Suppression for Luminance Difference of Stereo Image-Pair Based on Improved Histogram Equalization

Transcription

1 Suppresson for Lumnance Dfference of Stereo Image-Par Based on Improved Hstogram Equalzaton Zhao Llng,, Zheng Yuhu 3, Sun Quansen, Xa Deshen School of Computer Scence and Technology, NJUST, Nanjng, Chna.School of Informaton and Control Engneerng, NUIST, Nanjng, Chna.3School of Computer Scence and Technology, NUIST, Nanjng, Chna Abstract. In order to recover the depth and obtan the 3-D coordnates of the feature ponts n front of bnocular stereo camera, hgh-precson stereo matchng s very mportant. Image gray based matchng method s a major approach wth ts smple calculaton and low complexty. Generally the matchng accuracy relates to the lumnance dfference of the mage-par and hgher accuracy needs lower lumnance dfference. Hstogram equalzaton s commonly used when the lumnance dfference of the mage-par beng balanced, but the mage gray dynamc range wll be changed and artfact wll be appearance. In order to overcome these drawbacks, an mproved hstogram equalzaton method was proposed. Ths method combnes the local nformaton and mddle axs hstogram equalzaton to balance the brghtness. Both theoretcal analyss and expermental results show that ths approach can suppresses lumnance dfference and mprove matchng accuracy of stereo mage-par effectvely. Keywords: stereo mage-par; lumnance dfference; mddle axs hstogram equalzaton Introducton Wth the ncreasng applcaton n 3-D vson technology, demand for hgher tmelness and accuracy are ncreasng. Image gray based method and feature extracton based method are commonly used. But gray based method has an mportant poston, because the mathematcal models, convergence speed, postonng accuracy and error estmates wth quanttatve analyss and research fndngs s smple and low complexty []. However, ths method has an assumpton that the same target n the left and rght mage has the same gray value. Ths assumpton does not meet the actual stuaton. In fact, mage acquston process wll be nterfered by dfferences lght and brghtness between the stereo camera, so the brghtness of the same target n the left and rght mages wll have a greater dfference. Therefore, when usng gray based method for better match and accuracy fundamentally, suppresson for lumnance Ths work was supported by the Natonal Scence Foundaton of Chna, the Natonal Scence Foundaton of Jangsu Provnce and Doctoral Fund of Mnstry of Educaton of Chna (RFDP) under grant no , BK0084 and

2 dfference of stereo mage-par s necessary. To transform the mage and suppresson for lumnance dfference, hstogram equalzaton and related mprovements are often used. But, most knds of method has ts drawbacks. In ths paper, a new mage equalzaton method was proposed. Ths method combnes the local nformaton and mddle axs hstogram equalzaton. Expermental results show that, the proposed method can effectvely correct brghtness dfferences, keep the mage gray dynamc range and can mprove the matchng accuracy wth lttle mage detals lost. Essental dfference n hstogram equalzaton Lumnance dfference of stereo mage-par can be reflected n dfferent gray of the same object n mage-par and dfferent dynamc range n mage hstogram. An approprate method to adjust the mage hstogram of stereo mage-par to be the same s necessary. If we consder two magesi andi, whose cumulatve hstogram arehandh. In order to make HandH to be the same, we have to choose a cumulatve hstogramh and contrast them to be as correspondh. IfH s the dentty functon on [0,], each magei becomes H ( I ),.e. each hstogram s equalzed. All of the approach based on hstogram equalzaton can be attrbuted to select the approprate mappng ruleh. Proposton : f : Ω [ 0, ] ( Ω R, =, ) s the mage-par, I h s the mage hstogram ofi, the cumulatve hstogram H :[ 0, ] [ 0, ] of I s: H ( x) = x h 0 ( t) dt Proposton : f F :[0,] [0,] s a contnuous monotoncally ncreasng functon, thenf of the new mage s: H H o F = H oh, and F ) s a new mage, the cumulatve hstogram = ( I. Hstogram equalzaton The selecton of H n hstogram equalzaton (HE) approach s the cumulatve hstogram of the mage tself. Hstogram equalzaton s the approach that nonlnearly stretchng the orgnal grayscale of the mage accordng to the mappng rule. 08

