Robust Soft Shadow Mapping with Backprojection and Depth Peeling
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1 paper 2008/3/20 15:47 page 19 #1 Vol. 13, No. 1: Robust Soft Shadow Mappng wth Backprojecton and Depth Peelng Lous Bavol, Steven P. Callahan, and Claudo T. Slva Scentfc Computng and Imagng Insttute, Unversty of Utah Abstract. Soft shadow mappng s an attractve soluton to the problem of realtme soft shadows because t works wth any knd of rasterzable geometry (n partcular alpha-transparent textures and har), t does not requre any precomputaton, and t s smple to mplement on the GPU. However, state-of-the-art approaches have several lmtatons that prevent them from beng practcal for all scenes. Frst, parameter tunng s requred to avod surface acne. Second, gaps between shadow map pxels are ether gnored, whch results n lght bleedng, or handled usng gap fllng, whch results n overshadowng. We present a more robust soft shadow mappng technque, based on a recent backprojecton algorthm, that uses depth peelng to address the problems of surface acne and lght bleedng. Our algorthm uses a mult-layer shadow map to reduce lght bleedng, and mdpont shadow maps to handle self-shadowng more robustly. It provdes hgh-qualty soft shadowng for complex scenes, whle stll mantanng nteractve renderng rates. Source code s avalable onlne. 1. Introducton Shadow mappng [Wllams 78] s a real-tme algorthm for renderng hard shadows from pont lghts that maps very well to GPUs. In ths classc algorthm, a prelmnary pass renders the scene from the vewpont of the lght nto a depth buffer (dubbed a shadow map). Then, mage fragments are transformed to the mage space of the lght, and ther depths are compared to the A K Peters, Ltd /06 $0.50 per page
2 paper 2008/3/20 15:47 page 20 #2 20 journal of graphcs tools shadow map depths to determne f the fragment s occluded from the lght. The advantages of shadow mappng are ts speed and smplcty. A physcally-based soft shadow mappng algorthm wth self-shadowng was proposed recently by Guennebaud et al. [Guennebaud et al. 06], whch computes a percentage of lght seen from every pxel n the mage. Ths s done by backprojectng the occluders n the shadow map onto the lght plane and determnng the magntude of the occluson. The algorthm addresses many of the ssues of prevous approaches, but stll overshadows, manly because t extends the occludng samples to prevent lght bleedng. Our algorthm extends ths backprojecton approach to reduce artfacts. We represent the vsblty of an area lght usng multple depth layers, smlar to [Keatng and Max 99] and [Agrawala et al. 00]. We extract our layers usng depth peelng [Evertt 02], whch can be performed effcently on graphcs hardware. Ths allows us to remove most lght bleedng artfacts wthout extendng the shadow map samples. In addton, by usng the mdponts between layers, our algorthm reduces the problem of surface acne. 2. Soft Shadow Mappng wth Backprojecton Soft shadows rendered usng percentage closer flterng (Percentage Closer Soft Shadows PCSS) [Fernando 05] usually look plausble and are effcent enough to be used n vdeo games on current graphcs hardware. However, PCSS s smlar to tracng rays from a pont lght to the scene rather than from a pont to be shaded to the lght. Unlke PCSS, the backprojecton algorthm [Guennebaud et al. 06] approxmates the result of ray tracng from the pont to be shaded. To avod dong actual ray tracng, t consders the samples from a sngle shadow map as mcropatches n world space and computes the amount of occluson of the mcropatches seen from the pont to be shaded. Because t s more physcally based, backprojecton produces soft shadows of hgher qualty than PCSS. Besdes, self-shadowng s easer to handle wth backprojecton snce false occluders tend to backproject outsde the lght area. We provde a bref summary of the backprojecton algorthm here. Assumng a square area lght and square shadow map pxels, the algorthm proceeds as tradtonal shadow mappng by renderng the scene from the vewpont of the lght to create a shadow map of depth values. Then, the scene s rendered from the vewpont of the eye and each pxel s shaded based on some shadow map tests. Each shadow map sample s frst tested for approxmate occluson usng a tradtonal depth test based on ts based depth value. Ths test s necessary to dscard samples behnd the pont to be shaded relatve to the lght. If the sample passes the test, t s backprojected onto the lght based on ts actual depth value. Ths backprojected sample clamped to the lght area results n a percentage of lght seen by the pont to be shaded.
