Patent Application: US-201113096488-A

Abstract:
a computer - implemented method for estimating a pose of an articulated object model that is a computer based 3 d model of a real world object observed by one or more source cameras , including the steps of obtaining a source image from a video stream ; processing the source image to extract a source image segment maintaining , in a database , a set of reference silhouettes , each being associated with an articulated object model and a corresponding reference pose ; comparing the source image segment to the reference silhouettes and selecting reference silhouettes by taking into account , for each reference silhouette , a matching error that indicates how closely the reference silhouette matches the source image segment retrieving the corresponding reference poses of the articulated object models ; and computing an estimate of the pose of the articulated object model from the reference poses of the selected reference silhouettes .

Description:
fig1 schematically shows an overview over a real world scene 8 , the scene 8 comprising a real world object 14 such as a human , being observed by two or more source cameras 9 , 9 ′, each of which generates a video stream of source images 10 , 10 ′. the system and method according to the invention generates a virtual image 12 showing the scene 8 from a viewpoint of a virtual camera 11 which is distinct from the viewpoints of the source cameras 9 , 9 ′. optionally , from a sequence of virtual images 12 a virtual video stream is generated . an apparatus according to the invention comprises a processing unit 15 which performs the image processing computations implementing the inventive method , given the source images 10 , 10 ′ and generating one or more virtual images 12 . the processing unit 15 is configured to interact with a storage unit 16 for storing source images 10 , virtual images 12 and intermediate results . the processing unit 15 is controlled by means of a workstation 19 typically comprising a display device , a data entry device such as a keyboard and a pointing device such as a mouse . the processing unit 15 may be configured to supply a virtual video stream to a tv broadcasting transmitter 17 and / or to video display devices 18 . fig2 schematically shows a 3d model 1 of the scene 8 , comprising an articulated object model 4 of the real world object 14 . the 3d model 1 typically further comprises other object models , e . g . representing other humans , the ground , buildings etc ( not shown ). the articulated object model 4 comprises joints 2 that are connected by links 3 , roughly corresponding to bones or limbs in the case of the model of a human . each joint 2 is defined as a point in 3d - space , and each link 3 can be represented by a straight line connecting two joints 2 through 3d - space . furthermore , a variety of projection surfaces 5 that may be associated with the links 3 of the articulated object model 4 are shown . this association comprises an at least partly fixed geometric relationship between the projection surfaces 5 and the link , consequently , the projection surfaces 5 move with the link . according to different embodiments of the invention , the projection surfaces 5 are ( from left to right ) ellipsoidal bodies ; cylindrical bodies ; or a set of billboards 6 forming a billboard fan 7 . the association between a link and a projection surface can be , for example , that the link ( i . e . a straight line joining the two joints connected by the link ) defines a major axis of such an ellipsoidal body or cylinder , or lies within the plane of one or more such billboards . billboards 6 per se , for projecting virtual views , are known in the art . in the present invention , two or more planar billboards 6 are associated with a single link 3 of the articulated object model 4 . each billboard 6 is associated with one source camera 9 . the plane of the billboard 6 comprises the link 3 , with the orientation of the billboard 6 around the link 3 being defined by the location of the associated source camera 9 . preferably , the billboard 6 is normal to the shortest line between the source camera 9 and the direction of the link 3 . all the billboards 6 for one link 3 form together a billboard fan 7 . the images of the source cameras 9 are projected onto the associated billboards 6 of each link 3 , and then projected into virtual camera 11 , and blended together , from the billboards 6 of the link 3 , to form the virtual image 12 of the link 3 . thus , the billboards 6 of the link 3 do not occlude one another . however , they may occlude the billboards 6 of another link 3 . one aim of the present invention is to enable virtually unconstrained free - viewpoint rendering of human subjects from a small set of wide - baseline video footage . we use a representation based on articulated billboards 6 . the basis of this model is a 3d human skeleton structure 4 ( see fig2 ). every bone or link 3 , represented by a 3d vector b i and the position of its end - joint 2 x i , corresponds to a major component of the real world body 14 , e . g ., the torso or the extremities . with each bone we associate a fan 7 of billboards 6 , which contains