Panorama Mosaic Optimization for Mobile Camera Systems

Transcription

1 S. J. Ha et al.: Panorama Mosac Optmzaton for Moble Camera Systems Panorama Mosac Optmzaton for Moble Camera Systems Seong Jong Ha, Hyung Il Koo, Sang Hwa Lee, Nam Ik Cho, Soo Kyun Km, Member, IEEE 27 Abstract In order to enable the real-tme mage mosac n moble devces that have very lmted computng power and memory, we propose an effcent mage mosac algorthm wth nteger arthmetc. The proposed algorthm s focused not only on the computatonal effcency, but also on the performance mprement of mage mosac. For the effcent projecton wthout transform estmaton, we obtan successve mages through the semtransparent vew fnder whch shows the fxed amount of rght part of prevously captured mage. We project each mages onto cylndrcal surface by the proposed projecton equaton and nteger arthmetc. We algn the projected mages by herarchcal hexagon search and a matchng measure that s robust to llumnaton changes caused by dfferent exposures and vgnette dstorton. Fnally, the mages are naturally blended usng color compensaton and dynamc programmng based sttchng. The proposed mosac algorthm s embedded and tested n moble phone systems. Accordng to varous tests and experments, the proposed algorthm shows good panorama composton n real-tme compared wth the other PC-based methods. Index Terms Embedded panorama mosac, color compensaton, nteger arthmetc, sttchng I. INTRODUCTION When we see splendd scenes, such as sea horzons, mountans, and prospects from the top, we wsh to capture them n a sngle photograph. However, the usual cameras have relatvely narrow vew angles to capture the scenes at once. We have no choce but to take a pcture as small as the scenes are ncluded n a camera vew, whch dmnshes the objects n sze to be ndstngushable and results n reduced mage resoluton. Panoramc mage mosac s a soluton to capture the scenes n a sngle mage of hgh resoluton []. It composes wde vew mages from multple mages whch nclude the same scenes partally at the slghtly dfferent vewponts. The mage mosac needs many mage processng topcs, such as feature extracton, transform estmaton between mages, mage warpng onto mosac surfaces, local algnment of warped mages, boundary sttchng, blendng, and so on. Many algorthms on mage mosac have been developed so far. The most mportant and classcal works are related wth Seong Jong Ha, Hyung Il Koo, Sang Hwa Lee, and Nam Ik Cho are wth School of Electrcal Engneerng and Computer Scence, Seoul Natonal Unversty, Kwanak-gu, Seoul, 5-742, South Korea ( emals: oanchy@spl.snu.ac.kr, hkoo@spl.snu.ac.kr, lsh@pl.snu.ac.kr, ncho@snu.ac.kr ). Soo Kyun Km s wth Samsung Electroncs Co., Ltd., South Korea (emal: sookyun.km@samsung.com). Sang Hwa Lee s the correspondng author (e-mal: lsh@pl.snu.ac.kr). Contrbuted Paper Manuscrpt receved August 3, /7/$2. 27 IEEE feature extracton and transform estmaton between mages. Szelsk consdered spatal transform between mages as an 8-parameter perspectve moton model, and used Levenberg- Marquardt algorthm to fnd mage correspondences [4]. Some researchers thought spatal transform as a 3-parameter rotatonal moton model. Szelsk and Brown estmated the spatal relaton between mages by updatng rotatonal matrces [8], [9]. Lowe used scale nvarant feature transform (SIFT) features to estmate the transformaton between mages [], [4]. After obtanng the moton model parameters and transformatons between mages, each mage s transformed and projected onto the common mosac surface. Most of the mage mosac algorthms select cylndrcal or sphercal surfaces as the mosac surface, and project mages onto the surface by the estmated transformatons and moton models. Then, the projected mages are composed nto a sngle mage seamlessly. To synthesze multple mages nto a sngle large one, Freeman sttched the mages usng dynamc programmng on the mosac surface [7]. Featherng [6], mult-band blendng [3], [], and mage gradents [], [2] were used to make the boundares between the projected mages smooth. Some approaches to get rd of exposure dfference and radometrc dstorton were also proposed. Uyttendaele compensated the exposure dfferences usng block-based exposure adjustment [6]. Goldman elmnated vgnette aberraton by ntroducng ant-vgnette functons [3]. The mosac algorthms presented abe show good performances n the usual scenes. However, snce all of the works on mage mosacs are developed and mplemented on general personal computer (PC) envronments, we have to transmt the captured mages to a PC for generatng mosac mages. Ths paper proposes and optmzes an embedded panorama mosac algorthm for moble camera systems lke dgtal cameras and moble phone cameras. The PC-based mosac algorthms descrbed before do not work well on the moble camera systems because of the lmtatons of computatonal power and memory of hand-held devces. The proposed mosac algorthm operates on the usual moble camera systems n realtme. We can verfy the mosac results rght after all the mages are acqured by the moble magng systems. In order to enable the real-tme panoramc mosac n moble camera systems, we propose an effcent mage mosac algorthm wth nteger arthmetc and programmng optmzaton. The proposed algorthm s focused not only on the computatonal effcency, but also on the performance mprement of each step needed for mage mosac. We consder spatal transform between mages as 3-parameter

2 28 rotatonal model, and use semtransparent panoramc vewer to capture the successve mages. Snce the mages acqured through the panoramc vew fnder have a predetermned rotatonal transformaton, we don t have to perform the estmaton of correspondences and transforms whch need much computatonal load. For the fast projecton of mages onto the mosac surface, we do not use the conventonal transforms whch contan trgonometrc functons, but modfy the transformatons nto nteger functons. The projected mages onto the mosac surface are well algned by a robust error metrc and fast hexagon-based search n the ntegral mage space. The exposure dfferences and color dstortons are also compensated n syntheszng projected mages. Fnally, we sttch the mages by usng dynamc programmng and blend the mage boundares lnearly. The proposed technque optmzes the mathematcal operatons for mage mosac wth nteger arthmetc, and s operated real-tme n portable camera systems wthout loss of performance. The users can check the mosac results as soon as mages are acqured usng the proposed mosac system. The rest of paper s organzed as follows. We descrbe the camera moton model and panoramc vew fnder n Secton 2. Secton 3 explans the proposed mage mosac algorthms and optmzaton methods n detal. Expermental results wth moble phones are shown n Secton 4. Fnally, we conclude the paper n Secton 5. II. MOTION MODEL OF CAMERA For fast and stable mosac results, we have to smplfy some procedures n the mosac algorthm. Especally, snce feature ponts extracton and transform estmaton requre much nonlnear floatng pont computaton and are unstable n some cases, t s desrable to omt the processes under reasonable constrants. We assume that the users me ther cameras to capture erlapped scenes only n one drecton. In other words, the mosac system generates the horzontal (or vertcal) panoramc vews. The camera moton and transformatons between successve mages can be modeled as a specfc form under the assumpton. Then, the camera moton s descrbed as horzontal (or vertcal) rotaton wth fxed angle θ and focal length f. The followng subsectons relate the camera moton wth transform functon n the mage coordnates. A. Camera Moton and Panoramc Vew Fnder The successve mages for mage mosac should be captured wth some erlapped regons. The correspondences between erlapped regons are exploted to estmate transformatons of mages and to algn the warped mages. When there s no erlapped regon or correspondences between mages, the mosac s not performed. To get the constant erlapped area between captured mages n the case of horzontal panorama composton, the camera must be rotated by a fxed angle along the y-axs. We set the rotaton angle along the y-axs usng mage dmenson. IEEE Transactons on Consumer Electroncs, Vol. 53, No. 4, NOVEMBER 27 Fg.. Top vew of geometry of camera moton. Two successve mages are captured by rotatng a camera along the y-axs. When we fx the amount of erlapped area between two mages, the rotaton angle θ s determned by the focal length of camera and mage wdth. Let a and b n Fg. be the frst and second mages respectvely. The rotaton angle of camera s θ and the focal