3 paper 2008/3/20 15:47 page 21 #3 L. Bavol, S.P. Callahan, C.T. Slva: Robust Soft Shadow Mappng 21 Fgure 1. Backprojecton works by computng the projected area A on the lght source of a shadow map sample s from a shaded pont p. The backprojecton algorthm s based on accumulatng the percentage of the lght source that each shadow-map sample s occludng (see Fgure 1). A shadow-map sample s a depth value z s n eye space, representng the dstance between the shadow map plane and the sample. Based on ths dstance, the wdth of the sample s proportonal to z s. Then, gven the depth z of the pont to be shaded p and the dfference between z and z s, the backprojected sze of the sample s a scale operaton. The backprojected szes of the sample n the x and y drectons are computed, and clamped to the lght sze. Concretely, the normalzed coordnates B of the backprojecton bounds of a sample of depth z s seen from a pont to be shaded p of depth z s: B = b left b rght b bottom b top = (du 0.5) (du + 0.5) (dv 0.5) (dv + 0.5) ( w n r z z s)( ) 1 z z s l (1) where (u s, v s ) and (u, v) are respectvely the shadow map coordnates of the sample and the pont to be shaded (n pxels), du = u s u, dv = v s v, w s = w n r z s s the sze of the sample (n world-space), w and n are respectvely the wdth and depth of the lght plane (n world-space), r s the wdth of the shadow map (n pxels), z s the depth of the pont to be shaded (n worldspace), and l s the wdth of the lght (n world-space). The ntersecton of the backprojected sample wth the lght s performed by clampng B by [-0.5,0.5]. The shadow contrbuton of a sample s the area of the clamped backprojecton area A = (b rght b left )(b top b bottom ). Note that the depths z and z s must be vew-space depths (lnear), not post-projecton depths from a tradtonal shadow map (non lnear).
4 paper 2008/3/20 15:47 page 22 #4 22 journal of graphcs tools (a) Fgure 2. Lght bleedng s caused by gaps between shadow map pxels as seen from an area lght. Here we show the errors that a sngle shadow map (a) produces n a smple scene wth soft shadows (b). (b) Ths algorthm assumes that every sample of the shadow map wth a depth less than z s s a potental occluder. To reduce ths set of samples, a conservatve kernel s the ntersecton of the near plane (z = n) of the shadow map wth the shadow frustum defned by the pont to be shaded and the square lght. The center of the search regon s gven by projectng the pont to be shaded n lght space, as n regular shadow mappng. The wdth (n pxels) of the kernel s gven by w 0 = r l n w ( 1 n 1 z ). The search regon can be reduced by fetchng a local mnmum depth from a herarchcal shadow map [Guennebaud et al. 06, Guennebaud et al. 07]. Another optmzaton s to perform adaptve screen-space shadow samplng [Guennebaud et al. 07] to avod oversamplng large low-frequency penumbra. Such samplng optmzatons are orthogonal to our approach of usng a mult-layer shadow map. Though backprojecton s more accurate than PCSS, there are stll a few artfacts that need to be addressed. Frst, the algorthm suffers from surface acne artfacts that are currently reduced usng a hand-tuned depth bas. Ths problem s common to most algorthms based on mage-based representatons of a scene. Second, the orgnal backprojecton algorthm suffers from overshadowng. 3. Soft Shadow Mappng Artfacts Due to the dscrete nature of shadow maps, small overlaps and gaps may occur between shadow map pxels seen from a gven pont to be shaded. Ths problem affects all the soft shadow mappng algorthms that approxmate the orgnal geometry by a set of shadow-map samples unprojected nto world space. Gaps result n lght bleedng, whereas overlaps result n overshadowng.
5 paper 2008/3/20 15:47 page 23 #5 L. Bavol, S.P. Callahan, C.T. Slva: Robust Soft Shadow Mappng 23 (a) Fgure 3. (a) The dandelon scene shows that gap fllng [Guennebaud et al. 06] can result n shadows that are too dark. (b) A ray-traced mage of the dandelon scene shows the correct shadowng. (b) In addton, surface acne appears because the ponts seen from the eye do not correspond exactly to the ponts seen from the lght. We do not address the problem of removng occluson overlaps. However, we do address the ssues of lght bleedng and surface acne Lght Bleedng Lght bleedng occurs when there s a gap between shadow map pxels seen from the pont to be shaded. Thus, surfaces that are n the penumbra of the frst object, as seen from the lght, wll not get shadows from other objects that may fully occlude the surface. Ths s a sgnfcant problem for any scene wth multple overlappng shadows and s magnfed wth hgher depth ranges. Fgure 2 shows an example of ths case where objects closest to the lght nterfere wth the shadows cast from objects closer to the shadow. One approach to resolvng the problem of lght bleedng s to overestmate the shadow by extendng the shadow map pxels, as n the orgnal backprojecton algorthm. Ths gap fllng approach does not work properly for shadows of thn objects such as har (see Fgure 3).
