Extinction Transmittance Maps
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Extinction Transmittance Maps Pascal Gautron * Cyril Delalandre * Technicolor Research & Innovation Jean-Eudes Marvie * Figure 1: Production-quality clouds (600 × 400 × 300) rendered at 45 fps. Our solution gathers local extinction for a simple formulation of light transmission in heterogeneous media. We provide high quality results while remaining independent from the volume representation. The interaction between light and participating media involves complex physical phenomena such as light absorption and scatter- ing. The radiance transmitted through a medium then depends on the variations of scattering and extinction along potentially complex light paths, yielding soft light shafts and shadowing (Figure 1). Computing light scattering in these media usually requires com- plex offline computations [Cerezo et al. 2005]. Some real-time ap- plications are based on heavy precomputations [Zhou et al. 2008]. Some others introduce restrictions such as approximate diffusion schemes, or specific volume representations. In particular, [Jansen and Bavoil 2010] extend the concept of deep shadow maps [Lokovic and Veach 2000] by representing the vari- ations of opacity within the medium in Fourier space: each pixel of the Fourier Opacity Map stores a set of projection coefficients. Opacity variations are then unprojected from the coefficients to evaluate the overall opacity of the medium for each visible parti- cle. This technique is highly effective, and the map is built by ac- cumulating the contributions of each particle independently using alpha blending. However, this method only represents an opacity information and cannot account for actual light scattering. This limitation is raised in [Delalandre et al. 2011]: instead of representing opacities, each pixel of the Transmittance Function Map (TFM) stores a Fourier transform of the medium transmittance along light rays. Single scattering is then estimated in a ray march- ing process, in which the light reduced intensity is deduced from the transmittance values. While providing accurate results and real- time performance, the evaluation of the medium transmittance at a point requires the knowledge of the overall extinction along the entire light path. The generation of the map then requires a ray marching through the participating medium. This technique is then usable only for voxelized media, overlooking other representations such as the dynamic particle clouds massively used in video games. Extinction Transmittance Maps: We introduce Extinction Transmittance Maps (ETM), a technique combining the advantages of both Fourier Opacity Maps and Trans- mittance Function Maps while avoiding their respective drawbacks. As for [Jansen and Bavoil 2010] and [Delalandre et al. 2011], our method borrows from the principle of shadow mapping where a vir- tual camera is oriented towards the medium from the location of the light source. This camera is used to create the Extinction Transmit- tance Map, into which the contents of the medium are rendered to build a set of Fourier coefficients representing the local variations of the extinction parameters (Figure 2). To generate the final image we reformulate the transmittance function to evaluate the contribu- tion of each visible volume sample directly from the ETM. * {pascal.gautron, cyril.delalandre, jean-eudes.marvie}@technicolor.com Figure 2: Rendering a participating medium involves evaluating the transmittance T from the light source to each sample point p i to estimate light transfer. The ETM is generated from the local extinc- tion σ t at volume samples such as particles. Analytical integration then provides the global transmittance T along light rays. When Projecting Local Extinction... In [Delalandre et al. 2011] each pixel of the TFM is generated by marching through the medium to evaluate its transmittance along light rays. In the case of particle-based media, marching through the particles is not tractable without prior voxelization. To over- come this problem, our approach is based on the projection of the local extinction coefficient of the medium as a set of Discrete Co- sine Transform (DCT) coefficients c j : c j = 1 d max ∑ i d i σ t (p i )b j (x i ) (1) where d max is the maximum traversal length of the light ray. The j-th DCT function is b j (x i )= k j cos (2x i + 1) iπ 2d max , k j being its normalization factor. Each particle i is described by its location p i , distance to the light source x i and traversal distance d i . A representation of the extinction function can then be obtained from any kind of volume representation, avoiding the need for a ray marching. In the next step we reformulate the transmittance directly in terms of the projection coefficients. ... Leads to Global Transmittance The medium transmittance along a light ray follows an exponential rule according to the extinction σ t , which can be expressed using the coefficients of the ETM: T (p i )= exp - Z p i l σ t (z)dz = exp - ∑ j Z p i l c j b j (x z )dz ! (2)
Transcript of Extinction Transmittance Maps
Extinction Transmittance Maps
Pascal Gautron ∗ Cyril Delalandre ∗
Technicolor Research & InnovationJean-Eudes Marvie ∗
Figure 1: Production-quality clouds (600×400×300) rendered at 45 fps. Our solution gathers local extinction for a simple formulation oflight transmission in heterogeneous media. We provide high quality results while remaining independent from the volume representation.