length s f. Snce the camera rotates only n the horzontal drecton, the cylndrcal surface s the most sutable one for the projecton and composton of panoramc mages. The mages are projected onto the cylndrcal surface that has a radus of R, and the projected mages, A and B are generated. The arc C n Fg. s the erlapped part of two projected mages. Let φ be the half of vew angle. Then, t s determned by camera parameters, W and f, W /2 φ = arctan( ), f where W s the wdth of mage. Let τ be the rato of erlapped area n the projected mages. Snce the angle of C becomes 2φ θ and the arc length of C s R(2 φ θ ), τ s derved as 2Rφ Rθ θ τ = =. () 2Rφ 2φ When the rato τ s set, the angle of camera rotaton θ s determned as θ = 2 φ( τ), (2) whch s a man parameter of perspectve projecton matrces between successve mages. Thus, we can obtan transformatons wthout feature correspondences when we know the rotaton angle θ. We make a panoramc vew

3 S. J. Ha et al.: Panorama Mosac Optmzaton for Moble Camera Systems 29 fnder to acqure the successve mages of horzontal rotaton wth fxed erlapped area. As shown n Fg. 2, we warp a part of prevously acqured mage onto LCD to gude users to take pctures wth horzontal rotaton of fxed angle. Users acqure the next mage when the real mage through camera vew fnder s almost matched to the warped mage part. The warpng s performed by the specfc transformaton matrx descrbed n the next subsecton. By the panoramc vew fnder, we can omt the process of feature extracton, estmaton of correspondences and transformatons, whch need large amount of computaton. It should be noted that the part of prevously captured mage on LCD s the projected (rotated) mage along the camera moton, not the orgnal part as t was. Snce the same scene becomes warped and transformed wth respect to the dfferent vewponts, we should consder the current and prevous mages at the same vewpont when we match them. Thus, the prevous mage part s transformed wth respect to the camera moton so that the vewponts of mages are equvalent. The rotaton matrx s presented n the exponental form, R = e Θ, θ3 θ2 Θ = θ3 θ, θ2 θ where θ, θ 2, θ 3 are three rotaton angles. By the assumpton that camera rotates only n the y-axs and the focal length s fxed, we set f = f n K and θ = θ3 = n R. Because the angle between successve mages s set to be θ n (2), the transformaton matrx (3) between successve mages s smplfed as cosθ f snθ H j =. (4) f snθ cosθ Fg. 2. Panoramc vew fnder. part of prevously acqured mage to be warped (red quadrangle regon), next mage to be taken usng panoramc vew fnder. The whte rectangle regon s compared wth the warped red quadrangle regon n. B. Transforms between Images We assume that the focal length f of camera s fxed for all of the mages. If the focal length vares for each mage, we have to estmate correspondences and transforms of mages. Ths s the usual case n the PC-based mosac algorthms whch do not work well n the moble camera systems. The th th transformaton matrx between two mages ( and j mages) by the camera moton [9] s defned as H K R R K (3) j = j j, where the ntrnsc camera matrx defned as f K = f. K for the th mage s III. PROCEDURE OF GENERATING MOSAIC IMAGES A. Projecton onto Mosac Surface The acqured mages are transformed usng (4) before projectng the mages drectly onto the cylndrcal surface. To project the transformed mages onto the cylndrcal surface, we convert 3 dmensonal (3D) real coordnates nto 2D mage coordnates through the pnhole camera model X Y ( x, y) = ( f, f ), Z Z (5) where ( X, Y, Z ) and ( x, y ) are ponts n 3D world coordnates and 2D mage coordnates, respectvely. Then, we project the ponts n the mage coordnates onto the cylndrcal surface. Let ( uv, ) be a pont on the cylndrcal surface wth radus R as shown n Fg. 3. The coordnate ( uv, ) s equvalent to ( Rϕ, h) n the cylndrcal coordnates, ( uv, ) = ( Rϕ, h), where ϕ s the clockwse angle from the center axs and h s a heght from the orgn. The world coordnates ( X, Y, Z ) s represented as ( XYZ,, ) = ( Rsn ϕ, hr, cos ϕ). (6) From (5) and (6), the transformaton of ( uv, ) nto ( x, y ) n 2D mage coordnates becomes

