A Background Subtraction for a Vision-based User Interface *

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1 A Background Subtracton for a Vson-based User Interface * Dongpyo Hong and Woontack Woo KJIST U-VR Lab. {dhon wwoo}@kjst.ac.kr Abstract In ths paper, we propose a robust and effcent background subtracton algorthm for a vson-based user nterface. We separate a user of nterest as precsely as possble from the acqured mages n order to convey the user s ntenson properly nto the system through the vson-based user nterface. Although the background subtracton technques have been adopted n many vson-based nterfaces to extract or track movng objects of nterest n the mages, they stll suffer from the changes of lghtn such as shadows and hghlghtng. The proposed method removes effectvely such nterferences of lghtng changes by explotng pxel-wse statstcal characterstcs and threshold values n the well-known two color spaces (RGB and normalzed RG. Accordng to expermental results, the proposed algorthm can be appled to varous applcatons requrng real-tme segmentaton from the mage sequences on the fly. Keywords: Background Subtracton, Threshold Selecton, Color Space.. Introducton In the last few decades, there have been many studes whch substtute the conventonal user nterfaces wth new types of nterfaces lke vson, gesture, voce, and other sensors. Especally, the advantages of a vson-based nterface over other sensors are to calbrate easly, nteract wth the systems naturally and remove the cumbersome devces from users. In general, the vson-based user nterfaces are dvded nto two types []. One s the contact vson-based nterface whch generally uses markers worn by the user. The other s the non-contact vson based nterface whch generally uses the background subtracton technques. The contact vson-based nterface s able to extract nformaton of nterest by smply trackng the markers. However, t has some drawbacks. For example, the contact-based nterface requres the user to wear markers. As a result, when markers are occluded or when multple markers are used, t s hard and error prone to track them []. The non-contact vson-based nterfaces overcome the lmtatons of the contact vson-based nterfaces. ote that the prevous background subtracton technques whch s used n non-contact vson-based user nterfaces have exploted the statstcal and/or probablstc color dfferences between a current mage and the reference mage, whch s traned durng a certan perod of tme or the number of frames [3][4][5]; the speed dfferences of movng objects [6]; the characterstcs of stereo mages [7]; and hybrd [8]. The results of these background subtracton technques are robust and effectve enough to apply to the vson-based user nterfaces. However, there are some restrctons and complextes to be resolved. For nstance, most of them ntroduce ther own complex color models or one representatve threshold value [3][4][5]. And motonless users and texture smlartes of nterests are also dffcultes to be used n the vson-based user nterface [6][7]. In ths paper, we propose a robust and pragmatc background subtracton technque for the vson-based user nterface. The proposed method explots the well-known RGB color space and normalzed RGB color space nstead of ntroducng complex color models. Meanwhle, we use each pxel s statstcal characterstcs n the both color spaces. We assume that each color channel has dfferent characterstcs and the characterstcs of pxel-wse values over tme follow Gaussan dstrbuton [5]. By usng these propertes, we are able to determne pxel-wse threshold values sem-automatcally as a functon of mean and standard devatons of the pxels durng the background tranng perod. The proposed method reduces the complextes and restrctons of the prevous studes. It s a smpler and more pragmatc background subtracton technque for the real-tme vson-based user nterface. Ths paper s organzed as follows. In secton, we explan the detaled algorthm and mplementaton of the proposed method. In secton 3, we show the expermental results and dscuss the concluson n secton 4.. Background Subtracton Algorthm The general background subtracton technque s to subtract a current mage from the reference mage. Although varous cues (color, moton, block, etc.) are utlzed n many studes, the proposed method explots the characterstcs of the pxel s color values n the wellknown two color spaces (RGB and normalzed RG. It s needed to determne the optmal threshold values n the background subtracton technques. In ths secton, we explan the propertes of each color space and how to determne the pxel-wse optmal threshold values. In * Ths work s sponsored by KJIST and ICU Dgtal Meda Lab.