The interaction between light and participating media involvescomplex physical phenomena such as light absorption and scatter-ing. The radiance transmitted through a medium then depends onthe variations of scattering and extinction along potentially complexlight paths, yielding soft light shafts and shadowing (Figure 1).
Computing light scattering in these media usually requires com-plex offline computations [Cerezo et al. 2005]. Some real-time ap-plications are based on heavy precomputations [Zhou et al. 2008].Some others introduce restrictions such as approximate diffusionschemes, or specific volume representations.
In particular, [Jansen and Bavoil 2010] extend the concept of deepshadow maps [Lokovic and Veach 2000] by representing the vari-ations of opacity within the medium in Fourier space: each pixelof the Fourier Opacity Map stores a set of projection coefficients.Opacity variations are then unprojected from the coefficients toevaluate the overall opacity of the medium for each visible parti-cle. This technique is highly effective, and the map is built by ac-cumulating the contributions of each particle independently usingalpha blending. However, this method only represents an opacityinformation and cannot account for actual light scattering.
This limitation is raised in [Delalandre et al. 2011]: instead ofrepresenting opacities, each pixel of the Transmittance FunctionMap (TFM) stores a Fourier transform of the medium transmittancealong light rays. Single scattering is then estimated in a ray march-ing process, in which the light reduced intensity is deduced fromthe transmittance values. While providing accurate results and real-time performance, the evaluation of the medium transmittance ata point requires the knowledge of the overall extinction along theentire light path. The generation of the map then requires a raymarching through the participating medium. This technique is thenusable only for voxelized media, overlooking other representationssuch as the dynamic particle clouds massively used in video games.
Extinction Transmittance Maps:
We introduce Extinction Transmittance Maps (ETM), a techniquecombining the advantages of both Fourier Opacity Maps and Trans-mittance Function Maps while avoiding their respective drawbacks.
As for [Jansen and Bavoil 2010] and [Delalandre et al. 2011], ourmethod borrows from the principle of shadow mapping where a vir-tual camera is oriented towards the medium from the location of thelight source. This camera is used to create the Extinction Transmit-tance Map, into which the contents of the medium are rendered tobuild a set of Fourier coefficients representing the local variationsof the extinction parameters (Figure 2). To generate the final imagewe reformulate the transmittance function to evaluate the contribu-tion of each visible volume sample directly from the ETM.
∗{pascal.gautron, cyril.delalandre, jean-eudes.marvie}@technicolor.com
Figure 2: Rendering a participating medium involves evaluatingthe transmittance T from the light source to each sample point pi toestimate light transfer. The ETM is generated from the local extinc-tion σt at volume samples such as particles. Analytical integrationthen provides the global transmittance T along light rays.
When Projecting Local Extinction...
In [Delalandre et al. 2011] each pixel of the TFM is generated bymarching through the medium to evaluate its transmittance alonglight rays. In the case of particle-based media, marching throughthe particles is not tractable without prior voxelization. To over-come this problem, our approach is based on the projection of thelocal extinction coefficient of the medium as a set of Discrete Co-sine Transform (DCT) coefficients c j:
c j =1
dmax∑
idiσt(pi)b j(xi) (1)
where dmax is the maximum traversal length of the light ray. Thej-th DCT function is b j(xi) = k j cos
((2xi +1) iπ
2dmax
), k j being its
normalization factor. Each particle i is described by its location pi,distance to the light source xi and traversal distance di.
A representation of the extinction function can then be obtainedfrom any kind of volume representation, avoiding the need for a raymarching. In the next step we reformulate the transmittance directlyin terms of the projection coefficients.
... Leads to Global Transmittance
The medium transmittance along a light ray follows an exponentialrule according to the extinction σt , which can be expressed usingthe coefficients of the ETM:
T (pi) = exp(−∫ pi
lσt(z)dz
)= exp
(−∑
j
∫ pi
lc jb j(xz)dz
)(2)
Figure 3: Transmittance function along a light ray through two media: smoke (left) and a test medium with sharp variations (right). Comparedto the actual transmittance (blue), our method (red) features less oscillations than TFM (green) in both cases.