6 paper 2008/3/20 15:47 page 24 #6 24 journal of graphcs tools (a) (b) Fgure 4. Self-shadowng ssues, usng a unform depth test. (a) A depth bas too small results n surface acne. (b) A depth bas too large results n the ncorrect placement of shadows Surface Acne Self-shadowng s tradtonally handled by computng a depth for the pont to be shaded (z) and for the shadow map sample (z s ). A pont s consdered n shadow f and only f z s < z. However, due the dscrete nature of the shadow map, surface acne (false self-shadowng) appears n the fnal mage because shadow-map samples behnd the vsble surfaces are peakng through. To counter ths, a depth bas s usually appled to move the occluders underneath the surface farther away from the pont to be shaded. Ths bas s usually based on the slope of the shadow map (glpolygonoffset). The shadow test then becomes z s + bas(z s ) < z. A depth bas that s too small results n alasng, whle a depth bas that s too large results n ncorrectly placed shadows. Unfortunately, the depth bas often requres manual tunng to acheve good mage qualty. Fgure 4 shows the errors that occur when usng a unform depth bas to correct surface acne. 4. Removng the Artfacts To mnmze the problems of lght bleedng, overshadowng, and surface acne, we ntroduce two enhancements to the orgnal backprojecton algorthm mult-layer shadow maps for reducng gaps causng lght bleedng, and multlayer mdpont shadow maps for reducng surface acne. These modfcatons are descrbed n detal n ths secton.
7 paper 2008/3/20 15:47 page 25 #7 L. Bavol, S.P. Callahan, C.T. Slva: Robust Soft Shadow Mappng 25 (a) Fgure 5. Multple layers of shadow maps reduces lght bleedng artfacts by fllng gaps seen from the area lght. Here we show a shadow map usng two layers dstngushed by dfferent shades of gray (a) and the resultng soft shadows (b). (b) 4.1. Mult-Layer Shadow Maps To create a mult-layer shadow map, for every frame we render the entre scene multple tmes from the lght usng depth peelng [Evertt 02] wth a fxed number of layers (see Fgure 5). The dea behnd depth peelng s to capture one layer of depth for each renderng pass, startng wth the nearest fragments at each pxel, the second nearest, the thrd nearest, and so on. Evertt [Evertt 02] ntroduced a smple approach to depth peelng on commodty hardware. The frst pass renders the scene normally and results n depths for the nearest surface. In subsequent passes, the depth buffer computed n the prevous pass s used to peel away depths less than or equal to those already captured n prevous passes. Thus, each pass generates a depth buffer for the th nearest surface. For shadow mappng, ths depth peelng results n multple layers, each contanng the occluders world-space dstances to the lght plane. After the shadow map passes, the shadow ntensty of each pxel n the mage s computed as before, by projectng the pxel onto the shadow map and testng shadow map samples for occluson usng a conservatve search regon. Each sample coordnate n the shadow map corresponds to a beam wth the orgn at the center of the lght, gong through the shadow map sample (see Fgure 5). By samplng the depth values of the frst k samples for a gven shadow map sample coordnate, we effectvely take the frst k hts along the correspondng lght beam. We effcently reduce lght bleedng by computng the occluson of every sample along a lght beam and usng the furthest occludng sample from the lght. In practce, we found that by usng only three layers we can remove most lght bleedng artfacts, as was noted n [Agrawala et al. 00].
