Mitchel, TW;
Brown, B;
Koller, D;
Weyrich, T;
Rusinkiewicz, S;
Kazhdan, M;
(2020)
Efficient Spatially Adaptive Convolution and Correlation.
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Abstract
Fast methods for convolution and correlation underlie a variety of applications in computer vision and graphics, including efficient filtering, analysis, and simulation. However, standard convolution and correlation are inherently limited to fixed filters: spatial adaptation is impossible without sacrificing efficient computation. In early work, Freeman and Adelson (1991) have shown how steerable filters can address this limitation, providing a way for rotating the filter as it is passed over the signal. In this work, we provide a general, representation-theoretic, framework that allows for spatially varying linear transformations to be applied to the filter. This framework allows for efficient implementation of extended convolution and correlation for transformation groups such as rotation (in 2D and 3D) and scale, and provides a new interpretation for previous methods including steerable filters and the generalized Hough transform. We present applications to pattern matching, image feature description, vector field visualization, and adaptive image filtering.
| Type: | Working / discussion paper |
|---|---|
| Title: | Efficient Spatially Adaptive Convolution and Correlation |
| Open access status: | An open access version is available from UCL Discovery |
| Publisher version: | https://doi.org/10.48550/arXiv.2006.13188 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10102686 |
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