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利用二維影像產生影子

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(4) @BC D&)<E(F'GH& IJKL. MNOP63QRS.   !"# is accompli-shed by identifying the portion of the base. plane which is in shadow in an image with respect to $%&'()*+,-./0123. the. reference. points. using. the. view-invariant. 4567"89467:;8<.=>. cross-ratios and some geometric properties associated. ?@ABC*%&DEFGH*I8. with perspective projection. The approach can be. <.23JK467LMNOP23QR. extended easily to solve more general problems which. ST U4V"WXYZ[*23V\U. involve multiple objects as well as multiple planar. ]^_`Q*ST Uab4cdefg234. surfaces on which object shadows are to be cast.. :I8h(1"W67ij23k. !l4mnopqrst*uvUI8BVph. -%™š›œ4. wx(1Cy467;+,zYZuv. U4{|S}~8€. !4=>~1‚. BžŸ4   ¡YZ¢£4  V. wVƒmnop„B 4†‡"C*67ˆ. 4¤¥¦§s‚w~4¨©"ª«467. ‰Š‹Œ4Ž‘’“p”•–*2382. ¬­:;8  =>?@A%®gkO4. 3!l–*no——". z  /0”•s  

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(6) . ˜ (Keyword: Shadow generation, Perspective.    4 ²³´µ¶· I8uv   

(7)     ¸F–¹º4¹». projection. ). !lq¼½423p¾¿B ÀÁ²ÂÃÄ· ÅÆÇ!. This paper presents a novel approach to generating. l   p"€È¸4ÉÊI8. object. (2D). Y23ËM{Ì"BÍ7?¸Î. shadow. ÏÐb”ÑÒÓ4   ¾¿Ç+,C*. generation are usually based on 3D geometry. In this.    4 

(8)   1‚wkԏ4Õo;Ö. paper, we present a way of deriving accurate shadows. s„B"B×ØÙÚ23ÕoÛ]^. of a 3D object which requires only stereo images of the. É;ÖÔÏÜÔSÜ423ÕoÝ;kÞ4. object taken from two different viewpoints. For each. ÒÓ"B GH) ! 467”ߦ”4/0. view of the object, the object shadows can be. ×ØÎÏËMàáâãBäåæ]^. generated for point light sources located along the line. ç "YZ*ÔϏ4Uäå4ߦèh. connecting the two view points. The approach assumes. éêq]^4. that at least five reference points on the base plane,. çí³î zY°±4ߦèïPU;„B. where the object shadow is to be cast upon, can be. \"B"k'(4  67[*  . identified in the stereo images. The shadow generation. #$ :sðldÛäålñ[*ÔÏÜ42. shadows. inform-ation.. using. Previous. two-dimensional approaches. of. U4. UÐb"ëéê¿4èìZ]^.

(9) 3U"ÛPUlñ]^4lds{ò>‘23. ë A¯B¯C æ D üU4VI8B d4VpJ. 4ÕoïPU;B\". K4w°(1(÷t4 a¯b¯c æ d)ï cross ratio 4. <óô67œõö. S}~. [ A , B , C , D ] = [a , b , c , d ] ¨WœðdÆpü*U4 cross ratio èë òý<UBVp4JK°±ïüU4°± I8Œ4ÎÏ" BW%™DEij23kB4opqr st*uvU;Mòý<USd4"B÷< œ÷ü¨?t*uvUI8JKw°k8D EI8Bt¹º4[ðYdpw(ü*uv UQ*Yd4U(;t*uvU4 a)8Q*œ‘QðYd4{U". ÷ . ÷ -. ÷ <. ÷œ÷-àáøù)238t*uvUk ºõ4t¹ºÛQ*ST U V1 æ V2 kúÏ4 VL÷œ÷-23¹»kûõ4ÒÓ(Ü÷ <¯÷ü)Ý;U]^àá°Z V1 œ V2 gk4 "NuvUI8BVpJK4w(1ï ›òý4. U:IϏC*4°±"þ. ëDEI8Z÷(÷üÒÓ¹»4 dœt¹ºYd4{Uï23¨]^Z V2 k 4ÝIÎÏ"1DEGH> , S}~ cross-ratio 1®(po4{U L ϏJK4" v

(10) 3D Ðbð dp4ü*U A¯B¯C æ D (÷t)ïABCD4 cross-ratioIÕùõ[A, B, C, D]. [A, B , C , D ]=. AC • BD BC • AD. ÷ ü.