8 paper 2008/3/20 15:47 page 26 #8 26 journal of graphcs tools 4.2. Mdpont Shadow Maps As descrbed above, surface acne results from an ncorrect depth bas. Several approaches have been developed to adaptvely compute the depth bas. One common method s to use the glpolygonoffset functon n OpenGL. Ths functon offsets the depth of the rasterzed fragments by a constant epslon and a coeffcent proportonal to the maxmum slope of the depth values around the pxel. Ths method requres tunng the slope parameter to remove surface acne, whch can be dffcult for complex scenes. The mdpont shadow map algorthm [Woo 92] uses the average depth of the frst two surfaces encountered from the vewpont of the lght for the selfshadowng test. Ths algorthm works for both closed and non-closed objects. Usng a mdpont shadow map removes most of the ssues wth self-shadowng. However, t too has mnor ssues. Frst, lght bleedng may appear when the mdpont and the orgnal pont are too far away. Ths can be fxed usng a maxmum depth bas [Weskopf and Ertl 03]. Second, surface acne may reman at corners where the mdpont and the orgnal surface meet. We found that these artfacts are mnor n relaton to the artfacts that are nherent to a lmted-resoluton shadow map, thus we use an extenson of mdpont shadow mappng to handle self-shadowng. For a gven sample coordnate n the shadow map, we sample a fxed number of depths n our mult-layer shadow map. We then compute based depth values correspondng to the mdponts between the layers. We use the based depth values for handlng self-shadowng and the orgnal depths for computng the actual shadow contrbutons. Then, the samples are processed startng from the deepest shadow map layer and the frst non-zero shadow contrbuton s selected and added to the shadow. 5. Examples and Dscusson Apart from the shadow map resoluton, the man qualty parameter of our algorthm s a maxmum number of samples per pxel max nspp. We compute the wdth of the square search regon as descrbed n the backprojecton algorthm. If the number of samples n the search regon s less than max nspp, we process all the sample coordnates n the search regon. Otherwse, we use an adaptve step so that the search area s sampled unformly wth max nspp samples. We compute step = (regon nspp)/(max nspp), and we scale the world-space sze of the samples w s by step when backprojectng the samples. Ths unform samplng method can be combned wth lght-space optmzatons to reduce the sze of the search regon conservatvely [Guennebaud et al. 07, Schwarz and Stammnger 07]. Note that t may ntroduce mnor artfacts because the samplng pattern shfts wth the pont to be shaded.
9 paper 2008/3/20 15:47 page 27 #9 L. Bavol, S.P. Callahan, C.T. Slva: Robust Soft Shadow Mappng 27 (a) Fgure 6. Though multple layer shadow mappng reduces lght bleedng substantally, some rare falure cases reman. (a) In ths scene contanng two mcropatches, our algorthm would only count the contrbuton of the nearest mcropatch (s 1) to the shaded pont. However, the partal contrbuton of the second patch (s 2) should be added. (b) Mdponts can ntroduce lght bleedng. Ths case can be handled by lmtng the dfference between the orgnal depth and the mdpont depth. (b) Snce the man bottleneck n the algorthm s computng per-pxel shadows, we use a deferred shadowng ppelne whch computes the shadows only for the vsble fragments. We use a predcate n the shadow shader to avod computng shadows of background pxels or pxels wth black dffuse colors. Thus, the speed of the algorthm depends on the number of non-background and non-black pxels, the resoluton of the shadow map, the maxmum number of samples per pxel, and the number of depth layers. For all our scenes, we used three shadow map layers and acheved mages that look smlar to ray tracng (see Fgure 7). Our technque s useful for reducng lght bleedng when usng backprojecton and gap fllng renders unacceptable shadows, such as for har-lke objects. Though the algorthm we have ntroduced removes most of the lght bleedng and surface acne artfacts that we descrbe n Secton 3, some ssues may stll arse n rare cases. Frst, our soluton to lght bleedng s not guaranteed to remove all lght bleedng snce t uses a fxed number of layers. For nstance, for a smple scene such as an oblque quad, lght may stll bleed though. Also, our technque may ncorrectly gnore the contrbuton of some mcropatches, leavng some lght bleedng (see Fgure 6). In practce, we have not notced ths effect, as t s probably compensated by overshadowng from overlappng backprojectons. Second, although the algorthm uses mdpont shadow mappng and removes much of the surface acne wthout parameter
