Importance Sampling of Partitioned Domains Using Data Trees

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Solution Overview

Problem

The sampling speed for importance sampling of partitioned domains has not been fully optimized, particularly in Monte Carlo and quasi-Monte Carlo methods, where functions are defined by discrete energy densities, such as textured light sources in computer graphics.

Innovation Solution

A system and method for importance sampling of partitioned domains involve partitioning a domain into sets, assigning probabilities to each set, and generating samples based on these probabilities using data trees like Huffman trees or kd-trees, which are constructed using heuristics to minimize traversal depth and ensure well-distributed samples.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Productivity

If traditional Monte Carlo or quasi-Monte Carlo methods are used for importance sampling of partitioned domains, then sampling can be performed, but the sampling speed has not been fully optimized

Engineering Contradiction:

Improvesampling speedVSAvoidtime for integral estimation

Core Design Contradiction:

ProductivityVSLoss of time

Solution Approach 1:

The domain is partitioned into multiple sets, and a separate probability is assigned to each set. This segmentation allows for more targeted and efficient sampling by treating each partition independently with its own probability distribution, thereby optimizing the overall sampling speed.

Inventive Principle:

Principle #1Segmentation

Solution Approach 2:

Probabilities are pre-assigned to each partitioned set before the sampling process begins. This preliminary assignment of probabilities enables the sampling algorithm to make informed decisions about which regions to sample more frequently, improving sampling efficiency without requiring iterative optimization during the sampling process.

Inventive Principle:

Principle #10Preliminary action

2Measurement precision

If deterministic samples are used in quasi-Monte Carlo methods, then convergence is improved, but sampling speed optimization remains incomplete

Engineering Contradiction:

Improveconvergence of integral estimationVSAvoidsampling speed

Core Design Contradiction:

Measurement precisionVSProductivity

Solution Approach 1:

Different sampling strategies are applied to different partitions based on their local probability characteristics. High-probability partitions may use deterministic sampling for better convergence, while low-probability partitions can use simpler sampling methods, optimizing both precision and speed locally across the entire domain.

Inventive Principle:

Principle #3Local quality

Solution Approach 2:

The sampling approach dynamically adapts to the probability distribution of each partition. By making the sampling strategy dependent on the local probability characteristics, the method achieves both improved convergence where needed and maintained speed in other regions.

Inventive Principle:

Principle #15Dynamics

Data Source

PatentUS8131770B2System, method, and computer program product for importance sampling of partitioned domains

Publication Date: 2012.03.06 NVIDIA CORP

AI summary

A system, method, and computer program product are provided for importance sampling of partitioned domains. In operation, a domain is partitioned into a plurality of sets. Additionally, a probability is assigned to each of the plurality of sets. Furthermore, samples are generated from the plurality of sets, the samples being generated according to the probability of a corresponding set.