3 Therefore, the result s to make the number of pxels of each grayscale roughly the same and the dstrbuton of the mage hstogram changng nto a "unform" dstrbuton. But, ths approach has many drawbacks, such as reducng of mage grayscale, dsappearance of mage detal, through enhancement, artfact etc. []. See Fg., detals after hstogram equalzaton s almost not dstngushable from the vegetaton, especally n the rght part of the mage (see n partcular the part n the rectangular zone).. Hstogram specfcaton Hstogram specfcaton (HS) s a transformed approach based on hstogram equalzaton. It s dversfed especally n selectng the approprate mappng ruleh. As for stereo mage-par, f one of the mages s chosen as a reference, the other mage s specfed by the reference cumulatve hstogramh, the two mages wll be as the same mage hstogram. Is not changed, Is changed nto H oh ( I ). The method mantans the orgnal gray dynamc range wth the lower blnd transformaton. If the mages have smlar gray dynamc range,ths approach s approprate. But, f the mages have large dfferences n brghtness. See Fg., artfacts are obvous especally n the left part of the mage (see n partcular the part n the rectangular zone) (a) Image r, the correspondng hstogram hr (b) Image rafter hstogram equalzaton, the hstogram hr Fgure : Effect of hstogram equalzaton

4 (a) orgnal I orgnal I (b) (c) I after HS (d) I after HS Fgure : Effect of hstogram specfcaton.3 Mddle axs hstogram equalzaton Through the analyss above, both approaches have shortcomngs. Hstogram equalzaton flattens the global orgnal mage hstogram dynamc range. Whle, hstogram specfcaton produces a certan loss of mage detal and artfact, although t can mantan the orgnal mage hstogram dynamc range better. These shortcomngs wll reduce the stereo matchng accuracy. Thus, the change level of mage gray dynamc range and the lost of orgnal mage detal must be consdered when selectng the approprate mappng rule before correctng stereo mage-par brghtness. Obvously, f the axs located n the mddle of the two cumulatve hstograms s made as the mappng rule, the mage cumulatve hstogram of the par wll be transformed closer. We can easly fnd the balance relatonshp between the mage hstogram dynamc range and mage detal. Suppose that the mage parsi andi, ther cumulatve hstogram shandh, the mddle of the curve located n the two mages cumulatve hstogram s H. IandI have the same cumulatve hstogram H o and the mage-par wth the same gray-scale dynamc range. In = H F concluson, ths approach can not only reduce the mage hstogram dynamc range change, but also mantan mage detal wthout ncreasng or decreasng obvously. 0

5 3 Theory of mddle axs hstogram equalzaton To llustrate the theory of mddle axs hstogram equalzaton, two artfcal gray mages whch has dstnct gray dynamc range was made. One has hgher gray value, whle the other has lower value. See Fg.3, The cumulatve hstograms contans four lnes placed n a unfed coordnate, H andh s the cumulatve hstograms of orgnal mage, H 3s the numercal average ofhandh, H s the average poston of HandH, H s a straght lne. Obvously, H 3s not the best average result of HandH, because of the new structure n transformed mage, see Fg. 3(d). Ths new structure wll affect the further applcaton [3]. H maybe the better average whch can be calculated from H + H H =. Image transformed by the mddle axs wll has the same gray dynamc range and mantan mage detal wthout ncreasng or decreasng obvously, see Fg. 3(e) (a) I and the correspondng mage hstogram (b) Image after H (c) I and the correspondng mage hstogram (d) Image after H 3

6 0.8 H H3 0.6 H H (e) Cumulatve hstogram H, H H H,, 3 Fgure 3: orgnal mages and the correspondng mage hstogram, transformed mages after the correspondng cumulatve hstograms 4 Proposed algorthm In ths paper, we note global mddle axs mage equalzaton as GMIE. A new approach combnng the local and GMIE was proposed. The new approach s named as block adaptve mddle axs mage equalzaton (BAMIE). The BAMIE based approach can make every pxel adapt to ts surroundngs, better result can be obtaned on lumnous dfference correcton and therefore more detals can be mantaned. Generally, the sze of IandI s set tom N, a real-tme wndow sze sw and step length sw /, two zero matrx I and I wth the same sze as IandI. The steps of BAMIE are as follows: take I wth sze of W n I W and take I wth sze of W n I W from the top left pxel of the mage; calculate the cumulatve hstogram of I W mddle axs H of andi, marked as H W W andh W ; calculate the H W andh W accordng to the nonlnear mappng modelf andf fromh equalzaton, = F H oh W, F H oh W H + H H = H W andh W ; calculate based on mage = ; transform the wndow mage gray value through the formula n(4), that s F I ), F I ) ; I = ( W W I = ( W W puti andi W nto W I and I n the correspondng poston;reuse steps()-(6

