Improvement of Histogram Equalization for Minimum Mean Brightness Error

Transcription

1 Proceedngs of the 7 WSEAS Int. Conference on Crcuts, Systems, Sgnal and elecommuncatons, Gold Coast, Australa, January 7-9, 7 3 Improvement of Hstogram Equalzaton for Mnmum Mean Brghtness Error AAPOG PHAHUA*, FUSAK CHEEVASUVI**, SAKREYA CHIWOG** *Electrcal Engneerng, **Instrumentaton Engneerng *Rajamangala Unversty of echnology Phar akhon, orth Bangkok Campus **Kng Mongkut s Insttute of echnology Ladkrabang Bangkok,HAILAD. * ** Abstract: - hs Research presents the mage enhancng usng a mean-separate hstogram equalzaton method. It can preserve the orgnal brghtness to a certan extends. o provde maxmum brghtness preservaton,. t separates the nput mage s hstogram nto n based on nput mean before equalzng them ndependently. he mage ntally s separated from, and 8 class by calculated threshold level and each class s hstogram equalzed to entre mage, and gets lowest AMBE (AMBE : the absolute dfference between nput and output mean). he result found that AMBE gradually reduces when the separaton s ncreased. Key-Words: - Improvement hstogram equalzaton, mnmum mean brghtness error, absolute mean brghtness error Introducton Improvement of Hstogram Equalzaton s a bass method of ncreasng contrast for an mage. hs s by mappng the grey scale of the nput mage whch passed the converson from cumulatve densty functon. Hstogram entre mage wll help wden the hstogram wth confned scattered nformaton; therefore, the output provdes hgh dfferences. hs becomes popular n satellte mage or radar mage. he problem s that after hstogram equalzaton, the mean of brghtness of the output much converted from the orgnal so that t can not be used as mentoned n [3]. In ths artcle, however, the statstcs s used for separatng hstogram of the orgnal nto n group or sub-hstogram (n=,,3...). Each group s equalzed hstogram ndependently as well as the mean brghtness of each secton should be kept as ntended. hs s to keep the mean brghtness of the mage after hstogram equalzed whch mostly close to the mean brghtness of the orgnal. In [], the method of Mnmum Mean Brghtness Error B-Hstogram Equalzaton (MMBEBHE) s presented. Hstogram of orgnal mage s dvded nto two groups by grey scale whch s the ntal threshold. he grey scale whch s lower than and hgher than must be equalzed ndependently.e. of [] s the result of calculated absolute mean brghtness error (AMBE). Each chosen, the result of mean brghtness error, s reduced. Due to usng all pxels n grey scale, the ncomplete mean brghtness error s found. Hence, n ths research, the method of selectng from separated group s provded. If the sutable s found, we wll go further to how many pxels n grey scale must be used. When the group on the left of s equalzed, the least mean brghtness error occurred. Hstogram Equalzaton Hstogram Equalzaton to get HE mage s determned the mage as. Densty functon of probablty defned by p ( k ) = () When K=,,., L- when k s the number of pxels n each grey scale that appeared n the mage and, s all ponts n the orgnal. After gettng p( k ), the cumulatve densty functon of PDF s calculated that s c( x) = k j = p( () When k = x, whch k =,,.., L- and c( L- ) = s the lowest grey scale and L- s the hghest grey scale. So that defnton functon of mage transformaton f(x) refer to the cumulatve densty functon as k j )