4 22 IEEE Transactons on Consumer Electroncs, Vol. 53, No. 4, NOVEMBER 27 We can also save much memory and computatons by usng the symmetry of mage coordnates. As shown n Fg. 4, the center of mage s consdered as the orgn, and a quarter of nput mage s projected usng (8) and nteger arthmetc. Then, the rest 3 quarters of mage are projected usng the spatal symmetry. Fg. 3. Cylndrcal mosac surface and ts 3D coordnate system. Each mage captured by a camera s projected onto the cylndrcal surface. The real world coordnate s expressed as ( XYZ,, ), mage coordnate as ( x, y ), and cylndrcal one as ( uv, ). Rsnϕ h ( xy, ) = f, f Rcosϕ Rcosϕ v = f tan( u R), f. R cos( ur ) (7) Equaton (7) s the conventonal way to project an mage onto the cylndrcal surface. However, t s dffcult to perform the projecton (7) wth nteger operatons due to the trgonometrc functons. We modfy the projecton equaton (7) for nteger arthmetc as v ( xy, ) = ftan( ur), f R cos( u R ) Rsn( u R) v = f, f R R sn ( u R) R R sn ( u R) u v = f, f, R u R u (8) where sn( ur ) s approxmated to ur. We observe that u R s usually satsfed n our mosac system (64x48 mages and R 32 ). Based on the observaton of our mosac system, we modfy the usual projecton equaton (7) nto (8) for fast operaton. The proposed equaton elmnates the trgonometrc functons whch consume much computatonal tme n the moble devces. The square root 2 2 functon R u n (8) can be calculated by the nteger programmng usng fast Bresenham algorthm, whch s developed for drawng crcles [2]. In the experments, we wll show that the proposed projecton equaton (8) has lttle geometrc dstorton, whle requrng very lttle computatonal complexty than the conventonal equaton (7). Fg. 4. Symmetry of mage coordnates when projectng a rectangle onto the cylndrcal surface. We can save the computatons and memores usng the coordnates symmetry. The left upper quarter of mage s frst transformed usng (8), and the other quarters are transformed by the spatal symmetry. B. Images Algnment Though the successve mages are acqured by the panoramc vew fnder, the users are prone to make errors n rotatonal moton and fttng the objects nto the vew fnder. The errors cause the dscrepancy between real camera moton and the fxed model of our assumpton, whch results n msalgnment of successve mages on the cylndrcal mosac surface. Hence, we need to algn the projected mages locally on the mosac surface. The local algnment s performed by block-based moton search n the erlapped regons. We ntroduce a robust error measure for the better mage algnment, and use hexagon-based search and an ntegral mage [5] for fast operaton. The ntegral mage at x = ( x, y) represents the sum of all the pxel values n a rectangular regon such that Int ( x ) = I (, j) (see Fg. 5 ). Once the ntegral x, j y mage s generated for every pxel n the mage, the sum of pxels n a shaded block n Fg. 5 can be calculated wth four addtons, I nt ( x 4 ) I nt ( x 2 ) I nt ( x 3 ) + I nt ( x ). The ntegral mage calculates block-based error metrc much faster.

5 S. J. Ha et al.: Panorama Mosac Optmzaton for Moble Camera Systems 22 Fg. 5. Integral mage. Defnton, sum of pxels n the shaded regon by usng ntegral mage. The proposed error metrc consders the llumnaton dfference due to exposure changes and vgnette. It explots llumnaton means of erlapped mage regons, E u I x u I u I x I (9) 2 ( ) = [( ( + ) ( )) ( ( ) )], x R where I and I are the erlapped mage area n the successve two mages I and I. I ( ) x s a lumnance value at x, and I and I are lumnance means n the erlapped area. Note that I s a part of I, and mes n I. Thus, the mean I s constant whereas I vares wth the moton vector u. We search for the optmal locatons of projected mages such that u mnmzes the error metrc, arg mn E( u ). () I ( u ) must be calculated whenever u vares, whch requres too much computaton. We use the ntegral mage to reduce the computatonal complexty n moton search. And we utlze hexagon-based search for faster operaton [5]. The ntegral mage and hexagonal search enable the local algnment process faster wth nteger arthmetc. C. Color and Lumnance Compensaton If the exposure s fxed when takng pctures of the same scene, the erlapped areas of mages have the same lumnance and colors. However, snce the exposure usually changes at the dfferent vewponts, there are brghtness and color dfference between mages. For color and lumnance