Filtering Non-Linear TransferFunctions on Surfaces

Abstract

Abstract-Applying non-linear transfer functions and look-up tables to procedural functions (such as noise), surface attributes, or even surface geometry are common strategies used to enhance visual detail. Their simplicity and ability to mimic a wide range of realistic appearances have led to their adoption in many rendering problems. As with any textured or geometric detail, proper filtering is needed to reduce aliasing when viewed across a range of distances, but accurate and efficient transfer function filtering remains an open problem for several reasons: transfer functions are complex and non-linear, especially when mapped through procedural noise and/or geometry-dependent functions, and the effects of perspective and masking further complicate the filtering over a pixel's footprint. We accurately solve this problem by computing and sampling from specialized filtering distributions on the fly, yielding very fast performance. We investigate the case where the transfer function to filter is a color map applied to (macroscale) surface textures (like noise), as well as color maps applied according to (microscale) geometric details. We introduce a novel representation of a (potentially modulated) color map's distribution over pixel footprints using Gaussian statistics and, in the more complex case of high-resolution color mapped microsurface details, our filtering is view-and light-dependent, and capable of correctly handling masking and occlusion effects. Our approach can be generalized to filter other physical-based rendering quantities. We propose an application to shading with irradiance environment maps over large terrains. Our framework is also compatible with the case of transfer functions used to warp surface geometry, as long as the transformations can be represented with Gaussian statistics, leading to proper view-and light-dependent filtering results. Our results match ground truth and our solution is well suited to real-time applications, requires only a few lines of shader code (provided in supplemental material), is high performance, and has a negligible memory footprint.

Color‐mapped noise vector fields for generating procedural micro‐patterns

“…By taking advantage of the two dimensions of the color‐maps, we can generate a wider range of patterns, such as non‐concentric blots and interleaved stripes. Our noise model comes with a filtering technique using Heitz et al method [HNPN14]. Finally, we presented estimators of the footprint statistics in real‐time, allowing for procedural real‐time generation and rendering.…”

“…This is difficult because H is nonlinear (it cannot move out of the integral) and N is procedural (H •N cannot be stored and pre-filtered). To achieve this, we apply the filtering method developed by Heitz et al [HNPN14]. They have shown that Equation (3) is equal to the combination of the colors in the color map H weighted by the filter and their presence in N over the pixel footprint P. This way, Equation ( 3) is equal to…”

“…Bergner et al [BMWM06] present a method to estimate the Nyquist frequency of the composition using spectral analysis. Heitz et al [HNPN13; HNPN14] propose a technique to pre‐filter non‐linear composition functions stored in a color map. Filtering methods need statistical information about the noise in the pixel footprint, such as mean and variance.…”

“…However, this erases many local variations and the results are over-smoothed. The noise model presented in this paper can be filtered using Heitz et al method [HNPN14] with two-dimensional function and we present a real-time estimation of the required statistical information in the pixel footprint. This real-time estimation allows us to obtain a real-time implementation of the LEANmapping algorithm for the filtering of normal-maps [OB10].…”

Bi‐Layer textures: a Model for Synthesis and Deformation of Composite Textures

“…This widens the set of textures that can be faithfully reproduced, as shown in Figure 15. Moreover, this method is compliant with anti-aliasing [HNPN14].…”