Xln FPGA n Proc SPIE eal-tme Image Processng Jan 2008 vol 6811 pp 68110F (1-8) [8] D Prokn and M Prokn eal-tme ppelned rank flter Int J Imagng Scence Eng vol 1 no 1 pp [9] D Prokn and M Prokn Low hardware complet ppelned rank flter IEEE Trans Crcuts Sst II Ep Brefs vol 57 no 6 pp [10] T W Lee J H Lee and S B Choo FPGA mplementaton of a 33 wndow medan flter based on a new effcent bt-seral sortng algorthm n Proc 7th Korea-ussa Int Smp KOUS 2003 pp [11] S A Fahm P Y K Cheung and W Luk Novel FPGA-based mplementaton of medan and weghted medan flters for mage processng n Proc Int Conf Feld Programmable Logc and Applcatons Aug 2005 pp [12] T S Huang G J Yang G Y Tang Fast two dmensonal medan flterng algorthm IEEE Trans Accoust Speech Sgnal Proc vol ASSP-27 pp [13] B K Kar and D K Pradhan A new algorthm for order statstc and sortng IEEE Trans Sgnal Process vol 41 no 8 pp Aug 1993 [14] K Oflazer Desgn and mplementaton of a sngle chp 1-D medan flter IEEE Trans Acoust Speech Sgnal Processng vol 31 no 5 pp Oct 1983 [15] L W Chang and J H Ln A bt-level sstolc arra for medan flter IEEE Trans Sgnal Process vol 40 no 8 pp Aug 1992 [16] K Benkrd D Crookes and A Benkrd Desgn and mplementaton of a novel algorthm for general purpose medan flterng on FPGAs n Proc IEEE Int Smp Crcuts Sst 2002 vol 4 pp [17] Z Vascek and L Sekanna Novel hardware mplementaton of adaptve medan flters n Proc 11th IEEE Desgn and Dagnostcs of Electronc Crcuts and Sstems Workshop Apr 2008 pp 1-6 [18] S M Meena and K Lnganagouda ank based merge sortng network archtecture for 2D medan and morphologcal flters n Proc Int Advance Computng Conf Mart 2009 pp [19] J Scott M Pusater and M U Mushtaq; Comparson of 2D medan flter hardware mplementatons for real-tme stereo vdeo n Proc 37th IEEE Appled Imager Pattern ecognton Workshop Oct 2008 pp 1 6 [20] V Vjakumar D Ebenezer and P T Vanath Detal preservng medan based flter for mpulse nose removal n dgtal mages n Proc 9th Int Conf Sgnal Processng Oct 2008 pp