Adaptive manifolds for real-time high-dimensional filtering
Eduardo S. L. Gastal, Manuel M. Oliveira · ACM Transactions on Graphics · 2012
We present a technique for performing high-dimensional filtering of images and videos in real time. Our approach produces high-quality results and accelerates filtering by computing the filter's response at a reduced set of sampling points, and using these for interpolation at allNinput pixels. We show that for a proper choice of these sampling points, the total cost of the filtering operation is linear both inNand in the dimensiondof the space in which the filter operates. As such, ours is the first high-dimensional filter with such a complexity. We present formal derivations for the equations that define our filter, as well as for an algorithm to compute the sampling points. This provides a sound theoretical justification for our method and for its properties. The resulting filter is quite flexible, being capable of producing responses that approximate either standard Gaussian, bilateral, or non-local-means filters. Such flexibility also allows us to demonstrate the first hybrid Euclidean-geodesic filter that runs in a single pass. Our filter is faster and requires less memory than previous approaches, being able to process a 10-Megapixel full-color image at 50 fps on modern GPUs. We illustrate the effectiveness of our approach by performing a variety of tasks ranging from edge-aware color filtering in 5-D, noise reduction (using up to 147 dimensions), single-pass hybrid Euclidean-geodesic filtering, and detail enhancement, among others.