Scale-Covariant and Scale-Invariant Gaussian Derivative Networks

Abstract This paper presents a hybrid approach between scale-space theory and deep learning, where a deep learning architecture is constructed by coupling parameterized scale-space operations in cascade. By sharing the learnt parameters between multiple scale channels, and by using the transformatio...
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Autor*in:	Lindeberg, Tony [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2021

Schlagwörter:	Scale covariance Scale invariance Scale generalisation Scale selection Gaussian derivative Scale space Deep learning

Anmerkung:	© The Author(s) 2021

Übergeordnetes Werk:	Enthalten in: Journal of mathematical imaging and vision - Dordrecht [u.a.] : Springer Science + Business Media B.V, 1992, 64(2021), 3 vom: 23. Dez., Seite 223-242
Übergeordnetes Werk:	volume:64 ; year:2021 ; number:3 ; day:23 ; month:12 ; pages:223-242

Links:	Volltext

DOI / URN:	10.1007/s10851-021-01057-9

Katalog-ID:	SPR046546782

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allfields	10.1007/s10851-021-01057-9 doi (DE-627)SPR046546782 (SPR)s10851-021-01057-9-e DE-627 ger DE-627 rakwb eng Lindeberg, Tony verfasserin (orcid)0000-0002-9081-2170 aut Scale-Covariant and Scale-Invariant Gaussian Derivative Networks 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2021 Abstract This paper presents a hybrid approach between scale-space theory and deep learning, where a deep learning architecture is constructed by coupling parameterized scale-space operations in cascade. By sharing the learnt parameters between multiple scale channels, and by using the transformation properties of the scale-space primitives under scaling transformations, the resulting network becomes provably scale covariant. By in addition performing max pooling over the multiple scale channels, or other permutation-invariant pooling over scales, a resulting network architecture for image classification also becomes provably scale invariant. We investigate the performance of such networks on the MNIST Large Scale dataset, which contains rescaled images from the original MNIST dataset over a factor of 4 concerning training data and over a factor of 16 concerning testing data. It is demonstrated that the resulting approach allows for scale generalization, enabling good performance for classifying patterns at scales not spanned by the training data. Scale covariance (dpeaa)DE-He213 Scale invariance (dpeaa)DE-He213 Scale generalisation (dpeaa)DE-He213 Scale selection (dpeaa)DE-He213 Gaussian derivative (dpeaa)DE-He213 Scale space (dpeaa)DE-He213 Deep learning (dpeaa)DE-He213 Enthalten in Journal of mathematical imaging and vision Dordrecht [u.a.] : Springer Science + Business Media B.V, 1992 64(2021), 3 vom: 23. Dez., Seite 223-242 (DE-627)271179465 (DE-600)1479363-5 1573-7683 nnns volume:64 year:2021 number:3 day:23 month:12 pages:223-242 https://dx.doi.org/10.1007/s10851-021-01057-9 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 64 2021 3 23 12 223-242
spelling	10.1007/s10851-021-01057-9 doi (DE-627)SPR046546782 (SPR)s10851-021-01057-9-e DE-627 ger DE-627 rakwb eng Lindeberg, Tony verfasserin (orcid)0000-0002-9081-2170 aut Scale-Covariant and Scale-Invariant Gaussian Derivative Networks 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2021 Abstract This paper presents a hybrid approach between scale-space theory and deep learning, where a deep learning architecture is constructed by coupling parameterized scale-space operations in cascade. By sharing the learnt parameters between multiple scale channels, and by using the transformation properties of the scale-space primitives under scaling transformations, the resulting network becomes provably scale covariant. By in addition performing max pooling over the multiple scale channels, or other permutation-invariant pooling over scales, a resulting network architecture for image classification also becomes provably scale invariant. We investigate the performance of such networks on the MNIST Large Scale dataset, which contains rescaled images from the original MNIST dataset over a factor of 4 concerning training data and over a factor of 16 concerning testing data. It is demonstrated that the resulting approach allows for scale generalization, enabling good performance for classifying patterns at scales not spanned by the training data. Scale covariance (dpeaa)DE-He213 Scale invariance (dpeaa)DE-He213 Scale generalisation (dpeaa)DE-He213 Scale selection (dpeaa)DE-He213 Gaussian derivative (dpeaa)DE-He213 Scale space (dpeaa)DE-He213 Deep learning (dpeaa)DE-He213 Enthalten in Journal of mathematical imaging and vision Dordrecht [u.a.] : Springer Science + Business Media B.V, 1992 64(2021), 3 vom: 23. Dez., Seite 223-242 (DE-627)271179465 (DE-600)1479363-5 1573-7683 nnns volume:64 year:2021 number:3 day:23 month:12 pages:223-242 https://dx.doi.org/10.1007/s10851-021-01057-9 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 64 2021 3 23 12 223-242