a billboard 6 for every input image l i of a subject ( see fig2 ). more specifically , for each l i the corresponding billboard plane is defined by the joint x i the bone direction b i and the vector b i ×( c j − x i ), where c i is the camera position of l i . hence , the billboards 6 are aligned with the character bones and as orthogonal as possible to their associated input views 10 , 10 ′. the basic idea of our method is to compute a 3d pose of the articulated billboard model , i . e ., a spatial joint configuration of the underlying skeleton structure 4 , which brings its 2d projection into correspondence with the subject &# 39 ; s pose in each input frame of the video . after this alignment , a texture map and alpha mask is generated for each billboard 6 from its associated view 10 , 10 ′. however , a fully automatic computation of a single 3d pose , which is perfectly consistent with all input views , may not be possible in the presence of issues such as imperfect camera calibration or low texture resolution . in such cases , a semi - automatic , data - driven approach is applied , which operates in three consecutive phases : a 2d pose estimation and template - based image segmentation , the construction of the articulated 3d billboard model , and the actual rendering . first , for the 2d pose estimation in each individual input view , we utilize a database of silhouettes , temporal motion coherence of subjects in the video , and motion capture data to assist the user in fast and accurate placement of joints 2 . given these 2d joint positions , a segmentation of the image into the different body parts , i . e ., the torso or the limbs , is computed using a human template model in order to map image - pixels to billboards ( see section 2 “ pose estimation and template - based segmentation ”). the second phase of the algorithm integrates the pose and texture information from all individual views and generates the final articulated billboard model for rendering . this processing step includes an optimization of the 3d joint positions and a compensation for camera calibration errors , which optimizes the texture overlap for each model segment , i . e ., for each fan 7 of billboards 6 . a final alpha - mask and texture optimization eliminates visible seams and discontinuities between adjacent billboards ( see section 3 “ construction of the articulated 3d billboard model ”). the last step is the actual real - time rendering of novel views . section 4 describes an algorithm for a fully gpu - based , view - dependent per - pixel blending scheme , which is optimized for rendering articulated billboard models efficiently while preserving the photorealism of the original input video . in the first phase of the method we compute an initial guess of the subject &# 39 ; s 14 joint positions in image space and a segmentation of the pixels into the different body parts . for calibration of the intrinsic and extrinsic camera parameters we currently use the method of thomas [ tho06 ]. as mentioned previously a fully automatic pose estimation and segmentation is very challenging due to the relatively low resolution and quality . accordingly , we propose the following semi - automatic approach which minimizes the required user - interaction to only a few mouse - clicks . then , given the joint 2 positions , the segmentation of the subject &# 39 ; s 14 body parts is computed by fitting a human template model with a known segmentation to the input video frames . we assume that a coarse segmentation of the subject 14 from the background is available , e . g ., using chroma keying or background substraction . fig3 a shows a typical example of a segmented image 13 in our application scenario . the basic idea to compute an initial guess of a subject &# 39 ; s pose , i . e ., the 2d positions of the skeleton joints 2 , is to compare it to a database of silhouettes , for which the respective skeleton poses are known ( see fig3 b ). first , for each view h , we normalize for differently sized subjects by re - sampling the silhouette 13 on a 32 × 40 grid and stack the binary silhouette information at each grid point into a vector y j ε [ 0 , 1 ] n , with n = 32 × 40 . then , for each v j , our algorithm finds the best matching k entries in the database , which minimize the error where w is an entry in the database , q its corresponding 2d joint positions , and m is the number of skeleton joints . the vector p i contains the joint coordinates from the previous video frame . the first term of eq . ( 1 ) ensures a proper match of the silhouettes whereas the second term exploits temporal motion coherence of subject &# 39 ; s in the video . in other words , minimization of ( 1 ) returns the database entry that looks most like the current image and whose joint 2 positions are closest to the joint positions from the preceding image . this is of particular help to resolve left - right ambiguities in the silhouettes . the influence of the second term can be weighted by the value λ . for the first frame of a sequence we simply set λ = 0 , for all other frames we used a value of λ = 0 . 