A compact factored representation of heterogeneous subsurface scattering

Peers, Pieter; Berge, Karl vom; Matusik, Wojciech; Ramamoorthi, Ravi; Lawrence, Jason; Rusinkiewicz, Szymon; Dutré, Philip

doi:10.1145/1179352.1141950

Cited by 18 publications

(25 citation statements)

References 20 publications

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“…This corresponds most closely to the setups in [Seitz et al 2005;Peers et al 2006;Ng et al 2009]. It is somewhat distinct from relighting with distant illumination [Debevec et al 2000], where a single lighting direction illuminates the entire surface.…”

Section: Light Transport Acquisitionsupporting

confidence: 64%

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A Dual Theory of Inverse and Forward Light Transport

Bai

Chandraker

et al. 2010

Lecture Notes in Computer Science

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A cornerstone of computer graphics is the solution of the rendering equation for interreflections, which allows the simulation of global illumination, given direct lighting or corresponding light source emissions. This paper lays the foundations for the inverse problem, whereby a dual theoretical framework is presented for inverting the rendering equation to undo interreflections in a real scene, thereby obtaining the direct lighting. Inverse light transport is of growing importance, enabling a variety of new applications like separation of individual bounces of the light transport, and projector radiometric compensation to display images free of global illumination artifacts in real-world environments that exhibit complex geometric and reflectance properties. However, solving the inverse problem involves the inversion of a large light transport matrix (acquired by measurement on real scenes). While straightforward matrix inversion is intractable for most realistic resolutions, there is scant prior work on either theoretical foundations or fast computational algorithms to meet the objectives of inverse light transport.In this paper, we develop a mathematical theory that exposes the duality of forward and inverse light transport. Forward rendering also formally involves a matrix or operator inversion, which is conceptually equivalent to a multi-bounce Neumann series expansion. We show the existence of an analogous series for the inverse problem. However, the convergence is oscillatory in the inverse case, with more interesting conditions on material reflectance. Importantly, we give physical meaning to this duality, by showing that each term of our inverse series cancels an interreflection bounce, just as the forward series adds them.In algorithmic terms, we develop the analog of iterative finite element methods like forward radiosity to efficiently solve light transport inversion. Our iterative inverse light transport algorithm is very fast, requiring only matrix-vector multiplications, and follows directly from the dual theoretical formulation. We also explore the connections to forward rendering in terms of Monte Carlo and wavelet-based techniques. As an initial practical application, we first acquire the light transport of a real static scene, and then demonstrate iterative inversion for radiometric compensation on high-resolution datasets, as well as rapid separation of the bounces of global illumination. *

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Section: Light Transport Acquisitionsupporting

confidence: 64%

“…First, many fast techniques for acquiring the light transport of real scenes have been proposed in recent literature [Debevec et al 2000;Masselus et al 2003;Peers et al 2006]. Precomputed light transport is popular even for synthetic rendering [Sloan et al 2002;Ng et al 2003;Hasan et al 2006].…”

Section: Motivationmentioning

confidence: 99%

A Dual Theory of Inverse and Forward Light Transport

Bai

Chandraker

et al. 2010

Lecture Notes in Computer Science

Self Cite

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“…Capture and re-render systems-both for general subsurface scattering materials [18], [37] and specifically for human skin [12], [16]-compute specialized material models from photographs of a physical scattering object. After this capture computation, the internal model can be warped into new geometry and rerendered.…”

Section: Capture and Re-render Systemsmentioning

confidence: 99%

“…However, because of the complexity of the scattering within these materials, efficient and accurate subsurface rendering is challenging and previous approaches have limitations. Monte Carlo (MC) algorithms [20], [26], [38] accurately solve the general subsurface rendering problem but their hours-per-image cost makes them impractical for most applications; algorithms using the dipole diffusion bidirectional surface scattering reflectance distribution function (BSSRDF) [27] are fast, even real-time, but can only model homogeneously scattering materials; and, though capture and re-render systems [12], [16], [18], [37] can quickly generate high-quality images, they can only redisplay captured material models.…”

Section: Introductionmentioning

confidence: 99%

Heterogeneous Subsurface Scattering Using the Finite Element Method

Arbree

Walter

Bala

2011

IEEE Trans. Visual. Comput. Graphics

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Abstract-Materials with visually important heterogeneous subsurface scattering, including marble, skin, leaves, and minerals, are common in the real world. However, general, accurate and efficient rendering of these materials is an open problem. In this paper, we describe a finite element (FE) solution of the heterogeneous diffusion equation (DE) that solves this problem. Our algorithm is the first to use the FE method to solve the difficult problem of heterogeneous subsurface rendering. To create our algorithm, we make two contributions. First, we correct previous work and derive an accurate and complete heterogeneous diffusion formulation. This formulation has two key elements: an accurate model of the reduced intensity (RI) source, the diffusive source boundary condition (DSBC), and its associated render query function. Second, we solve this formulation accurately and efficiently using the FE method. Using there results, we can render subsurface scattering with a simple four step algorithm. To demonstrate that our algorithm is simultaneously general, accurate and efficient, we test its performance on a series of difficult scenes. For a wide range of materials and geometry, it produces, in minutes, images that nearly match path traced references, that required hours.

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“…Note that the detailed spatial patterns and anisotropic subsurface scattering in the real material are well preserved with the reconstructed light transport matrix, while the results generated by interpolation clearly exhibit artifacts. Also note that to capture the light transport effects with a similar resolution, brute force methods [Goesele et al 2004;Peers et al 2006] need dense light sampling, which is prohibitively expensive and time consuming. We show relighting results of the reconstructed light transport matrix in the companion video.…”

Section: Subsurface Scatteringmentioning

confidence: 99%

Kernel Nyström method for light transport

et al. 2009

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Figure 1: Relighting results using the light transport matrix reconstructed by our method. Complex light transport effects, including caustics (a), complex occlusions (b), and a mixture of caustics, complex occlusions, inter-reflections, and subsurface scattering (c) are all faithfully reproduced. AbstractWe propose a kernel Nyström method for reconstructing the light transport matrix from a relatively small number of acquired images. Our work is based on the generalized Nyström method for low rank matrices. We introduce the light transport kernel and incorporate it into the Nyström method to exploit the nonlinear coherence of the light transport matrix. We also develop an adaptive scheme for efficiently capturing the sparsely sampled images from the scene. Our experiments indicate that the kernel Nyström method can achieve good reconstruction of the light transport matrix with a few hundred images and produce high quality relighting results. The kernel Nyström method is effective for modeling scenes with complex lighting effects and occlusions which have been challenging for existing techniques.

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A compact factored representation of heterogeneous subsurface scattering

Cited by 18 publications

References 20 publications

A Dual Theory of Inverse and Forward Light Transport

A Dual Theory of Inverse and Forward Light Transport

Heterogeneous Subsurface Scattering Using the Finite Element Method

Kernel Nyström method for light transport

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