allfields_unstemmed	10.1007/s10851-021-01057-9 doi (DE-627)SPR046546782 (SPR)s10851-021-01057-9-e DE-627 ger DE-627 rakwb eng Lindeberg, Tony verfasserin (orcid)0000-0002-9081-2170 aut Scale-Covariant and Scale-Invariant Gaussian Derivative Networks 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2021 Abstract This paper presents a hybrid approach between scale-space theory and deep learning, where a deep learning architecture is constructed by coupling parameterized scale-space operations in cascade. By sharing the learnt parameters between multiple scale channels, and by using the transformation properties of the scale-space primitives under scaling transformations, the resulting network becomes provably scale covariant. By in addition performing max pooling over the multiple scale channels, or other permutation-invariant pooling over scales, a resulting network architecture for image classification also becomes provably scale invariant. We investigate the performance of such networks on the MNIST Large Scale dataset, which contains rescaled images from the original MNIST dataset over a factor of 4 concerning training data and over a factor of 16 concerning testing data. It is demonstrated that the resulting approach allows for scale generalization, enabling good performance for classifying patterns at scales not spanned by the training data. Scale covariance (dpeaa)DE-He213 Scale invariance (dpeaa)DE-He213 Scale generalisation (dpeaa)DE-He213 Scale selection (dpeaa)DE-He213 Gaussian derivative (dpeaa)DE-He213 Scale space (dpeaa)DE-He213 Deep learning (dpeaa)DE-He213 Enthalten in Journal of mathematical imaging and vision Dordrecht [u.a.] : Springer Science + Business Media B.V, 1992 64(2021), 3 vom: 23. Dez., Seite 223-242 (DE-627)271179465 (DE-600)1479363-5 1573-7683 nnns volume:64 year:2021 number:3 day:23 month:12 pages:223-242 https://dx.doi.org/10.1007/s10851-021-01057-9 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 64 2021 3 23 12 223-242
allfieldsGer	10.1007/s10851-021-01057-9 doi (DE-627)SPR046546782 (SPR)s10851-021-01057-9-e DE-627 ger DE-627 rakwb eng Lindeberg, Tony verfasserin (orcid)0000-0002-9081-2170 aut Scale-Covariant and Scale-Invariant Gaussian Derivative Networks 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2021 Abstract This paper presents a hybrid approach between scale-space theory and deep learning, where a deep learning architecture is constructed by coupling parameterized scale-space operations in cascade. By sharing the learnt parameters between multiple scale channels, and by using the transformation properties of the scale-space primitives under scaling transformations, the resulting network becomes provably scale covariant. By in addition performing max pooling over the multiple scale channels, or other permutation-invariant pooling over scales, a resulting network architecture for image classification also becomes provably scale invariant. We investigate the performance of such networks on the MNIST Large Scale dataset, which contains rescaled images from the original MNIST dataset over a factor of 4 concerning training data and over a factor of 16 concerning testing data. It is demonstrated that the resulting approach allows for scale generalization, enabling good performance for classifying patterns at scales not spanned by the training data. Scale covariance (dpeaa)DE-He213 Scale invariance (dpeaa)DE-He213 Scale generalisation (dpeaa)DE-He213 Scale selection (dpeaa)DE-He213 Gaussian derivative (dpeaa)DE-He213 Scale space (dpeaa)DE-He213 Deep learning (dpeaa)DE-He213 Enthalten in Journal of mathematical imaging and vision Dordrecht [u.a.] : Springer Science + Business Media B.V, 1992 64(2021), 3 vom: 23. Dez., Seite 223-242 (DE-627)271179465 (DE-600)1479363-5 1573-7683 nnns volume:64 year:2021 number:3 day:23 month:12 pages:223-242 https://dx.doi.org/10.1007/s10851-021-01057-9 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 64 2021 3 23 12 223-242
allfieldsSound	10.1007/s10851-021-01057-9 doi (DE-627)SPR046546782 (SPR)s10851-021-01057-9-e DE-627 ger DE-627 rakwb eng Lindeberg, Tony verfasserin (orcid)0000-0002-9081-2170 aut Scale-Covariant and Scale-Invariant Gaussian Derivative Networks 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) 2021 Abstract This paper presents a hybrid approach between scale-space theory and deep learning, where a deep learning architecture is constructed by coupling parameterized scale-space operations in cascade. By sharing the learnt parameters between multiple scale channels, and by using the transformation properties of the scale-space primitives under scaling transformations, the resulting network becomes provably scale covariant. By in addition performing max pooling over the multiple scale channels, or other permutation-invariant