5 for all our examples . the joint 2 positions are also processed in normalized coordinates with respect to the subject &# 39 ; s bounding box . using this error e s , the k = 3 best matching silhouettes and their corresponding 2d joint positions for each single view l i are retrieved from the database . in order to select the most plausible 2d pose from each of these sets we run a multi - view optimization for each combination of poses : we compute the 3d rays from each camera c j center through the retrieved joint positions in l i . then , we compute the 3d representative for each joint 2 which is closest to the corresponding rays . fig4 shows an example with two cameras 9 , 9 ′. the measure for the quality of a particular combination of poses is the accumulated sum of distances of each 3d joint from its respective rays . in order to make this procedure more robust to the often inaccurate camera calibration , this multi - view optimization also includes a simple correction step . for each silhouette , a 2d offset in the image plane is introduced as an additional parameter . when minimising the accumulated sum of distances , these 2d offsets are varied as well , using the levenberg - marquardt algorithm . this calibration correction proved to be very effective : for some silhouette images the necessary 2d offset for minimizing the error measure can be as high as 8 pixels . in summary , the abovementioned optimisation is performed for each combination of the best matching silhouettes for each view . for example , given two cameras , and having found for each camera ( or view ) three best matching silhouettes , then the multi - view optimization is performed nine times . for each camera , the 2d pose is chosen which gives the smallest accumulated sum of distances over all the optimimization runs . as demonstrated in fig3 c , this silhouette - based pose estimation and joint optimization generally provides a good guess of the subject &# 39 ; s 2d joint positions in each view 4 . with a simple interface the user can then manually correct these positions by moving the joints ( see fig5 a ). after this manual joint refinement step the silhouette and joint positions are preferably immediately added to the database . the increase of poses in the database has proven to lead to significantly better matches for new sequences . in application scenarios where no silhouette information is available at all , the user can resort to placing all joints manually . even with accurate 2d joints a robust segmentation of the image into the subject &# 39 ; s body parts is still a difficult problem . using a database of segmented silhouettes instead of the above binary silhouette segmentation is not a desirable option , since creating such a database would be extremely complex and time - consuming , and we could still not expect to always find sufficiently accurate matches . instead , we fit a generic , pre - segmented 3d template model to the images . this has the considerable advantage that we get a good starting solution for the segmentation process and that we can easily resolve occlusions . however , fitting a 3d model requires , for each particular input view , the computation of a 3d pose whose projection perfectly aligns with the 2d joints . a 3d pose leading to a perfect match in all views can often not be found due to calibration inaccuracies or slight joint misplacements . therefore , we fit a 3d model per input view . a solution for computing an approximate 3d pose for articulated models from a single image has been presented by hornung et al . [ hdk07 ]. given the 2d joint positions x i for an image l j , their approach uses a database of 3d motion capture data to find a set of 3d joint positions x i whose projection approximately matches the 2d input joints ( see fig5 b ). we provide a simple but effective modification to their algorithm for computing the required accurate fit . this is done as follows : the approximate 3d match is deformed , such as to align with the 2d joints , according to the following algorithm : through each 3d joint x i , we create a plane parallel to the image plane of l j . then , we cast a ray from the camera center c j through the corresponding target joint position x i in l j and compute its intersection with the plane . the 3d pose is then updated by moving each x i to the respective intersection point and updating the 3d bone coordinate systems accordingly . in other words : this procedure assumes that the distance from the camera to the joint is correct , and adjusts the 3d position of the joint to match the image while keeping the distance from the camera constant . the result is the required 3d pose which projects exactly onto the previously estimated 2d joints . the 3d template model can now be fitted to the image by deforming it according to this computed 3d pose using standard techniques for skeleton - based animation [ lcf00 ] ( see fig5 c ). please note that this algorithm generally does not preserve the limb lengths of the original 3d skeleton and therefore , enables an adaptation of the 3d template mesh to fit the subject &# 39 ; s dimensions more accurately . the fitted , pre - segmented template model does not perfectly segment the input frame l j and might not completely cover the entire silhouette . therefore , a refinement of the segmentation is done in three simple steps . in a first step , a colour model is learned per body segment based on automatically selected confident pixels of the pre - segmented body parts ( see fig6 a ). in a second step , the trained colour model is used to label the unconfident pixels leading to a segmentation adjusted to the subjects body dimensions and silhouette ( see fig6 b ). in a third step , a morphological closing operation removes outliers as depicted in fig6 c . to determine the confident pixels , we project a slightly thinned and thickened version of the template model into the image and label the silhouette pixels accordingly . pixels which receive the same label in both projections are marked as confident pixels and labeled with the corresponding body segment . all remaining pixels within the silhouette are labeled as unconfident as shown in fig6 a . by learning the colour model online , we provide a robust segmentation algorithm being able to handle segmentation in uncontrolled environments . changing lighting conditions , subject specific appearance or view dependent appearance can thus be handled reliably . the pose estimation and segmentation procedure is performed for every view and input frame from which free - viewpoint renderings are to be generated . as a result , the segmentation approach using successive 2d pose estimation and 3d template fitting automatically handles occluded body parts , is robust even for low image quality and resolution , and requires only a small amount of simple user interaction during the refinement of joint positions . we use the computed 3d joint positions of section 2 . 1 as an initial pose for the final articulated billboard representation . if a 3d joint of the articulated billboard model is not optimally positioned , the texture resulting from the rendering of all billboards of a billboard fan will not align ( see fig7 a ). in this section , we describe how the 3d joint positions can be optimized based on a quantitative measure of the alignment of the billboard textures . in the following , we first define a scoring function for a position of a joint in one view and for one camera pair . this scoring function is then extended to several views and cameras . using this scoring function and anthropometric constraints the 3d pose of the articulated billboard model is optimized . finally , we will describe a seam correction which removes texture discontinuities between adjacent billboards . to score the quality of a joint position of an output view v , all billboards adjacent to this joint are evaluated . for each fan of billboards , the alignment of its billboards for a pair of input views ( l 1 , l 2 ) is scored by a pixel - wise comparison of the projected textures . for every output pixel p of v , the per - pixel score s l2 , l2 ( p ) is defined as s i 1 , i 2 ⁡ ( p ) = { 1 - ɛ ⁡ ( v i 1 ⁡ ( p ) , v i 2 ⁡ ( p ) ) , p ⁢ ⁢ active ⁢ ⁢ in ⁢ ⁢ i 1 ⁢ ⁢ and ⁢ ⁢ i 2 0 , otherwise ( 2 ) where v li ( p ) is the colour contribution of a billboard associated with view l j to pixel p . ε (•) is a colour distance measure in rgb . the active pixels are defined as those pixels in the output view v which receive a valid colour contribution from the input views l 1 and l 2 . the segmentation generated in section 2 . 3 is used to reliably resolve occlusion . the score for a joint in a view v is the normalized sum of all pixels s i 1 , i 2 ⁡ ( v ) = ∑ p ∈ v ⁢ s i 1 , i 2 ⁡ ( p ) ⁢ n ⁡ ( p ) ∑ p ∈ p v ⁢ n ⁡ ( p ) . ( 3 ) the normalization factor n ( p ) is 1 , if at least one of the two pixels is active and 0 , otherwise . thus , the scoring function measures the matching of texture values , while n ( p ) penalizes non - aligned parts as in fig7 a . these pixel - wise operations are efficiently implemented on the gpu using fragment shaders . in summary , the procedure according to ( 1 ) and ( 2 ) determines to which degree the image contributions from the different cameras match , as seen from the virtual viewpoint and in the virtual output image , and only for those pixels for which the output image receives a contribution from both source cameras . for more than two input views , we define the score as a weighted average of all camera pairs , where the weight for each camera pair depends on the angle β i1 , i2 between the respective viewing directions , with narrow angles receiving a higher weight : s ⁡ ( v ) = ∑ ( i 1 , i 2 ) ∈ ℐ ⁢ s i 1 , i 2 ⁡ ( v ) ⁢ ω ⁡ ( β i 1 , i 2 ) ∑ ( i 1 , i 2 ) ∈ ℐ ⁢ ω ⁡ ( β i 1 , i 2 ) , ( 4 ) where is the set of all pairs of input views and ω ( β ) is , for example , a gaussian weight : ω ⁡ ( β ) = ⅇ - β 2 2 ⁢ σ 2 . ( 5 ) the value for 6 was empirically determined to be 0 . 32 . finally , the score of the joint position is the normalized sum of the scores in all evaluated views : s v = 1  v  ⁢ ∑ v ∈ v ⁢ s ⁡ ( v ) , ( 6 ) since the scoring of the joint position depends on the evaluated views , we need a suitable set υ . in order to cover a reasonable range of viewing positions , we evaluate the scoring function at the camera positions of all input views and the virtual views in the center between each camera pair . for the position optimization of a joint , we evaluate sυ at spatially close candidate positions on a discrete , adaptive 3d grid . the grid is refined in a greedy manner around those candidate positions which achieve a higher score sυ , until a given grid resolution is reached ( empirically set to 1 . 