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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2015
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1505.00412 |
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| _version_ | 1866909083155562496 |
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| author | Galiano, Gonzalo Velasco, Julián |
| author_facet | Galiano, Gonzalo Velasco, Julián |
| contents | We introduce an exact reformulation of a broad class of neighborhood filters, among which the bilateral filters, in terms of two functional rearrangements: the decreasing and the relative rearrangements.
Independently of the image spatial dimension (one-dimensional signal, image, volume of images, etc.), we reformulate these filters as integral operators defined in a one-dimensional space corresponding to the level sets measures.
We prove the equivalence between the usual pixel-based version and the rearranged version of the filter. When restricted to the discrete setting, our reformulation of bilateral filters extends previous results for the so-called fast bilateral filtering. We, in addition, prove that the solution of the discrete setting, understood as constant-wise interpolators, converges to the solution of the continuous setting.
Finally, we numerically illustrate computational aspects concerning quality approximation and execution time provided by the rearranged formulation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1505_00412 |
| institution | arXiv |
| publishDate | 2015 |
| record_format | arxiv |
| spellingShingle | On a fast bilateral filtering formulation using functional rearrangements Galiano, Gonzalo Velasco, Julián Computer Vision and Pattern Recognition 68U10 We introduce an exact reformulation of a broad class of neighborhood filters, among which the bilateral filters, in terms of two functional rearrangements: the decreasing and the relative rearrangements. Independently of the image spatial dimension (one-dimensional signal, image, volume of images, etc.), we reformulate these filters as integral operators defined in a one-dimensional space corresponding to the level sets measures. We prove the equivalence between the usual pixel-based version and the rearranged version of the filter. When restricted to the discrete setting, our reformulation of bilateral filters extends previous results for the so-called fast bilateral filtering. We, in addition, prove that the solution of the discrete setting, understood as constant-wise interpolators, converges to the solution of the continuous setting. Finally, we numerically illustrate computational aspects concerning quality approximation and execution time provided by the rearranged formulation. |
| title | On a fast bilateral filtering formulation using functional rearrangements |
| topic | Computer Vision and Pattern Recognition 68U10 |
| url | https://arxiv.org/abs/1505.00412 |