(11) ÷ 4 ÷ t BCƒDE. H LS I 4¨;¨? I U,. B÷<?)(op¹»dÆ4. Ïà+!"5"z6401k1y I8hÎ(1". d×ظ(œqrQðt¹ºYd4{U(ë. 8W7k2 8I79:"s) k1 œ k2 —Zs. V1 æ V2 S;zŠ4DEI8 œ¹». ) l1`; l2 8‘”ѹ»dÆ4 d. d{!" 90#4QðYd)"B÷<k. :I,zT467Ϗ";¿ï;4<U P’¯. 4QðYdpp$k'4œ¹»d4{U. Q’¯R’¯S’¯T’8 U’(÷4);¿=öøùB÷. 8%Xü*uvU4<*UÝI8,1%®. >œ÷?"÷@œ@ï;%*764þ÷.  cross ratio è"?)&'B%®p(è4)w~. ;ABC4". B C<*UgDE×ØK*B%® cross ratio gà+S,s(-./è401". ÷ >. ÷ 2 8÷24 K1 U?þ3; CE œ L1 4{U" ë÷4 l1 œ ce 44{U k1=(k1x , k1y)M[C, H, K1, E]=R ïDEI8Ϗ. Rh (c − e ) − c x (hx − ex ) k1x = x x x R (c x − e x ) − hx + ex. ÷ ?.

(12) p4M°±g#C€U8#C€¹4 :N?4OPî¶ÄQ³´¶#. ü=RœSR. B$%™'()*T54671 "SV-ã€O U 23VW4X®7DE NOQR–o3Y±BmnoZíIJ¶ ÂÃÄ[¶\ p4Vnopst*4uvU" DEk'(467\]^°ZQRV Uc dpò°±g:I8BQRVp" 4]^_;MRVp4uv UB%RVpw(23B íIJ¶ ÂÃÄ[¶ pk` ÷ @. 4ÒÓ"\]^_`p$cdefgDEI8 a–4LCNO,€bc4 U = >"C*67I8Š‹Œ4Žqa–d4e 1þ–*23!lq–o3Õo—" tuvf [1] Woo, P. Poulin and A. Fournie, "A Survey of Shadow Algorithms,". IEEE. Computer. Graphics. and. Applications, vol. 10, no. 6, Nov. 1990, pp. 13-32. [2] A. Appel, "Some Techniques for Shading Machine Renderings of Solids," Proc. AFIPS JSCC, vol. 32, 1968,. ÷ @. pp. 37-45. [3] F. Crow, "Shadow Algorithms for Computer Graphics,". s)p$4=ö\]^_`QRV4 Ua b4 defg23cD4I8( 1"BC\DE×Ø,Q*=>~”•#. Computer Graphics (Proc. SIGGRAPH), vol. 11, no. 3, Aug. 1977, pp. 242-248. [4] P. Atherton, K. Weiler, and D. Greenberg, “Polygon. 23ò>U4ks:°BT dp"#. Shadow. 23ò>¹4ksad:×Ø{ZU. SIGGRAPH), vol. 12, no. 3, Aug. 1978, pp. 275-281.. Gener ation,". Computer. Graphics. (Proc.. EFÌznG"B#k'4 d8B#. [5] L. Williams, "Casting Curved Shadows on Curved. kH4{U:I8ÛaI4=öϏ"#4 d. Surfac es," Computer Graphics (Proc. SIGGRAPH), vol.. I8Ϗ;¨?DEJW dp4Q*U*. 12, no. 3, Aug. 1978, pp. 270-274.. ;23$K4<UL%*ï ,p$67k. [6] T. Whitted, "An Improved Illumination Model for. Ϗ434"WX#4{UJ;”ѹ4. Shaded Display," CACM, vol. 23, no. 6, June 1980, pp.. dæ”ÑLð¹4dab4{U"¨ WB#Lð dp23<U4ò>*ë ïks”ÑWU4¹ad4:I8 ~#(1"\]^°ZQ Uab4 d. 343-349..

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