compensaton, we assume that the objects n the scene have Lambertan surfaces [8]-[2]. The radance reflecton from the object surface decdes pxel color rrespectve of camera vewponts as PC = f( LC). () We model the pxel color to be proportonal to the lght radance as [7], [8] P, C = α LC (2) where L C s the radance of a color channel C (R, G, and B), and α s a proportonal coeffcent. Gven an erlapped area of two mages, the pxel color of x can be descrbed as P ( x) = α L, P ( x ) = α L, (3) u, C C, C C where P, ( x ) s the pxel color at x n the erlapped area C of the th mage. Hence, we can assume that two pxel values at the same poston have a lnear relaton. Specfcally, due to nose and erroneous local algnment, we use the mean n the erlapped area for the lnear relaton, α P ;, C P, C (4) α, where P C, s the mean value of the th erlapped mage for channel C. The lnear model s defned n the RGB color space whereas the color space of portable cameras s usually the YCbCr. In the case of Y component, t s the lnear combnaton of R, G, and B components, and (4) s stll satsfed,.e., P ; α P (5), Y, Y α. In the case of color components, Cb and Cr, they are not the lnear combnatons of RGB, but ther AC components are lnear combnaton of RGB. We modfy (4) and propose a color compensaton technque n the YCbCR color space usng lumnance means as follows: ) Calculate P,Y and P, Y, α P α = (6), Y ( ). P, Y 2) If the st mage s the reference and the th mage s compensated, compensate the lumnance values n the th mage, α P, Y( x) = P, Y( x ). (7) α 3) Compensate two chromnance components, α P, C' ( x) = ( P, C' ( x ) 28) + 28, C ' { Cb, Cr}. (8) α The color compensaton process s performed n the whole mage, not only n the erlapped regon. Thus, the lumnance and colors of mages are globally regularzed, whch reduces abrupt changes between mages and makes the mage boundares unseen. D. Sttchng Usng Dynamc Programmng After algnng the projected mages locally, we synthesze the erlapped areas to make a mosac mage. If the pxels n the erlapped areas are syntheszed by weghted sums as n the conventonal panorama methods, there are some blurrng and boundary artfacts as shown n Fg. 6. Ths s caused by the msalgnment n the subpxel accuracy n spte of the local algnment process. In order to allevate the blurrng and artfacts, we fnd a plausble boundary between mages n the erlapped regon by usng dynamc programmng method.

6 222 The resultng sttched mage s shown n Fg. 6. Dynamc programmng conssts of 3 steps, ntalzaton, matrx fllng (scorng), and trace back (algnment) as follows: ) Intalzaton Intalze the cost matrx Cxy (, ) for ( x, y) as Cxy (, ) = I% ( xy, ) I% ( xy, ), (9) whch stores the dfference of two color-compensated mages n the erlapped regon. 2) Matrx fllng (Scorng) Make a matrx wth the same sze of the cost matrx and fll t wth the mnmum cumulatve dfference along several paths from top to bottom. y = : C ( x, y) = C( x, y) y =, 2,3, L : C ( x, y) = mn[ C ( x, y ), C ( x, y ), C ( x+, y )] + C( x, y). 3) Trace back (Algnment) The optmal boundary s found by tracng back the path wth mnmum cost from bottom to top. Last row ( x, y ) = argmn C ( x, y). opt opt The next upper row xy, C ( x, y ) = C ( x, y ) C( x, y ), x { x, x, x + }, ( x, y ) = ( x, y ). If opt opt opt opt opt where opt opt opt then, opt opt opt Repeat the next upper row untl the frst row Fg. 6. Comparson of erlapped regon. weghted average of two erlapped mages, separatng two erlapped mages by mage sttchng. We see clearer and sharper rdges of mountan n. E. Lnear Blendng The last step of panorama mosac s to blend sttched boundares. Because the color compensaton and sttchng reduce blurrng and boundary artfacts enough, we use just IEEE Transactons on Consumer Electroncs, Vol. 53, No. 4, NOVEMBER 27 lnear blendng. 