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Optimized Fourier Bilateral Filtering
We consider the problem of approximating a truncated Gaussian kernel using Fourier (trigonometric) functions. The computation-intensive bilateral filter can be expressed using fast convolutions by applying such an approximation to its range kernel, where the truncation in question is the dynamic ran...
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Published in: | IEEE signal processing letters 2018-10, Vol.25 (10), p.1555-1559 |
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description | We consider the problem of approximating a truncated Gaussian kernel using Fourier (trigonometric) functions. The computation-intensive bilateral filter can be expressed using fast convolutions by applying such an approximation to its range kernel, where the truncation in question is the dynamic range of the input image. The error from such an approximation depends on the period, the number of sinusoids, and the coefficient of each sinusoid. For a fixed period, we recently proposed a model for optimizing the coefficients using least squares fitting. Following the compressive bilateral filter (CBF), we demonstrate that the approximation can be improved by taking the period into account during the optimization. The accuracy of the resulting filtering is found to be at least as good as the CBF, but significantly better for certain cases. The proposed approximation can also be used for non-Gaussian kernels, and it comes with guarantees on the filtering accuracy. |
doi_str_mv | 10.1109/LSP.2018.2866949 |
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The computation-intensive bilateral filter can be expressed using fast convolutions by applying such an approximation to its range kernel, where the truncation in question is the dynamic range of the input image. The error from such an approximation depends on the period, the number of sinusoids, and the coefficient of each sinusoid. For a fixed period, we recently proposed a model for optimizing the coefficients using least squares fitting. Following the compressive bilateral filter (CBF), we demonstrate that the approximation can be improved by taking the period into account during the optimization. The accuracy of the resulting filtering is found to be at least as good as the CBF, but significantly better for certain cases. The proposed approximation can also be used for non-Gaussian kernels, and it comes with guarantees on the filtering accuracy.</description><identifier>ISSN: 1070-9908</identifier><identifier>EISSN: 1558-2361</identifier><identifier>DOI: 10.1109/LSP.2018.2866949</identifier><identifier>CODEN: ISPLEM</identifier><language>eng</language><publisher>New York: IEEE</publisher><subject>Accuracy ; Approximation ; Approximation algorithms ; Approximation error ; Bilateral filter ; fast approximation ; Filtration ; Fourier basis ; Fourier series ; Kernel ; Matlab ; Optimization</subject><ispartof>IEEE signal processing letters, 2018-10, Vol.25 (10), p.1555-1559</ispartof><rights>Copyright The Institute of Electrical and Electronics Engineers, Inc. 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The computation-intensive bilateral filter can be expressed using fast convolutions by applying such an approximation to its range kernel, where the truncation in question is the dynamic range of the input image. The error from such an approximation depends on the period, the number of sinusoids, and the coefficient of each sinusoid. For a fixed period, we recently proposed a model for optimizing the coefficients using least squares fitting. Following the compressive bilateral filter (CBF), we demonstrate that the approximation can be improved by taking the period into account during the optimization. The accuracy of the resulting filtering is found to be at least as good as the CBF, but significantly better for certain cases. The proposed approximation can also be used for non-Gaussian kernels, and it comes with guarantees on the filtering accuracy.</description><subject>Accuracy</subject><subject>Approximation</subject><subject>Approximation algorithms</subject><subject>Approximation error</subject><subject>Bilateral filter</subject><subject>fast approximation</subject><subject>Filtration</subject><subject>Fourier basis</subject><subject>Fourier series</subject><subject>Kernel</subject><subject>Matlab</subject><subject>Optimization</subject><issn>1070-9908</issn><issn>1558-2361</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNo9kEFLxDAQhYMouK7eBS8F8dg6kzRtctTFqlBYwb2Hpk0kS3e7Jt2D_npTunia9-C9meEj5BYhQwT5WH9-ZBRQZFQUhczlGVkg5yKlrMDzqKGEVEoQl-QqhC0ACBR8QR7Wh9Ht3K_pkmo4emd88uz6ZjS-6ZPK9VG4_dc1ubBNH8zNaS7JpnrZrN7Sev36vnqq05ZKHFNkneg6zRlaxNaWqKU1qIG2kjKq8xIbzTrbFrTVk7fRWJ5rkJZT6NiS3M9rD374Ppowqm38aR8vKopYYpHLoowpmFOtH0LwxqqDd7vG_ygENbFQkYWaWKgTi1i5myvOGPMfF3nOuZTsD_ngWaI</recordid><startdate>20181001</startdate><enddate>20181001</enddate><creator>Ghosh, Sanjay</creator><creator>Nair, Pravin</creator><creator>Chaudhury, Kunal N.</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. (IEEE)</general><scope>97E</scope><scope>RIA</scope><scope>RIE</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7SP</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><orcidid>https://orcid.org/0000-0002-0474-5072</orcidid><orcidid>https://orcid.org/0000-0002-8136-605X</orcidid><orcidid>https://orcid.org/0000-0001-6435-1051</orcidid></search><sort><creationdate>20181001</creationdate><title>Optimized Fourier Bilateral Filtering</title><author>Ghosh, Sanjay ; Nair, Pravin ; Chaudhury, Kunal N.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c291t-13d8ddb531f11cf71b9fe1b02c9232b471ab3dfc62cb32b4f3dff54b09f520d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Accuracy</topic><topic>Approximation</topic><topic>Approximation algorithms</topic><topic>Approximation error</topic><topic>Bilateral filter</topic><topic>fast approximation</topic><topic>Filtration</topic><topic>Fourier basis</topic><topic>Fourier series</topic><topic>Kernel</topic><topic>Matlab</topic><topic>Optimization</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ghosh, Sanjay</creatorcontrib><creatorcontrib>Nair, Pravin</creatorcontrib><creatorcontrib>Chaudhury, Kunal N.</creatorcontrib><collection>IEEE All-Society Periodicals Package (ASPP) 2005-present</collection><collection>IEEE All-Society Periodicals Package (ASPP) 1998–Present</collection><collection>IEEE Electronic Library (IEL)</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>IEEE signal processing letters</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Ghosh, Sanjay</au><au>Nair, Pravin</au><au>Chaudhury, Kunal N.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Optimized Fourier Bilateral Filtering</atitle><jtitle>IEEE signal processing letters</jtitle><stitle>LSP</stitle><date>2018-10-01</date><risdate>2018</risdate><volume>25</volume><issue>10</issue><spage>1555</spage><epage>1559</epage><pages>1555-1559</pages><issn>1070-9908</issn><eissn>1558-2361</eissn><coden>ISPLEM</coden><abstract>We consider the problem of approximating a truncated Gaussian kernel using Fourier (trigonometric) functions. 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subjects | Accuracy Approximation Approximation algorithms Approximation error Bilateral filter fast approximation Filtration Fourier basis Fourier series Kernel Matlab Optimization |
title | Optimized Fourier Bilateral Filtering |
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