Estimation of noise in calculation of scattering medium luminance by MCRT

Ershov, Sergey; Zhdanov, Dmitrii Dmitrievich; Voloboy, Aleksei Gennadievich

doi:10.20948/mathmontis-2019-45-5

Cited by 12 publications

(27 citation statements)

References 17 publications

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“…In BDPM (with or without weights), the variance of the pixel luminance calculated from N F forward rays and N B backward rays (started from the same pixel) obeys the general law [7], see also [18]:…”

Section: Noisementioning

confidence: 99%

“…Therefore the optimal weights which minimize the noise functional in the classic MCRT and in BDPM are different. Since the BDPM noise is a quadratic functional over the ray contribution as it is shown in [7], it is also quadratic in weights. So while calculation of weights that minimize that noise functional looks mathematically trivial it is not so in practice.…”

Section: Introductionmentioning

confidence: 99%

“…In this work we investigate the weights optimal to BDPM and demonstrate the equations for them are qualitatively different from the famous Veach heuristics. This is because for the bidirectional Monte Carlo path tracing method or for BMCRT with photon maps the noise does not follow the rule like in the classic MCRT [7]. Therefore the optimal weights which minimize the noise functional in the classic MCRT and in BDPM are different.…”

Section: Introductionmentioning

confidence: 99%

“…As a result, after substitution the density of the join path into Veach-like formulae the authors can investigate dependence on the merging radius. The remaining problem is that this is still a one-sample density which is insufficient to treat "correlation terms" in BDPM [7], so accounting for the integration radius does not help much. Notice that our approach does not use the density of join paths, but only those of the light and camera paths, because the noise is an integral with narrow kernels due to "vertex merging", and these weakly converge to the delta function so that not causing much problems.…”

Section: Introductionmentioning

confidence: 99%

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Calculation of MIS weights for bidirectional path tracing with photon maps in presence of direct illumination

Ershov¹,

Voloboy²

2020

MathMon

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Multiple importance sampling (MIS) is a well-known method for noise reduction in Monte-Carlo ray tracing. It weights contributions from merging camera and light paths in different vertices. Since noise strongly depends on these weights, the problem of the optimal choice of weight to reach the minimal noise is very important. For bi-directional Monte-Carlo ray tracing with photon maps (BDPM), different join paths are not statistically independent because several light paths are checked against the same camera path and vice versa. As a result, the optimal weights which minimize the noise functional in the classic Monte Carlo ray tracing and in BDPM are different. In this paper we calculate weights for the simple reduced case of just two strategies, i.e. merging at just two vertices of camera ray. We show that these weights obey an integral equation which is qualitatively different from the well-known MIS formulae for uncorrelated samples. The integral equation is solved analytically in a closed form and one can see that the MIS weights for BDPM algorithm depend on the number of rays and scene geometry. In this paper we also correctly take into account the direct illumination to pixel luminance.

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Section: Noisementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Calculation of MIS weights for bidirectional path tracing with photon maps in presence of direct illumination

Ershov¹,

Voloboy²

2020

MathMon

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“…But its main problem is stochastic noise, and it strongly depends on the method of ray generation. Therefore a lot of studies are devoted to choice of the optimal probability distribution of ray scattering [2][3][4][5].…”

Section: Introductionmentioning

confidence: 99%

Calculation of MIS Weights for Bidirectional Path Tracing with Photon Maps

Ershov

Voloboy

Zhdanov

et al. 2020

CPT2020 the 8th International Scientific Conference on Computing in Physics and Technology Proceedings

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A widely used method for noise reduction in Monte-Carlo ray tracing is combing different means of sampling, known as multiple importance sampling (MIS). For bi-directional Monte-Carlo ray tracing with photon maps (BDPM), the join paths are obtained by merging camera and light sub-paths, and since several light paths are checked again the same camera path, and vice versa, the join paths obtained are not statistically independent. Thus the noise in this method obeys laws different from those in simple classic Monte-Carlo with independent samples so the weights that minimize that noise must also be calculated differently. This paper drives that weights for the simplest case when we mix contribution from only two vertices of camera ray. It shows that the weights obey an integral equation which is qualitatively different from the well-known MIS formulae for uncorrelated samples. Besides that, even if forget the integral operator, the weights depend on the integration sphere radius and the number of light rays used. The integral equation is solved analytically in a closed form and it is demonstrated how to perform the necessary calculations in BDPM.

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