7 ), and cumulate the I andi W ntoi and W I when the wndow movng every tme, untl all of mage hstogram s transformed; calculate every pxel value wth weghted accordng to cumulate tmes(bref mathematcal dervaton n annex,a new mage-par I and I are obtaned at last. 5 Experments and dscussons In order to llustrate our algorthm effectveness, we choose a standard mage-par and a real remote sensng mage-par contrast wth the results from hstogram equalzaton (HE), hstogram specfcaton (HS) and GMIE. 5. Effects on gray dynamc range Fg.5~Fg.0 shows an example of applyng the proposed algorthm BAMIE and also the results of applyng hstogram equalzaton (HE), hstogram specfcaton (HS) and GMIE. Although the angle varaton between both vews s small, the lght dfference s exsted. We can see clearly that the number of pxels of each gray roughly the same and the dstrbuton of the mage hstogram changng nto a "unform" dstrbuton after hstogram equalzaton; the hstogram s changed obvously after each mage hstogram specfcaton on the other; after GMIE the hstogram has almost the same gray dynamc range but not smooth; after BAMIE the hstogram has the same appearance especally. In short, hstogram after BAMIE became more dentcal and satsfed wth the assumpton of stereo matchng. The gray dynamc range changes the same after BAMIE. 5. Effects on mage detals and spectrum If we scan some mage detals (Fg.5 and Fg.8), we can see that the detals n BAMIE are rch and vsble. Ths algorthm s an effectve way to perform ths transformaton on dscrete data. Generally, the composton of an mage by a functon doesn t mantan the property to be well sampled, accordng to Shannon-Whttaker samplng theorem. Now, we want to get the match map of the area, the mage must be well sampled f we want a good precson. In order to check the effects of the dfferent transformatons on the spectrum expermentally, we made the followng 3

8 example: we specfyi oni, and we compute the modfcaton of Iva HE, HS, GMIE and BAMIE. From the Fg.(a)~(e) and table, we can see that the spectrums of Iva BAMIE reman more n the central square than that of others and the spectrums energy become balance between the mage-par. Most natural mages have a spectrum really concentrated n the center of ts support. It follows that after a transform lke a hstogram modfcaton, the spectrum sprawls but doesn t go much out of ts support. The ratos of energy presented llustrate that our algorthm s really useful n the applcatons of stereo matchng. Fgure 5: The orgnal mage-par and the transformed mage-par by HE, HS, AMIE, BAMIE 4

9 Fgure 6: The hstogram of the orgnal mage-par and the transformed mage-par by HE, HS, AMIE, BAMIE Fgure 7: The cumulatve hstogram of mage-par Fgure 0: The cumulatve hstogram of mage-par before and after BAMIE before and after BAMIE 5

10 Fgure 8: The orgnal mage-par and the transformed mage-par by HE, HS, AMIE, BAMIE Fgure 9: The hstogram of the orgnal mage-par and the transformed mage-par by BAMIE Fgure : The spectrums of I (remote sensng) and after the transformed by HE, HS, AMIE, BAMIE Table Spectrums energy remaned n central square orgnal HE HS GMIE BAMIE remote mage I remote mage I stranded mage I stranded mage I

11 5.3 Effect on matchng accuracy SSD [4] s a commonly used smlarty measure method,named the sum of squared dsparty. See Fg., the rght mage of remote sensng s the real-tme mage wth the sze of Take a reference wndow from the left mage at the random pont(0,0)wth the sze of 4. The expermental results show that,the matchng pont from the mage transformed by HE, HS, GMIE and BAMIE s( 3,0),(3,0),(3,0),(3,0). All the matchng ponts s correct and same, but the matchng accuracy s dfferent, see table. We take two random experment results and all the results show that mage-par transformed wth the proposed approach can reach the hgher matchng accuracy. (a) (b) (c) (d) (e) (a) (b) (c) 7

12 (d) (e) Fgure : The result of matchng based on gray match method Table orgnal Matchng accuracy HE HS GMIE BAMIE Experment Experment Conclusons The man contrbuton of ths paper s proposng a new approach noted as BAMIE whch combnng the advantage of local adaptve and GMIE. BAMIE based approach makes every pxel adapt to ts surroundngs, better result can be obtaned on lumnous dfference correcton and therefore more detals can be mantaned. Both theoretcal analyss and expermental results show that ths approach can suppresses lumnance dfference and mprove matchng accuracy of stereo mage-par effectvely. References:. L qang, Zhang bo. A gray mage based algorthm of fats matchng, Journal of Software, 006, 7(): 6-.. Tark Arc, Salh Dkb. A hstogram modfcaton framework and ts applcaton for mage contrast enhancement, IEEE Transactons On Image Processng, VOL. 8, NO. 9, September Jule Delon, Fne comparson of mages and other problems, Chp., pp.9-, Brown LG. A survey of mage regstraton technques. ACM Computng Surveys, 99, 4(4):