2 Proceedngs of the 7 WSEAS Int. Conference on Crcuts, Systems, Sgnal and elecommuncatons, Gold Coast, Australa, January 7-9, 7 36 f ( x) = ( L ) c( x) (3) he output mage of hstogram equalzaton, y ={y(,j)} can be defned as Υ = f (Χ) () = { f ( (, j) (, j) Χ} () Fgures (a) Orgnal mage of U Fgures (a) Orgnal mage of arctc hare Fgures (b) he output of U from HE Fgures (b) he output of arctc hare from HE he above nformaton, t can be sad that the HE can sgnfcantly transfer the mage brghtness. For example; Fgures (a) s the orgnal mage of arctc hare and Fgures (b) s the hstogram equalzed arctc hare whch conssts of 6 grey scales. In Fgures (b), t s found that the HE mage darker than the orgnal one, and there are more unnatural n each secton. hs s the result of HE whch changed too much brghtness of the mage. he most nterestng pont n HE s that t can transferred the grey scales of the orgnal to new grey scales wth ncreasng the relatonshp of cumulatve densty n orgnal and gnored the old grey scale of the orgnal. Fgures (a) s the orgnal of U and (b) s the HE mage whch s brghter than the orgnal. A lot of nose n whte color occurred on the background and the plane body contrast s reduced whch caused the loss of the sharpness. hs s because of the lmtaton of HE,.e. the mean brghtness of the orgnal mage may not be used. 3 Mnmum Mean Brghtness Error B-Hstogram Equalzaton We can defne the process n the form of a research as follow. Calculate to fnd the threshold value from cumulatve densty.

3 Proceedngs of the 7 WSEAS Int. Conference on Crcuts, Systems, Sgnal and elecommuncatons, Gold Coast, Australa, January 7-9, Separate the orgnal hstogram nto groups or sub-hstogram accordng to determned group whch calculated from. 3. Independently equalze hstogram nto each groups as the separaton n.. Calculate AMBE n each group. Calculaton the mean brghtness of mage s whch can be defned from he result s: 3 orgnal Requre to dvde hstogram nto groups so the smple case s: f g f g f g f g = = = = = 3 () = = f = o f g (6) f g = 3 f g = f g = f g = = = = = 3 orgnal Due to the dffculty of equaton e.g. n the frst group f choose s g or g 6 the equaton s: () when f g s grey scale frequency s grey scale = f g < orgnal but 6 = f g > orgnal For nstance; f hstogram s separate nto groups, the sutable threshold must be calculated, that s,, และ 3 and wll get,, 3 and whch s the mean of each group. If s all pxels n the mage, the pxels n each group wll equal,, 3 and after the mage s dvded nto groups so that the focus can get from the followng formula: = 3 (7) So that the pxel must be equalzed from some grey scales n g 6 to grey scales g to get the result as equaton (). he numbers of pxels whch transferred from g6 to g s Y that can be fnd out from equaton (3) and () f g f g f g f g f g f y g 3 3 ( ) = the result: orgna (3) Snce; Or: 3 3 = 3 (8) y = orgnal ( fg fg fg f3g3 fg g evertheless, the pxels has been transferred, a few errors stll occurred whch s E, e.g. f g ) () = 3 3 (9) E = orgnal ( fg fg... fg ( f y) g) () he requrement s but = orgnal When we get E, t s used n nd group. If s g, t wll be = = f g f g, =, () =... = 3 f6g6 f7g7... f9g9 ( f y) g = orgnal E (6) When some pxels n grey scale g are equalzed to jon g, we get y that s:

4 Proceedngs of the 7 WSEAS Int. Conference on Crcuts, Systems, Sgnal and elecommuncatons, Gold Coast, Australa, January 7-9, 7 38 ( y = orgnal E ) ( f6g6... f9g9 g ( f g ) (7) And the error from nd group s E ( g = orgnal E ) ( f6g6... f9g9 ( f y) (8) E s found out as n equaton (8). he pxels transformaton wll contnue untl before the last group. he last group cannot be transferred because we get all pxels throughout the mage. herefore, the mean brghtness from hstogram equalzaton n each group s E(Y) whch s used to calculate the absolute mean brghtness error. hat s.. AMBE = E( Υ) E( ) (9) When E() s the mean of orgnal mage and E(Y) s the mean of out put mage from HE 3(a) 3(b) Fgure 3(a) hstogram before and after equalzaton group Fgure 3(b) hstogram before and after equalzaton groups Hstogram of mage [] before and after equalzaton ( group) s llustrated n Fgures 3(a). In ths pcture, hstogram s not dvded. Pcture s equalzed n one group wth the lowest and hghest grey scales from to whch scattered throughout the mage. Hstogram separaton nto groups of pcture n Fgures 3(b) s found that t can be calculated threshold at 3 dfferent grey scales.e., and 3 sequentally. he calculated threshold s the pont of pxels transformaton and error calculaton of each group before contnung equalzaton Fndng Analyss when experment and compare the out put from pctures (Arctc hare, U, F6, Clock and Aeral) the absolute mean brghtness error (AMBE) s found by the method of the artcle n [], [3]. And ths research found that AMBE s decreased and able to keep more detal of the pcture as well as more natural sharpness and brghtness. able : Absolute mean brghtness error (AMBE) AMBE HE BBHE DSIHE MMBE propose method BHE [] [] [6] [7] Groups Groups 8 Groups Arctchare U F Clock Aeral

