Adaptive Sampling and Reconstruction using Greedy Error Minimization

晃晃

Adaptive Sampling and Recons***ction using Greedy Error Minimization

Fabrice Rousselle Claude Knaus y Matthias Zwicker

University of Bern University of Bern University of Bern

Abstract

We introduce a novel approach for image space adaptive sampling

and recons***ction in Monte Carlo rendering. We greedily mini-

mize relative mean squared error (MSE) by iterating over two steps.

First, given a current sample distribution, we optimize over a dis-

crete set of filters at each pixel and select the filter that minimizes

the pixel error. Next, given the current filter selection, we distribute

additional samples to further reduce MSE. The success of our ap-

proach hinges on a robust technique to select suitable per pixel fil-

ters. We develop a novel filter selection procedure that robustly

solves this problem even with noisy input data. We evaluate our ap-

proach using effects such as motion blur, depth of field, interreflec-

tions, etc. We provide a comparison to a state-of-the-art algorithm

based on wavelet shrinkage and show that we achieve significant

improvements in numerical error and visual image quality. Our ap-

proach is simple to implement, requires a single user parameter, and

is compatible with standard Monte Carlo rendering.

CR Categories: I.3.7 [Computer Graphics]: Three-Dimensional

Graphics and Realism—Raytracing;

Keywords: adaptive sampling and recons***ction

1 Introduction

Monte Carlo techniques compute pixel colors by (quasi-)randomly

sampling an integration domain that covers all light paths trans-

porting light from a source to the camera. The integration domain

may include effects such as depth of field, motion blur, and light

paths with multiple interreflections. Unless one computes an exces-

sive number of samples, this often leads to high pixel variance and

the typical noise artifacts in Monte Carlo rendering. There are two

main strategies to address this. The first is to distribute samples in

an optimal fashion, with respect to the problem at hand. The second

is to smooth out noise by applying suitable filters. Both strategies

can be applied in the high dimensional space of light paths or in

the image plane. We focus on strategies that operate in the image

plane.

We formulate the problem as follows: given a certain budget of

Monte Carlo samples, obtain an image that minimizes the relative

mean squared error (MSE) by distributing samples in a suitable

fashion in the image plane and by filtering the image with appro-

priate filters. We can interpret this as an optimization problem over

the space of sample distributions and image filters. Our core idea is

to make the problem tractable by restricting the space of filters to a

discrete set of predetermined filters per pixel. Each pixel may have

a different set of filters, but the set is predefined and not itself part

of the optimization. We use a simple greedy strategy to obtain an

approximate solution to the MSE minimization problem. Starting

from an initial set of samples, we iterate over two steps. First, for

each pixel we select the filter from its discrete set that minimizes the

pixel MSE given the current samples. Second, given the currently

chosen pixel filters, we distribute a new batch of samples that try to

further reduce MSE as much as possible. This process is repeated

until a termination criterion is fulfilled.



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