2 addton, we show how to use the determned threshold values n the proposed algorthm. ( r, g, b ) = ( I ( r, g, b ) µ ( r, g, b )) = 0 (5). Characterstcs of Color Space The human vson system recognzes the color of objects based on chromatcty and lumnance. Inspred by ths, we utlze the two well-known color spaces. In the RGB color space, each pxel has both chromatcty and lumnance elements. That s, n ths color space, two colors are dfferent f ether chromatcty or lumnance s dfferent. Therefore, when the background subtracton s done n RGB color space, shadow, shade and hghlghtng are recognzed as the user even though they are only dfferent n lumnance but almost same n chromatcty. It s dffcult to remove these lghtng effects from the user only usng RGB color space. Ths ssue makes some prevous works ntroduce ther own color models whch easly explot chromatcty and lumnance [3][4][5]. The separated representaton of the chromatcty and lumnance n one color model s able to determnes each pxel as precsely as possble. However, t requres much complex and expensve computaton. In the normalzed RGB color space, each pxel has only a chromatcty element. In ths color space, we can remove the lghtng nterferences because they have only lumnance dfferences from the background scene. We explot the characterstcs of the well-known two color spaces nstead of ntroducng a new color model. The proposed method dstngushes the user wthout cast shadows from the background scene.. Background Modelng In the proposed method, we tran the background mages n RGB and normalzed RGB color space, respectvely. Then, we can evaluate the mean and standard devaton at pxel s (R, color channels n the reference mage durng the background tranng. Each pxel of the reference mage s modeled as follows. < µ ( R, G,, ( R, G,, µ ( r, g,, ( r, g, > () where µ ( R, G, B ) and ( R, G, B ) s the vector of the mean and standard devaton of pxel s color channels n RGB color space. µ ( r, g, b ) and ( r, g, b ) s the vector of the mean and standard devaton of pxel s color channels n the normalzed RGB color space. The followng equatons are show how to compute the vector of the mean and standard devaton at pxel n RGB and normalzed RGB color space. µ ( R, G, B ) = µ ( r, g, b ) = = 0 = 0 = 0 I I ( R, G, B ) ( r, g, b ) ( R, G, B ) = ( I ( R, G, B ) µ ( R, G, B )) () (3) (4) where each I ( R, G, B ) and I ( r, g, b ) represents the vector of pxel s color channels n RGB and normalze RGB color space. s the number of traned mages..3 Threshold Selecton and Subtracton When we observe the varatons of pxels n the mage of statc background scene, they are easly modeled as a Gaussan dstrbuton. From ths observaton, the threshold value of pxel s mapped by functon of standard devaton of pxel. Th ( R, G, B ) = α ( R, G, B ) (6) Th ( r, g, b ) = β ( r, g, b ) (7) where Th ( R, G, B ) and Th ( r, g, b ) s threshold value of pxel n RGB and normalzed RGB color space, respectvely. α and β s the determnant constant whch determnes the confdence nterval. For example, f α = β =, t has about 95% confdence nterval. Ths determnant constant α and β determne the threshold ranges. Then we smply acheve threshold value at pxel usng standard devaton by choosng the determnant constants α and β. Although most of the background subtracton technques addressed how to determne the threshold values, there are few methods whch show the usages of the determned threshold values n the subtracton operatons. In the proposed method, we show how to effectvely use the determned threshold values to subtract the user from background scene. Equaton (8) and (9) s the determnant functon whch compares the color channels dfferences of pxel and the determned threshold values n RGB and normalzed RGB color space, respectvely. F = u( D ( R) Th ( R)) u( D ( G) Th ( G)) u( D ( Th ( ) (8) f = u( D ( r) Th ( r)) u( D ( g ) Th ( g )) u( D ( Th ( ) (9) D ( x ) = I ( x ) ( x ) (0) µ where F ( 0 F 3 ) and f ( 0 f 3 ) are the determnant functons whch characterze pxel n each color space. Here u s an unt step functon and t has ether 0 or. D ( x ) s the vector dfference between current mage and reference mage at pxel n RGB color space and normalzed RGB color space. Thus, f D ( x ) > Th (x), then t s. Otherwse, t s 0. Usng equaton (8) and (9), we can determne pxel as follows.