2 cm ). to avoid degenerate configurations with billboard fans of zero length , we additionally consider the anthropometric consistency [ nas09 ] during the evaluation of each pose . a joint position receives a zero score if one of the following constraints does not hold : the joint is on or above the ground . lengths of topologically symmetric skeleton bones ( e . g ., left / right arm ) do not differ more than 10 %. the lengths of adjacent bones are within anthropometric standards . distances to unconnected joints are within anthropometric standards . for the last two constraints , we use the 5th percentile of female subjects rounded down as minimal lengths and the 95th percentile of male subjects rounded up as maximal lengths . this grid - search optimization process is iteratively repeated over the skeleton . that is , in each iteration the position is optimized separately , as described , for each joint of the set of all joints . in our experiments , we found that it typically converges after 4 iterations . since the optimisation is based on target functions that are defined in the virtual image , no ultimately unnecessary parameters are determined , and overall efficiency is high . see fig7 for an articulated billboard model before ( 7 b ) and after ( 7 c ) optimization . due to sampling of the billboards &# 39 ; segmentation masks during rendering with projective texturing ( see fig8 a ), small discontinuities ( visible cracks ) between adjacent billboards may appear in the output view as shown in fig8 b : in the virtual image 12 , an output pixel from a first billboard 6 may fall , when projected into the segmented source image 10 , within a second segment 13 b that is assigned to an adjacent second billboard 6 ′, rather than into a first segment 13 a assigned to the first billboard 6 . consequently , the output pixel receives no colour contribution at all . to overcome this problem , these seam pixels have to be rendered for both adjacent billboards . therefore , we mark pixels as seam pixels in the input views if they cover billboards on two adjacent skeleton bones or links 3 ( e . g ., pixel enclosed by dashed lines in fig8 a ). to detect seam pixels , the segmentation mask is traversed for each input view . a pixel p is marked as seam pixel , if it fulfills both of the following conditions : at least one pixel p ′ in its 4 - neighborhood has a different label but comes from the same subject | depth ( p )− depth ( p ′)|& lt ; φ where depth (•) is the depth value at this pixel . the threshold φ distinguishes between occluding parts and connected parts . it was empirically set to φ = 3 cm . an example for the seam corrected segmentation mask and the resulting rendering improvement is shown in fig8 c . in the following we describe a rendering procedure for articulated billboards . we designed this algorithm according to the general criteria defined by buehler et al . [ bbm * 01 ]. due to our challenging setting with calibration errors and very sparse camera positioning , our particular focus is on : coherent appearance : adjacent billboards should intersect without cracks or disturbing artifacts and blend realistically with the environment . visual continuity : billboards should not suddenly change or pop up when moving the viewpoint . view interpolation : when viewing the scene from an original camera angle and position , the rendered view should reproduce that of the input camera . input to the rendering procedure are the articulated billboard model , the segmented input views ( section 2 . 3 ) and the seams computed in section 3 . 3 . for each rendered output frame , the articulated billboards are sorted back - to - front for a proper handling of occlusions . in order to meet the above goals , we perform a per - pixel blending procedure . we separate between per - camera weights which are computed once per billboard and the final per - pixel weights . for a smooth blending of the billboards 6 associated with one fan 7 of billboards 6 , we use the same gaussian weight as in eq . ( 5 ). to achieve an interpolation at an original camera view 10 , we introduce an attenuation function which ensures that all views from an original camera 9 perspective are identical to the corresponding camera source images 10 while still assuming a smooth transition between different views . the attenuation function is defined as ƒ ( iω max )= 1 for the source view iω max with the highest value of ω (•) ( that is , the closest source camera 9 ) and f ⁡ ( i ω max ) = 1 - ⅇ - d ⁡ ( v , i ω max ) 2 2 ⁢ σ 2 ( 7 ) for all other cameras l j . d ( v , iω max ) is the euclidean distance from the viewer &# 39 ; s virtual camera 11 position to the source camera 9 position of view iω max . the constant σ is empirically determined to be 1 meter , which is lower than the minimal distance between two source cameras 9 and thus does not lead to any discontinuities . the billboards of a billboard