6 pxels of each sde from the sttched boundary are used for lnear blendng. CPU OS MEMORY DISPLAY CAMERA TABLE I TEST DEVICE SPECIFICATION Intel PXA272 52MHz Wndows Moble 23 SE Edton 28MB ROM, 64MB RAM K TFT LCD.3 megapxel CMOS Fg. 7. Comparson of projecton errors. (dash curve) conventonal equaton, (sold curve) proposed projecton equaton. IV. EXPERIMENTAL RESULTS The proposed mage mosac algorthm s appled to a PDA phone wth the specfcaton n Table I. The mage sze s 64 48, and the focal length of test mages s 69 pxels. The radus of cylndrcal mosac surface s 76 pxels, whch s related wth the focal length. Frst, we evaluate the proposed projecton equaton (8) whch s the approxmaton of exact one (7). The projecton error s shown n Fg. 7, where dashed and sold lnes represent the projectons by (7) and (8) respectvely. The x-axs n Fg. 7 represents x coordnates of the captured orgnal mage, and the y-axs ndcates the correspondng locaton n the projected mage. Fg. 7 shows that the proposed projecton equaton causes errors by pxels at maxmum when mage s projected. The proposed method approxmates the usual conventonal formula based on the assumpton of R u. Thus, as u ncreases, the projecton error also ncreases. However, ths dstorton s not vsble n the projected mages. Fg. 8 shows the mages projected by the conventonal one and the proposed one wth a test mage. As shown n Fg. 8, the proposed method projects the mage wthout notceable dstortons compared wth (7). Because the error s not notceable n the VGA mages, there s no problem for the smaller mages. Therefore, the proposed equaton (8) s a reasonable approxmaton for fast projecton. The proposed projecton

7 S. J. Ha et al.: Panorama Mosac Optmzaton for Moble Camera Systems 223 takes.39 seconds whereas the conventonal one requres seconds on the same test devce. (c) Fg. 8. Projected mages. Orgnal mage (64 48), conventonal projecton, (c) proposed projecton. Fg.. Evaluaton of color compensaton. mult-band blendng [6], the proposed color compensaton followed by lnear blendng. Fg. 9. Test mages for the comparson of performances of error metrcs. Fg.. Local algnment results and ther zoomng. SAD, the proposed metrc. Second, we evaluate the proposed error metrc (9). Fg. 9 shows test mages wth promnent exposure dfference, and Fg. shows the results of local algnment by the error metrcs. As shown n Fg., f mages have exposure and brghtness dfferences, they are not well algned by SAD or SSD metrc, whereas the proposed error measurement algns the mages better by the lumnance compensaton. Thrd, we evaluate the proposed color compensaton wth test mages n Fg. 9. Fg. compares the proposed method wth mult-band blendng [6]. Fg. shows natural connecton n the erlapped areas, but stll some exposure dfference n the non-erlap areas. Fg. shows natural connecton n the erlapped regons wth less exposure and color dfferences. (c) Fg. 2. Comparson of mosac mage results by autosttch [6] and proposed mosac system. Fnally, the mosac performance of proposed algorthm s compared wth that of autosttch program whch s a PC-based mosac algorthm usng SIFT features and mult-band blendng [6]. Fg. 2 and Fg. 3 show the mosac results for outdoor and dstant ndoor scenes. Accordng to varous tests, the proposed system shows good performance both for ndoor and outdoor scenes. The proposed mosac system takes.2 seconds for four mages wthn 4M bytes memory, whereas the autosttch algorthm at 3GHz Pentum PC takes 5-6 seconds wth much more memory. Furthermore, the proposed mosac algorthm s robust for such smple scenes that there are lttle feature correspondences. Fg. 3 shows the robustness of proposed mosac system, where the autosttch program does not work well because of no SIFT feature matchng. Fg. 4 shows some mosac results by the proposed system.

8 224 IEEE Transactons on Consumer Electroncs, Vol. 53, No. 4, NOVEMBER 27 sttchng based on dynamc programmng, and lnear blendng. The proposed mosac system s embedded and tested n actual moble phone systems. Accordng to varous tests and experments, the proposed algorthm shows fast and good panorama composton compared wth the other PC-based and embedded algorthms. The proposed mosac system s expected to be embedded n the commercal moble phones and camera systems. (c) Fg. 3. Comparson of mosac mages. Four orgnal mages, autosttch [6], (c) proposed mosac system. The fourth mage n s not sttched by autosttch [6] because of no SIFT feature matchng. Fg. 4. Panorama results by the proposed mosac system. V. CONCLUSION Ths paper has proposed embedded panorama mosac algorthms for moble camera systems. The algorthms for mosac processes are optmzed by nteger programmng so that they operate real-tme n the usual potable camera systems. The proposed