3 I B : s H : = s B : H : 0 F 0 f f F < c c < c c () s where B s the background mage and B s the background mage wth cast shadows. H s s the segmented user mage wth shadows and H s the segmented user mage wthout shadows. In RGB and normalzed RGB color space, ts range s 0 c 3 and 0 c 3, respectvely. The proposed method uses the equaton () n order to properly separate H from B by adjustng c and c. For example, f we consder all the color channels n the both color spaces, then c and c are 3. Ths ndcates that all the color channels of pxel satsfy D ( x ) > Th ( x ). Or f we only take two color channels nto account, c and c are. In the case of consderng the characterstcs of each color space, we could determne c and/or c ndvdually. As shown n Fg., t represents the vector dfference between µ at pxel n the reference mage and I at pxel n the current mage. Th s the functon of the standard devaton at pxel. It s shown how the proposed method s used to classfy pxel n each color space. G 55 G space usng equaton (8). Then we quantze the result mage as a bnary map. As shown n Fg., the created bnary map s used as a mask mage n normalzed RGB color space. When we apply the mask mage nto the reference mage and current mage n normalzed RGB color space at the same tme, we smply dscard cast shadows from the user because shadows have only effects on lumnance. Through these two stages, we easly acheves the user mage ( H ) wthout cast shadows. Acqurng Reference mages Image µ ( R, ( R, µ ( r, ( r, - α normalze * > Foreground Object Map w/ Shadow AD AD - β Subtracton Operaton Red Green Blue * > Foreground Object Map w/o Shadow AD Movng Object Image Fgure. The proposed background subtracton algorthm. ( R, G, B ) and ( r, g, b ) denotes RGB and normalzed RGB color. µ and represent the mean and the standard devaton at pxel. Th ( R, I ( R, µ ( R, I ( r, Th ( r, 3. Expermental Results B R B µ ( r, ( Fgure. Color Spaces and the classfcaton of ts pxel. RGB Color Space ( ormalzed RGB Color Space. µ s the mean of pxel and I s the color value of pxel. Th s the threshold value at pxel..3 Background Subtracton Algorthm R As shown n Fg. 3, t shows the varaton of pxel over tme n each color channel n the RGB and normalzed RGB color space. The varaton of pxel over tme s dfferent n each color channel. Pxel Intensty RGB Color Space Red Pxel s Varaton Green Pxel s Varaton Blue Pxel s Varaton Pxel Intensty ormalzed RGB Color Space Red Pxel s Varaton Green Pxel s Varaton Blue Pxel s Varaton The proposed method has two stages [3][4][5]. One s tranng background and the other s subtractng from the traned background. However, as shown n Fg., each stage has two steps n the proposed method. In the frst stage, we tran background mages and make the reference mage n RGB and normalzed RGB color space, respectvely. Then n the second stage, we do subtract the current mage from the reference mage n each color space. In tranng background stage, we model background usng equaton (). Then we determne the threshold at pxel through equaton (6) and (7). After background modelng s done n each color space, we separate the user wth cast shadows from the background scene n RGB color Tme (Frames) Tme (Frames) Fgure 3. The varaton of pxel over tme n each color space. RGB color space: Red =.436, Green = , Blue = ( ormalzed RGB color space: Red =0.003, Green =0.005, Blue = Thus, n order to subtract a current mage from the reference mage, we have to explot the characterstcs of pxel ndvdually n each color channel. As shown n Fg. 4, t llustrates the subtracton results n the RGB and normalzed RGB color space, respectvely. ( 3

4 The results show that there are many subtracton errors to dscrmnate the pxel of the user n the current mage from the background scene when we use only one color space. In RGB color space, the proposed algorthm subtracts not only the user but also shadows from the background scene. In normalzed RGB color space, t removes most of cast shadows around the user. However, t also removes the actual parts of the user. As shown n Fg. 4 (d), t explots the two well-known color spaces and dscrmnates the user from the background scene. Although the proposed method uses the two color spaces, the result stll shows many errors due to msclassfcatons of the pxels n RGB color space and/or normalzed RGB color space. As shown n Fg. 5, t shows the results of the dfferent determnant constants α and β whch determne the threshold values n each color space. And then, t shows the result of the proposed method over the dfferent determnant constants α and β, n whch we used the default determnant functons 3 and ( (c) ( (d) (e) (f) Fgure 5. The determnant constants n RGB color space, n normalzed RGB color space and the results. α = 3 ( β = 3 (c) the subtracted result (d) α = 4.48 (e) β =.06 (f) the subtracted result. The determnant functons are 3 and (c) (d) Fgure 4. The subtracton results n RGB color space, n normalzed RGB color space and n both color spaces. A current mage. ( The subtracted mage n RGB color space. (c) The subtracted mage n normalzed RGB color space. (d) The subtracted mage n the proposed algorthm (α = β = f = 3). The results ndcate that the color dfferences between the user and the background scene n RGB color space are based on ether chromatcty or lumnance. However, the color dfferences between the user and the background scene n normalzed RGB color