Scalar Spatiotemporal Blue Noise Masks

Fig. 1. All images rendered using an exponential moving average (EMA) with α = 0.1. On the left is an image of the Disney Cloud [2020] rendered using stochastic single scattering, where free-flight distances are sampled using a series of blue noise masks over time. Traditional 2D blue noise masks (far left) are easy to filter spatially, but exhibit a white noise signal over time, making the underlying signal difficult to filter temporally. Our spatiotemporal blue noise (STBN) masks (right of large image) additionally exhibit blue noise in the temporal dimension, resulting in a signal that is easier to filter over time. On the far right, we show two crops of the main image, as well as their corresponding discrete Fourier transforms over both space (DFT(XY)) and time (DFT(ZY)). The Z axis is time. The ground truth is shown in the insets in the large image (upper and lower right corners).

[1]  Cameron N. Christou Optimal Dither and Noise Shaping in Image Processing , 2008 .

[2]  Johannes Hanika,et al.  Monte Carlo Methods for Volumetric Light Transport Simulation , 2018, Comput. Graph. Forum.

[3]  Frédo Durand,et al.  A Frequency Analysis of Monte-Carlo and other Numerical Integration Schemes , 2011 .

[4]  Kevin J. Parker,et al.  Digital halftoning using a blue-noise mask , 1991, Electronic Imaging.

[5]  Marcos Fajardo,et al.  Blue-noise dithered sampling , 2016, SIGGRAPH Talks.

[6]  Mathieu Desbrun,et al.  Blue noise through optimal transport , 2012, ACM Trans. Graph..

[7]  Peter Wonka,et al.  Screen-space blue-noise diffusion of monte carlo sampling error via hierarchical ordering of pixels , 2020, ACM Trans. Graph..

[8]  Chi-Wing Fu,et al.  Fast capacity constrained Voronoi tessellation , 2010, I3D '10.

[9]  Morgan McGuire,et al.  Hashed alpha testing , 2017, I3D.

[10]  Don P. Mitchell,et al.  Spectrally optimal sampling for distribution ray tracing , 1991, SIGGRAPH.

[11]  Gurprit Singh,et al.  Variance analysis for Monte Carlo integration , 2015, ACM Trans. Graph..

[12]  Anjul Patney,et al.  Spatiotemporal variance-guided filtering: real-time reconstruction for path-traced global illumination , 2017, High Performance Graphics.

[13]  M. Balzer,et al.  Capacity-Constrained Voronoi Diagrams in Finite Spaces , 2008 .

[14]  Jean-Claude Iehl,et al.  A low-discrepancy sampler that distributes monte carlo errors as a blue noise in screen space , 2019, SIGGRAPH Talks.

[15]  Lei Yang,et al.  A Survey of Temporal Antialiasing Techniques , 2020, Comput. Graph. Forum.

[16]  Alexander Keller,et al.  My favorite samples , 2019, SIGGRAPH Courses.

[17]  Tomas Akenine-Möller,et al.  Temporally dense ray tracing , 2019, High Performance Graphics.

[18]  S. Nayar,et al.  A practical analytic single scattering model for real time rendering , 2005, ACM Trans. Graph..

[19]  Aaron E. Lefohn,et al.  Spatiotemporal reservoir resampling for real-time ray tracing with dynamic direct lighting , 2020, ACM Trans. Graph..

[20]  Tomas Akenine-Möller,et al.  FLIP: A Difference Evaluator for Alternating Images , 2020, Proc. ACM Comput. Graph. Interact. Tech..

[21]  Mark Meyer,et al.  A theory of monte carlo visibility sampling , 2012, TOGS.

[22]  Chris Wyman,et al.  Exploring and expanding the continuum of OIT algorithms , 2016, High Performance Graphics.

[23]  S. Dammertz,et al.  Image Synthesis by Rank-1 Lattices , 2008 .

[24]  Carsten Dachsbacher,et al.  Gradient Estimation for Real-time Adaptive Temporal Filtering , 2018, PACMCGIT.

[25]  Laurent Belcour,et al.  Distributing Monte Carlo Errors as a Blue Noise in Screen Space by Permuting Pixel Seeds Between Frames , 2019, Comput. Graph. Forum.