Each definite integral can then be rewritten in terms of the indefiniteintegral B j of b j, yielding a new formulation for T :
T (pi) = exp
(−∑
jc j(B j(pi)−B j(l))
)(3)
where:
B j(p) =k jdmax
jπ
[sin((1+2xp)
jπ2dmax
)− sin
(jπ
2dmax
)]This unprojection scheme emphasizes the duality of our representa-tion: a set of potentially incoherent extinction samples is projectedinto the DCT basis regardless of the kind of representation used forthe volume. Then, the transmittance expressing the effect of eachparticle on all the others along the same light ray is recovered ana-lytically from the projection coefficients.
Our formulation also subtends a major efficiency difference be-tween TFM and our approach. As shown in Equation 2 the trans-mittance function follows an exponential rule which gets encodedwithin the coefficients of the TFM. On the contrary, the exponen-tial remains in its analytical form in Equation 3. Thus the coeffi-cients only encode the variations of the extinction along a light ray,which tend to be oscillatory in many media. This property makesthe DCT a method of choice for representing such variations, whileEquation 3 naturally preserves the exponential shape of the trans-mittance (Figure 3).
In the spirit of [Jansen and Bavoil 2010], final images are obtainedby rendering the particles from back to front, blending their contri-butions along camera rays. In voxelized media a simple ray march-ing is used. For each particle or sample point the medium trans-mittance is evaluated from the Extinction Transmittance Map. Theamount of light scattered towards the camera is then deduced fromthe light reduced intensity and the local scattering properties.
Results
Our algorithm offers real-time performance on a 3.6GHz Xeon withan nVidia GeForce GTX480 GPU. The presented images were ren-dered at a resolution of 1280×720 using a 1024×1024 ETM con-taining 4 coefficients per pixel. We compare our approach to theTFM and a GPU-based brute force reference solution for singlescattering. For comparison purposes, our tests are performed by raymarching through a voxelized medium. As shown in Figure 4 ourmethod tends to reduce ringing artifacts, typically present in imagesof very dense media generated using TFM. Such artifacts appear asstripes perpendicular to the lighting direction, and are particularlyvisible in the difference images. In our approach the error tendsto be spread over the entire medium, hence being less noticeableespecially in animated media.
Regarding rendering speed our method performs similarly to TFM,while avoiding the restrictions on the representation of the partici-pating media.
Reference - 2.4 fps TFM - 42 fps ETM - 42 fps
Figure 4: A plume of smoke rendered using Extinction Transmit-tance Maps and TFM, both with 4 coefficients per pixel. The rightpart of the images show the difference with a reference solution,with pixel intensities multiplied by 40 for legibility. The recon-struction errors plotted above typically appear as horizontal stripeswhen using TFM with dense media.
Production rendering also benefits from our method for higher ren-dering speed without compromising image quality. The genericityof our method allowed us to implement our approach as a shader forPixar’s RenderMan using its built-in, representation-agnostic vol-ume dicing. Our method is then implicitly compliant with otherPrMan components such as depth-of-field and motion blur.Extinction Transmittance Maps can then benefit to a wide range ofdomains, not only for real-time applications such as video gamesand interactive previsualization, but also for production rendering.
References
CEREZO, E., PEREZ, F., PUEYO, X., SERON, F., AND SILLION,F. 2005. A survey on participating media rendering techniques.The Visual Computer 21, 5, 303–328.
DELALANDRE, C., GAUTRON, P., MARVIE, J.-E., ANDFRANCOIS, G. 2011. Transmittance function mapping. In Pro-ceedings of I3D, 31–38.
JANSEN, J., AND BAVOIL, L. 2010. Fourier opacity mapping. InProceedings of I3D, 165–172.
LOKOVIC, T., AND VEACH, E. 2000. Deep shadow maps. InProceedings of SIGGRAPH, 385–392.
ZHOU, K., REN, Z., LIN, S., BAO, H., GUO, B., AND SHUM,H.-Y. 2008. Real-time smoke rendering using compensated raymarching. In Proceedings of SIGGRAPH, 1–12.
