Hair Scattering Importance Sampling via Cauchy Distribution

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Solution Overview

Problem

Current rendering technologies face challenges in efficiently rendering high-quality hair images due to the complexity of the hair bidirectional scattering distribution function (BSDF), which requires a large number of samples for Monte Carlo-based lighting techniques, leading to high computational costs and limiting the application of image-based lighting to hair rendering.

Innovation Solution

Importance sampling of the hair scattering function using a Cauchy distribution to reduce the number of samples required for rendering, allowing for more efficient computation of light interactions with hair and improving image quality.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Manufacturing precision

If Monte Carlo-based lighting techniques are used with standard sampling methods, then hair rendering quality can be achieved, but computational cost becomes prohibitively high

Engineering Contradiction:
Improvehair rendering qualityVSAvoidcomputational efficiency
Core Design Contradiction:
Manufacturing precisionVSProductivity

Solution Approach 1:

The patent pre-computes and stores the hair scattering function values in a lookup table before rendering. This preliminary action allows the rendering process to directly query pre-computed values rather than evaluating complex scattering equations in real-time, significantly reducing computational cost while maintaining rendering quality

Inventive Principle:
Principle #10Preliminary action

Solution Approach 2:

The patent transforms the sampling approach by changing from uniform random sampling to importance sampling based on the scattering function's probability density. By parameterizing the sampling distribution to match the scattering lobes' angular distribution, the method concentrates samples in regions of high contribution, achieving better quality with fewer samples

Inventive Principle:
Principle #35Parameter changes

2Measurement precision

If a large number of samples are used for Monte Carlo integration, then rendering accuracy improves, but rendering time increases significantly

Engineering Contradiction:
Improverendering accuracyVSAvoidrendering time
Core Design Contradiction:
Measurement precisionVSLoss of time

Solution Approach 1:

The scattering function is pre-evaluated and stored in a lookup table with high resolution. This preliminary computation of scattering values for many directions allows the rendering process to achieve high accuracy by querying pre-computed values rather than computing scattering equations repeatedly during rendering

Inventive Principle:
Principle #10Preliminary action

Solution Approach 2:

The patent changes the sampling strategy from uniform to importance sampling, where sample density is parameterized to match the scattering function's angular distribution. This parameter change ensures that samples are concentrated in directions where the scattering function has significant values, achieving accurate results with fewer samples and reduced rendering time

Inventive Principle:
Principle #35Parameter changes

3Manufacturing precision

If image-based lighting is applied to hair rendering, then lighting realism improves, but computational complexity increases

Engineering Contradiction:
Improvelighting realismVSAvoidcomputational complexity
Core Design Contradiction:
Manufacturing precisionVSDevice complexity

Solution Approach 1:

The patent pre-computes the interaction between image-based lighting environments and hair scattering properties, storing results in lookup tables. This preliminary action captures complex lighting-realism effects in advance, allowing the rendering system to apply pre-computed lighting data without recalculating complex scattering integrals for each lighting condition

Inventive Principle:
Principle #10Preliminary action

Solution Approach 2:

The patent parameterizes the lighting evaluation by using importance sampling with probability density functions that match the scattering lobes. This parameterization allows efficient evaluation of image-based lighting interactions by concentrating computational effort on the most significant light directions, reducing overall computational complexity while maintaining lighting realism

Inventive Principle:
Principle #35Parameter changes

Data Source

PatentEP2629266B1Ishair: Importance sampling for hair scattering
Publication Date: 2018.11.21 PACIFIC DATA IMAGES LLC
  • EP2629266B1 patent drawingFigure 1A~1B
  • EP2629266B1 patent drawingFigure 2A~2B
  • EP2629266B1 patent drawingFigure 3

AI summary

A technique for rendering an image of hair in a computer-generated scene is described. The scene includes a virtual light source and a hair virtual object comprising a material model. A hair shading function partly defining the material model is accessed. A set of random values is generated. The hair shading function is importance sampled by converting the set of random values into a set of light direction samples based on a Cauchy distribution. The probability density function of each converted light direction sample uses a Cauchy distribution. A light color value and a hair color value are computed for each light direction sample of the set of light direction samples. The light color values and the hair color values are weighted to determine a set of weighted values. A characteristic of a pixel representing part of the virtual object is determined based on the set of weighted values.