Performing High-Dimensional Filtering in Low-Dimensional Spaces

Abstract

High-dimensional filtering is a key component for many graphics, image, and video processing applications. Edge-preserving filters (an important class of high-dimensional ones), for instance, are essential for tasks like global-illumination filtering, tone mapping, denoising, detail enhancement, and non-photorealistic effects, among many others. Edge-preserving filtering can be implemented as a convolution with a spatially-varying kernel in image space, or with a spatially-invariant kernel in high-dimensional space. Performing the operation either way is computationally expensive, preventing its use in interactive and real-time scenarios. The talk will present two recent techniques we have developed for efficiently performing edgeaware filtering. The first one is based on a domain transform that allows highdimensional geodesic filtering to be performed in linear time as a sequence of 1-D filtering steps using a spatially-invariant kernel. The second technique works by sampling and filtering the input signal using a set of 2-D manifolds adapted to the original data. Its cost is linear in the number of pixels and in the dimensionality of the space in which the filter operates. These techniques are significantly faster than previous approaches, supporting high-dimensional filtering of images, videos, and global illumination effects in real time. In the talk, I will present several examples illustrating their use in graphics, image, and video processing applications.