pooling over scales, a resulting network architecture for image classification also becomes provably scale invariant. We investigate the performance of such networks on the MNIST Large Scale dataset, which contains rescaled images from the original MNIST dataset over a factor of 4 concerning training data and over a factor of 16 concerning testing data. It is demonstrated that the resulting approach allows for scale generalization, enabling good performance for classifying patterns at scales not spanned by the training data. Scale covariance (dpeaa)DE-He213 Scale invariance (dpeaa)DE-He213 Scale generalisation (dpeaa)DE-He213 Scale selection (dpeaa)DE-He213 Gaussian derivative (dpeaa)DE-He213 Scale space (dpeaa)DE-He213 Deep learning (dpeaa)DE-He213 Enthalten in Journal of mathematical imaging and vision Dordrecht [u.a.] : Springer Science + Business Media B.V, 1992 64(2021), 3 vom: 23. Dez., Seite 223-242 (DE-627)271179465 (DE-600)1479363-5 1573-7683 nnns volume:64 year:2021 number:3 day:23 month:12 pages:223-242 https://dx.doi.org/10.1007/s10851-021-01057-9 kostenfrei Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 64 2021 3 23 12 223-242
language	English
source	Enthalten in Journal of mathematical imaging and vision 64(2021), 3 vom: 23. Dez., Seite 223-242 volume:64 year:2021 number:3 day:23 month:12 pages:223-242
sourceStr	Enthalten in Journal of mathematical imaging and vision 64(2021), 3 vom: 23. Dez., Seite 223-242 volume:64 year:2021 number:3 day:23 month:12 pages:223-242
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Scale covariance Scale invariance Scale generalisation Scale selection Gaussian derivative Scale space Deep learning
isfreeaccess_bool	true
container_title	Journal of mathematical imaging and vision
authorswithroles_txt_mv	Lindeberg, Tony @@aut@@
publishDateDaySort_date	2021-12-23T00:00:00Z
hierarchy_top_id	271179465
id	SPR046546782
language_de	englisch
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author	Lindeberg, Tony
spellingShingle	Lindeberg, Tony misc Scale covariance misc Scale invariance misc Scale generalisation misc Scale selection misc Gaussian derivative misc Scale space misc Deep learning Scale-Covariant and Scale-Invariant Gaussian Derivative Networks
authorStr	Lindeberg, Tony
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topic_title	Scale-Covariant and Scale-Invariant Gaussian Derivative Networks Scale covariance (dpeaa)DE-He213 Scale invariance (dpeaa)DE-He213 Scale generalisation (dpeaa)DE-He213 Scale selection (dpeaa)DE-He213 Gaussian derivative (dpeaa)DE-He213 Scale space (dpeaa)DE-He213 Deep learning (dpeaa)DE-He213
topic	misc Scale covariance misc Scale invariance misc Scale generalisation misc Scale selection misc Gaussian derivative misc Scale space misc Deep learning
topic_unstemmed	misc Scale covariance misc Scale invariance misc Scale generalisation misc Scale selection misc Gaussian derivative misc Scale space misc Deep learning
topic_browse	misc Scale covariance misc Scale invariance misc Scale generalisation misc Scale selection misc Gaussian derivative misc Scale space misc Deep learning
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title	Scale-Covariant and Scale-Invariant Gaussian Derivative Networks
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title_full	Scale-Covariant and Scale-Invariant Gaussian Derivative Networks
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title_sort	scale-covariant and scale-invariant gaussian derivative networks
title_auth	Scale-Covariant and Scale-Invariant Gaussian Derivative Networks
abstract	Abstract This paper presents a hybrid approach between scale-space theory and deep learning, where a deep learning architecture is constructed by coupling parameterized scale-space operations in cascade. By sharing the learnt parameters between multiple scale channels, and by using the transformation properties of the scale-space primitives under scaling transformations, the resulting network becomes provably scale covariant. By in addition performing max pooling over the multiple scale channels, or other permutation-invariant pooling over scales, a resulting network architecture for image classification also becomes provably scale invariant. We investigate the performance of such networks on the MNIST Large Scale dataset, which contains rescaled images from the original MNIST dataset over a factor of 4 concerning training data and over a factor of 16 concerning testing data. It is demonstrated that the resulting approach allows for scale generalization, enabling good performance for classifying patterns at scales not spanned by the training data. © The Author(s) 2021