space are based on only chromatcty. In RGB color space, we dfferentate chromatcty as well as lumnance of the user from the background. Thus, we can observe the shadows around the segmented user. In normalzed RGB color space, we dfferentate only the chromatcty of the user from the background scene. We cannot see cast shadows around the user, but we can observe many false detectons n the user. As shown Fg. 4 (d), the result of the proposed method dscrmnated shadows from the user, whch uses two color spaces at the same tme. However, n ths stage, we just used the default determnant constants α =3 and β =3 as well as the default determnant functons F =3 and We yet need to adjust the determnant constants emprcally. From the results, α = 4.48 and β =.06 are the optmal determnant constants for the threshold functons at pxel durng the experments where we consdered all the color channels. By the determnant constants, the results show the mprovements of the subtracton n the comparson wth the results of the above fgures. In RGB color space, as shown Fg. 5 and (, the cast shadows around the user are reduced as the determnant constant α s ncreasng. In normalzed RGB color space, as shown Fg. 5 ( and (e), the msclassfed of the pxels n the user are declned as the determnant constant β s ncreasng. As the results are shown, the proposed method s not affected by ether RGB color space or normalzed RGB color space, but affected by the both color spaces. Therefore, t s necessary to fnd the optmal determnant constants n both RGB color space and normalzed RGB color space ether manually or automatcally for the threshold values at pxel. However, n spte of the enhancement n the result of the subtracton, we can stll mprove the subtracted mage of the user through the determnant functons. After we found the optmal determnant constants for the both color space, we need to fnd the determnant functons n the both color space. In the determnant functons, they represent how many color channels are consdered n the propose algorthm. As shown n Table, t shows the results through the determnant functons F and f whch characterze pxel n the mages. In ths experment, we adjusted the determnant functons F and f meanwhle we fxed the determnant constants as α = 4.48 and β =.06. 4

5 Table. The determnant functons n RGB color space, normalzed RGB color space and the results Determnant Functons RGB ormalzed RGB 4.48, β =.45, F = 3 and f =. The result clearly shows that t subtracts the user from the background scene wthout ntroducng a complex color model. However, we have to select the determnant constants and functons manually. f = 3 f = f = As we expected from the results, t s the optmal results when the both determnant functons are 3 and However, t has some subtracton errors n the user when the determnant functon s f = 3 n normalzed RGB color space. Ths leads to a false subtracton n the result mage. Therefore, we choose the determnant functons are 3 and f = rather than 3 and 4. Dscusson In ths paper, we proposed a pragmatc background subtracton technque for the vson-based user nterface. Instead of ntroducng a complcated color model, we exploted the characterstcs of the two well-known color spaces. The proposed method shows not only how the threshold values are chosen, bus also how to use the chosen values n the subtracton operatons. We showed that the proposed determnant functons ( F, f ) well classfed pxel as ether background or the user of nterest through the expermental results. However, we need further experments on how to fnd the optmal determnant constants and functons automatcally. References [] W. Woo,. Km, K. Wong and M. Tadenuma, Sketch on Dynamc Gesture Trackng and Analyss Explotng Vson-based 3D Interface, n Proc. SPIE PW-EI-VCIP'0, vol. 430, pp , Jan. 00 [] Kda, K., Ihara, M., Shwa, S., Ishbash, S., Moton trackng method for the CAVETM system, Sgnal Processng Proceedngs, 000 WCCC-ICSP th Internatonal Conference on, vol., 000 ( [3] T. Horprasert, D. Harwood, and L.S. Davs, A Statstcal Approach for Real-tme Robust Background Subtracton and Shadow Detecton, Proc. IEEE ICCV'99 FRAME-RATE Workshop, Kerkyra, Greece, September 999 [4] Ahmed Elgammal, Davd Harwood, and Larry Davs, onparametrc Model for Background Subtracton, 6th European Conference on Computer Vson, Dubln, Ireland, June/July 000. [5] A. Elgammal, R. Duraswam, D. Harwood and L. S. Davs Background and Foreground Modelng usng on-parametrc Kernel Densty Estmaton for Vsual Survellance, Proceedngs of the IEEE, July 00. (c) (d) Fgure 6. The subtracton results. a current mage ( the determnant constant α = 4.48 and functon F = 3 n RGB color space (c) the determnant constant β =.45 and functon f = n normalzed RGB color space. (d) The subtracted result. Accordng to the expermental results, we can acheve the optmal subtracted mage of the user by determnng α = [6] C. Km, W. Woo, and H. Jeon Determnaton of Optcal Flow by Stochastc Model, Journal of the Korea Informaton Scence Socety (KISS), vol.9, no.6, pp , ov., 99. [7] W. Woo and H. Jeon Stochastc Model for Unfcaton of Stereo Vson and Image Restoraton, Journal of the Korean Insttute of Telemetrc and Electroncs (KITE), vol.9-b, no.9, pp.37-49, Sep., 99 [8] W. Woo,. Km and Y. Iwadate, Object Segmentaton for Z-keyng Usng Stereo, n Proc. IEEE WCC-ICSP 00, vol., pp.49-54, Aug

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