5 Proceedngs of the 7 WSEAS Int. Conference on Crcuts, Systems, Sgnal and elecommuncatons, Gold Coast, Australa, January 7-9, 7 39 Concluson hs research presents the brghtness mprovement whch refers to and adds to the MMBEBHE (Mnmum Mean Brghtness error B- Hstogram Equalzaton). he hub s to separate hstogram by calculatng to fnd out the sutable threshold to get the lowest AMBE. hs s performed by separatng the orgnal mage nto groups, groups and 8 groups sequentally. he output of ths method showed the competence of mantanng the mean brghtness mostly the same as the brghtness of the orgnal mage that llustrated n the table of experment result. Fgures (d) Arctchare ( Groups) Fgures (e) Arctchare (8 Groups) Fgures Output of Arctc hare n varous methods Fgures (a) Arctchare (BBHE) Fgures (b) Arctchare (MMBEBHE) Fgures (a) U (BBHE) Fgures (c) Arctchare ( Groups) Fgures (b) U (MMBEBHE)

6 Proceedngs of the 7 WSEAS Int. Conference on Crcuts, Systems, Sgnal and elecommuncatons, Gold Coast, Australa, January 7-9, 7 smultaneously try to keep the contnuous reducton of AMBE. Fgures s U mage whch s dark background mage and more nose n whte color can be notceable n Fgures (b) due to the ncreasng of brghtness. Obvously, the equalzed out put of groups and 8 groups, the nose n whte color n group decreased and mostly dsappeared n groups and 8 groups. References: Fgures (c) U ( Groups) [] J.S.Lm, wo-dmensonal Sgnal and Image Processng, Prentce Hall, Englewood Clffs, ew Jersey, 99. [] Yeong-aeg km, Contrast Enhancement Usng Brghtness Preservng B-Hstogram Equalzaton, IEEE ransactons on Consumer Electroncs, February, 997. [3] Scott E Umbaugh, Computer vson and Image Processng, Prentce Hall : ew Jersey, 998. Fgures (d) U ( Groups) [] Yu Wan, Qan Chen and Bao-Mn Zhang., Image Enhancement Based On Equal Area Dualstc Sub- Image Hstogram Equalzaton Method. IEEE ransactons Consumer Electroncs,February,999. [] Young-tack Km and Yong-hun Cho, Image Enhancng Method Usng Mean-Separate Hstogram Equalzaton, Unted Stated Patent, Patent o.,963,66, Oct, 999. [6] Yu Wan, Qan Chen and Bao-Mn Zhang, Image Enhancement Based on Equal Area Dualstc Sub- Image Hstogram Equalzaton Method, IEEE ransactons on Consumer Electroncs, vol.,no.,pp. 68-7, Feb Fgures (e) U (8 Groups) Fgures Output of U n varous methods he Arctc hare n Fgures s a pcture wth brght background. he result of the performance of,, and 8 groups have better mean brghtness when compare wth the orgnal mage whch s more unnatural contrast.he groups and 8 groups present more natural mean brghtness; [7] Soon-Der Chen, Mnmum Mean Brghtness Error B-Hstogram Equalzaton n Contrast Enhancement, IEEE ransactons on Consumer Electroncs, ovember, 3. [8] Soon-Der Chen, Contrast Enhancement usng Recursve Mean-Separate Hstogram Equalzaton for Scalable Brghtness Preservaton, IEEE ransactons on Consumer Electroncs, ovember, 3.