system conssts of panoramc vew fnder, approxmated projecton onto cylndrcal surface, hexagon-based mage algnment usng robust error measurement and ntegral mage, color compensaton, mage REFERENCES [] R. Szelsk, Image algnment and sttchng: A tutoral, Prelmnary draft, Jan. 25. [2] J. E. Bresenham, A lnear algorthm for ncremental dgtal dsplay of crcular arcs, Commun. ACM, vol. 2, pp. -6, Feb [3] Y. Xong and K. Turkowsk, Regstraton, calbraton and blendng n creatng hgh qualty panoramas, IEEE Workshop on Applcatons of Computer Vson, pp , Oct [4] R. Szelsk, Vdeo mosacs for vrtual envronments, IEEE Computer Graphcs and Applcatons, pp. 22-3, Mar [5] C. Zhu, X. Ln, and L. Chau, Hexagon-based search pattern for fast block moton estmaton, IEEE Trans. Crcuts and Systems for Vdeo Technology, vol. 2, no. 5, May 22. [6] M. Uyttendaele, A. Eden, and R. Szelsk, Elmnatng ghostng and exposure artfacts n mage mosacs, Proc. Computer Socety Conf. CVPR, vol. 2, pp , Dec. 2. [7] A. A. Efros and W. T. Freeman, Image qultng for texture synthess and transfer, ACM SIGGRAPH, pp , Aug. 2. [8] H. Shum and R. Szelsk, Systems and experment paper: Constructon of panoramc mage mosacs wth global and local algnment, Int. Journal of Computer Vson, vol. 36, pp. -3, Feb. 2. [9] R. Szelsk and H. Shum, Creatng full vew panoramc mage mosacs and envronment maps, ACM SIGGRAPH, pp , Aug [] M. Brown and D. Lowe, Recognsng panoramas, Int. Conf. Computer Vson, vol. 2, pp , Oct. 23. [] A. Levn, A. Zomet, S. Peleg, and Y. Wess, Seamless mage sttchng n the gradent doman, Eur. Conf. Computer Vson, vol. IV, pp , May 24. [2] A. Zomet, A. Levn, S. Peleg, and Y. Wess, Seamless mage sttchng by mnmzng false edges, IEEE Trans. Image Processng, vol. 5, no. 4, Apr. 26. [3] D. B. Goldman and J. Chen, Vgnette and exposure calbraton and compensaton, Int. Conf. Computer Vson, vol., pp , Oct. 25. [4] D. G. Lowe, Dstnctve mage features from scale-nvarant keyponts, Int. Journal of Computer Vson, vol. 6, pp. 9-, N. 24. [5] P. Vola, M. Jones, Rapd object detecton usng a boosted cascade of smple features, IEEE Computer Socety Conf. on CVPR, vol., pp. 5-58, Dec. 2. [6] M. Brown and D. Lowe, Autosttch home page, [7] D. A. Forsyth and J. Ponce, Computer Vson: A Modern Approach, Prentce Hall, 23. [8] Wkpeda: Lambertan reflectance, Oct. 26. [9] S. Ln and S. W. Lee, Estmaton of dffuse and specular appearance, Int. Conf. Computer Vson, 999. [2] S. Shafer, Usng color to separate reflectance components, Color Research and Applcaton, vol., pp. 2-28, 985. Seong Jong Ha was born n Seoul, Korea, on December, 978. He receved the B.S. and M.S. degrees n electrcal engneerng from Seoul Natonal Unversty, Seoul, Korea, n 25 and 27, respectvely. He s currently a researcher n Insttute of New Meda & Communcaton, Seoul, Korea. Hs research nterests nclude panorama and superresoluton.

9 S. J. Ha et al.: Panorama Mosac Optmzaton for Moble Camera Systems 225 Hyung Il Koo was born n Daegu, Korea, on October 27, 977. He receved the B.S. and M.S. degrees n electrcal engneerng from Seoul Natonal Unversty, Seoul, Korea, n 22 and 24, respectvely. He s currently workng toward the Ph.D. degree n electrcal engneerng at Seoul Natonal Unversty. Hs research nterests nclude computer vson, and speech enhancement. Sang Hwa Lee receved the B.S., M.S., and Ph.D. n electrcal engneerng from Seoul Natonal Unversty, Seoul, Korea, n 994, 996, and 2, respectvely. Hs research nterests nclude mage processng, vdeo codng, computer vson, computer graphcs, and pattern recognton. Nam Ik Cho receved the B.S., M.S., and Ph.D. degrees n control and nstrumentaton engneerng from Seoul Natonal Unversty, Seoul, Korea, n 986, 988, and 992, respectvely. From 994 to 998, he was wth the Unversty of Seoul, Seoul, Korea, as an Assstant Professor of Electrcal Engneerng. He joned the School of Electrcal Engneerng, Seoul Natonal Unversty, n 999, where he s currently a Professor. Hs research nterests nclude speech, mage, vdeo sgnal processng, and adaptve flterng. Soo Kyun Km receved Ph. D. n Computer Scence & Engneerng from Korea Unversty, Seoul, Korea, n 26. He joned Telecommuncaton Network Busness at Samsung Electroncs Co., Ltd. from 26. Hs research nterests nclude moble graphcs, geometrc modelng, and nteractve computer graphcs.