Adaptive Manifolds for Real-Time High-Dimensional Filtering

Eduardo S. L. Gastal eslgastal@inf.ufrgs.br

and

Manuel M. Oliveira oliveira@inf.ufrgs.br

Instituto de Informática, UFRGS

ACM Transactions on Graphics.
Volume 31 (2012), Number 4, Proceedings of SIGGRAPH 2012, Article 33.

Contents

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 all N input pixels. We show that for a proper choice of these sampling points, the total cost of the filtering operation is linear both in N and in the dimension d of 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.

Paper

Full paper (18 MB, 13 pages)

ACM Copyright Notice: © ACM, 2012. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in ACM TOG, Vol. 31, 4, July 2012 — http://doi.acm.org/10.1145/2185520.2185529.

Source Code (NEW)

Adaptive-Manifold high-dimensional filter source code (3.1 MB) Version 1.0 for MATLAB

Video

Watch on YouTube

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Download WMV (33 MB)

Applications

Click here to view various examples illustrating some of the possible applications of our adaptive-manifold high-dimensional filter

Citation

Eduardo S. L. Gastal and Manuel M. Oliveira. "Adaptive Manifolds for Real-Time High-Dimensional Filtering". ACM Transactions on Graphics. Volume 31 (2012), Number 4, Proceedings of SIGGRAPH 2012, Article 33.

BibTeX

@article{GastalOliveira2012AdaptiveManifolds,
  author    = {Eduardo S. L. Gastal and Manuel M. Oliveira},
  title     = {Adaptive Manifolds for Real-Time High-Dimensional Filtering},
  journal   = {ACM TOG},
  volume    = {31},
  number    = {4},
  year      = {2012},
  pages     = {33:1--33:13},
  articleno = {33},
  note      = {Proceedings of SIGGRAPH 2012}
}
  

Keywords

Adaptive Manifolds, High-Dimensional Filtering, Euclidean filters, Bilateral filter, non-local-means filters, hybrid Euclidean-geodesic filters.

CNPq-Brazil fellowships and grants # 150550/2015-4, 158666/2010-0, 557814/2010-3, 200284/2009-6, 308936/2010-8, and 480485/2010-0.

Last updated: July 13, 2012.