fan are blended per - pixel . as shown in fig8 a , a camera look - up in the corresponding segmentation mask of each billboard is performed . this determines if the current output pixel p is on the body part belonging to this billboard . if so , then the corresponding colour contribution v i j ( p )= 0 from source view l j and its alpha value α i j ( p ) can be added to the output view v . otherwise , we set α i j ( p )= 0 i . e ., transparent . the latter case also occurs when the corresponding body part is occluded in and the colour information should be taken from other cameras . the resulting colour value v ( p ) of the screen pixel is then v ⁡ ( p ) = ∑ i j ∈ ℐ ⁢ v i j ⁡ ( p ) ⁢ w ⁡ ( i j , p ) ∑ i j ∈ ℐ ⁢ w ⁡ ( i j , p ) ( 8 ) with the set of all input views as in eq . ( 2 ) and the per - pixel weights w ( l j , p )= α l j ( p ) ω ( β i j ) ƒ ( i ω max ). ( 9 ) this is done for all colour channels separately . the resulting alpha value is α v ⁡ ( p ) = { α i ω max ⁡ ( p ) , if ⁢ ⁢ w ⁡ ( i ω max , p ) ≠ 0 ∑ i j ∈ ℐ ⁢ α i j ⁡ ( p ) ⁢ w ⁡ ( i j , p ) ∑ i j ∈ ℐ ⁢ α i j ⁡ ( p ) ⁢ ω ⁡ ( β i j ) , otherwise ( 10 ) where the first case applies , if the closest camera is used for this pixel . eq . ( 8 ) and eq . ( 10 ) make sure that the colour values are blended such that the factors sum up to 1 . however , the alpha values do not have to sum up to 1 , e . g ., if continuous alpha mattes are available instead of binary segmentation masks . in addition to this , billboards seen at an oblique angle or from the backside , i . e ., having a normal in an angle close to or more than 90 degrees away from the viewing direction , are simply faded out . for simplification , these factors are not shown in the equations . an example for blending of intensities ( i . e ., one colour channel ) of two cameras is shown in fig9 a where the azimuth and altitude angles are from spherical coordinates of the view position around the fan of billboards . the two peak points at ( 0 . 0 , 0 . 0 ) and ( 0 . 5 , 0 . 5 ) correspond to the positions of the source cameras . as it can be seen in the plot , when approaching these points the corresponding camera &# 39 ; s weight increases to 3d model 1 . 0 and all other camera weights decrease to 0 . 0 . therefore , in this case only the source camera is used which results in the exact reproduction of the source image . finally , to prevent non smooth edges at the boundaries of a fan of billboards with respect to the background , other billboard fans , and at locations where other input views receive the highest weight ( e . g ., due to occlusions on a billboard ), an additional gaussian smoothing step is applied . this is done adaptively as a post - process only at discontinuities detected and stored while rendering the billboards . fig9 b , c and d show an example : 9 b image without smoothing , 9 c with adaptive smoothing , 9 d locations where discontinuities have been eliminated through smoothing . fig1 shows a flow chart of a method according to the invention . in a first step 21 , at least one image per source camera 9 is acquired , either from a live video stream , or from stored images or video streams . in a second step 22 the 2d pose estimation is performed . in an optional third step 23 , the multi - view optimisation is performed . in a fourth step 24 , the 3d template fitting is performed . in a fifth step 25 , the segmentation of body parts is performed . in a sixth step 26 , the 3d pose optimization , based on the position scoring , is performed . in a seventh step 27 , the texture seam correction is performed . in an eighth step 28 , the camera blending of the billboards 6 of each billboard fan 7 is performed . in a ninth step 29 , the final image is stored and / or displayed . whereas the preceding explanation pertains to the representation and rendering of a single articulated object , the final image may comprise a plurality of articulated objects and images of a background and other objects . while the invention has been described in present preferred embodiments of the invention , it is distinctly understood that the invention is not limited thereto , but may be otherwise variously embodied and practiced within the scope of the claims . andújar c ., boo j ., brunet p ., fairén m ., navazo i ., vázquez p ., vinacua à . : omni - directional relief impostors . computer graphics forum 26 , 3 ( 2007 ), 553 - 560 . aubel a ., boulic r ., thalmann d . : lowering the cost of virtual human rendering with structured animated impostors . in wscg &# 39 ; 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08 ( 2008 ), pp . 1 - 9 . waschbúsch m ., wúrmlin s ., gross m . : 3d video billboard clouds . computer graphics forum 26 , 3 ( 2007 ), 561 - 569 . yamazaki s ., sagawa r ., kawasaki h ., ikeuchi k ., sakauchi m . : microfacet billboarding . in egrw &# 39 ; 02 ( 2002 ), pp . 169 - 180 . 1 3d model 2 joint 3 link 4 articulated object model 5 projection surface 6 billboard 7 billboard fan 8 scene 9 , 9 ′ source camera 10 , 10 ′ source image 11 virtual camera 12 virtual image 13 , 13 a , 13 b source image segment 14 real world object 15 processing unit 16 storage unit 17 transmitter 18 video display device 19 workstation