10 paper 2008/3/20 15:47 page 28 #10 28 journal of graphcs tools tunng, there are stll rare cases when the acne appears, such as when the resoluton of the shadow map s too low or the layers are very close together. One soluton to ths problem would be to take the second samples from the pont to be shaded nstead of the mdponts, but ths tends to result n lght bleedng, especally for non-closed objects. Thrd, because the backprojectons of shadow map samples may overlap, the algorthm tends to slghtly overshadow (see Fgure 7(k)). Though t s a substantal mprovement over the orgnal backprojecton algorthm, as the resoluton of the shadow map or the number of samples ncreases, ths problem becomes more pronounced. The technques we have descrbed n ths work sgnfcantly mprove overall qualty of real-tme soft shadow mappng. Furthermore, n our experments, we found that the algorthm worked robustly wthout the usual parameter tunng that s requred wth state-of-the-art technques. Because the results approach those of ray tracng n qualty, the algorthm could be effcently used as a prevew tool n a producton settng for scenes wth complex geometry and soft shadows. Acknowledgments. We thank Sony Computer Entertanment Amerca R&D for ther support, and Gael Guennebaud for helpful conversatons. Lous Bavol, Steven P. Callahan, and Cláudo T. Slva are funded by the Natonal Scence Foundaton (grants CCF , EIA , OISE , IIS , and CCF ), the Department of Energy, an IBM Faculty Award, Sanda Natonal Laboratores, Lawrence Lvermore Natonal Laboratory, the Army Research Offce, and a Unversty of Utah Seed Grant. References [Agrawala et al. 00] Maneesh Agrawala, Rav Ramamoorth, Alan Herch, and Laurent Moll. Effcent Image-Based Methods for Renderng Soft Shadows. In Proceedngs of ACM SIGGRAPH 2000, Computer Graphcs Proceedngs, Annual Conference Seres, pp , [Evertt 02] Cass Evertt. Interactve Order-Independent Transparency. Techncal report, NVIDIA Corporaton, [Fernando 05] Randma Fernando. Percentage-closer soft shadows. In SIG- GRAPH 05: ACM SIGGRAPH 2005 Sketches, p. 35, [Guennebaud et al. 06] Gaël Guennebaud, Loïc Barthe, and Mathas Pauln. Realtme soft shadow mappng by backprojecton. In Eurographcs Symposum on Renderng, pp , [Guennebaud et al. 07] Gaël Guennebaud, Loïc Barthe, and Mathas Pauln. Hgh- Qualty Adaptve Soft Shadow Mappng. In Eurographcs, 2007.
11 paper 2008/3/20 15:47 page 29 #11 L. Bavol, S.P. Callahan, C.T. Slva: Robust Soft Shadow Mappng 29 [Keatng and Max 99] Brett Keatng and Nelson Max. Shadow Penumbras for Complex Objects by Depth-Dependent Flterng of Mult-Layer Depth Images. In Eurographcs Workshop on Renderng, pp , [Schwarz and Stammnger 07] Mchael Schwarz and Marc Stammnger. Btmask Soft Shadows. Computer Graphcs Forum 26:3 (2007), [Weskopf and Ertl 03] Danel Weskopf and Thomas Ertl. Shadow Mappng Based on Dual Depth Layers. In Proceedngs of Eurographcs, pp , [Wllams 78] Lance Wllams. Castng Curved Shadows on Curved Surfaces. In Computer Graphcs (Proceedngs of SIGGRAPH 78), 12, 12, pp , [Woo 92] Andrew Woo. The shadow depth map revsted. In Graphcs Gems III, pp San Dego, CA, USA: Academc Press Professonal, Inc., Web Informaton: Lous Bavol, Scentfc Computng and Imagng Insttute, Unversty of Utah, 50 S. Central Campus Drve, Room 3490, Salt Lake Cty, UT 84112, USA Steven P. Callahan, Scentfc Computng and Imagng Insttute, Unversty of Utah, 50 S. Central Campus Drve, Room 3490, Salt Lake Cty, UT 84112, USA Cláudo T. Slva, Scentfc Computng and Imagng Insttute, Unversty of Utah, 50 S. Central Campus Drve, Room 3490, Salt Lake Cty, UT 84112, USA Receved August 8, 2006; accepted n revsed form January 18, 2008.
12 paper 2008/3/20 15:47 page 30 #12 30 journal of graphcs tools (a) (b) (c) (d) (e) (f) (g) (h) () (j) (k) (l) Fgure 7. Addng shadow map layers. Our algorthm wth unform samplng (max nspp = 121) compared to ray tracng wth 1,000 samples per pxel. Image Resoluton: Shadow Map Resoluton: GPU: GeForce 7800 GTX, CPU: AMD Opteron Processor 2.2 GHz. Left: Our algorthm wth 1 layer. Mddle: Our algorthm wth 3 layers. Rght: Ray tracng. Frst row: Happy Buddha (293,264 trangles). (a) 10.8 fps (b) 7.6 fps (c) 20 mn. Second row: Spder (3,316 trangles). (d) 13.4 fps (e) 8.7 fps (f) 7 mn. Thrd row: Dandelon (35,107 trangles). (j) 18.5 fps (k) 13.0 fps (l) 16 mn. Forth row: Close-up of the dandelon. (j) 11.5 fps (k) 7.6 fps (l) 50 mn.
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