Compressive Estimation for Signal Integration in Rendering

In rendering applications, we are often faced with the problem of computing the integral of an unknown function. Typical approaches used to estimate these integrals are often based on Monte Carlo methods that slowly converge to the correct answer after many point samples have been taken. In this work, we study this problem under the framework of compressed sensing and reach the conclusion that if the signal is sparse in a transform domain, we can evaluate the integral accurately using a small set of point samples without requiring the lengthy iterations of Monte Carlo approaches. We demonstrate the usefulness of our framework by proposing novel algorithms to address two problems in computer graphics: image antialiasing and motion blur. We show that we can use our framework to generate good results with fewer samples than is possible with traditional approaches. In rendering applications, we are often faced with the problem of computing the integral of an unknown function. Typical approaches used to estimate these integrals are often based on Monte Carlo methods that slowly converge to the correct answer after many point samples have been taken. In this work, we study this problem under the framework of compressed sensing and reach the conclusion that if the signal is sparse in a transform domain, we can evaluate the integral accurately using a small set of point samples without requiring the lengthy iterations of Monte Carlo approaches. We demonstrate the usefulness of our framework by proposing novel algorithms to address two problems in computer graphics: image antialiasing and motion blur. We show that we can use our framework to generate good results with fewer samples than is possible with traditional approaches.

Category:

Education

Tags:

• compressive rendering
• agl
• unm
• advanced graphics lab
• university of new mexico
• graphics
• signal integration
• rendering
• research
• montecarlo
• antialising
• motion blur
• video volume

[Kram1032]

I'd have a few questions:

First of all, did you find faster CS methods that reduce the highdimensionality problems?

Second, is this possible as a kind of online-learning effect? E.g. after processing, without having to do a maority of the calculations again, add more samples?

And finally, I found papers suggesting that the ideal fit for given data is given by the Uncertain Component Analysis.

Could one use that to find the most important missing sample at a given time?

[1ucasvb]

Amazing results!