abstractGer	Abstract This paper presents a hybrid approach between scale-space theory and deep learning, where a deep learning architecture is constructed by coupling parameterized scale-space operations in cascade. By sharing the learnt parameters between multiple scale channels, and by using the transformation properties of the scale-space primitives under scaling transformations, the resulting network becomes provably scale covariant. By in addition performing max pooling over the multiple scale channels, or other permutation-invariant pooling over scales, a resulting network architecture for image classification also becomes provably scale invariant. We investigate the performance of such networks on the MNIST Large Scale dataset, which contains rescaled images from the original MNIST dataset over a factor of 4 concerning training data and over a factor of 16 concerning testing data. It is demonstrated that the resulting approach allows for scale generalization, enabling good performance for classifying patterns at scales not spanned by the training data. © The Author(s) 2021
abstract_unstemmed	Abstract This paper presents a hybrid approach between scale-space theory and deep learning, where a deep learning architecture is constructed by coupling parameterized scale-space operations in cascade. By sharing the learnt parameters between multiple scale channels, and by using the transformation properties of the scale-space primitives under scaling transformations, the resulting network becomes provably scale covariant. By in addition performing max pooling over the multiple scale channels, or other permutation-invariant pooling over scales, a resulting network architecture for image classification also becomes provably scale invariant. We investigate the performance of such networks on the MNIST Large Scale dataset, which contains rescaled images from the original MNIST dataset over a factor of 4 concerning training data and over a factor of 16 concerning testing data. It is demonstrated that the resulting approach allows for scale generalization, enabling good performance for classifying patterns at scales not spanned by the training data. © The Author(s) 2021
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title_short	Scale-Covariant and Scale-Invariant Gaussian Derivative Networks
url	https://dx.doi.org/10.1007/s10851-021-01057-9
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up_date	2024-07-03T23:10:59.441Z
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fullrecord_marcxml	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR046546782</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230507135433.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">220322s2021 xx \|\|\|\|\|o 00\| \|\|eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s10851-021-01057-9</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR046546782</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s10851-021-01057-9-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Lindeberg, Tony</subfield><subfield code="e">verfasserin</subfield><subfield code="0">(orcid)0000-0002-9081-2170</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Scale-Covariant and Scale-Invariant Gaussian Derivative Networks</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2021</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© The Author(s) 2021</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract This paper presents a hybrid approach between scale-space theory and deep learning, where a deep learning architecture is constructed by coupling parameterized scale-space operations in cascade. By sharing the learnt parameters between multiple scale channels, and by using the transformation properties of the scale-space primitives under scaling transformations, the resulting network becomes provably scale covariant. By in addition performing max pooling over the multiple scale channels, or other permutation-invariant pooling over scales, a resulting network architecture for image classification also becomes provably scale invariant. We investigate the performance of such networks on the MNIST Large Scale dataset, which contains rescaled images from the original MNIST dataset over a factor of 4 concerning training data and over a factor of 16 concerning testing data. It is demonstrated that the resulting approach allows for scale generalization, enabling good performance for classifying patterns at scales not spanned by the training data.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Scale covariance</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Scale invariance</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Scale generalisation</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Scale selection</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Gaussian derivative</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Scale space</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Deep learning</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Journal of mathematical imaging and vision</subfield><subfield code="d">Dordrecht [u.a.] : Springer Science + Business Media B.V, 1992</subfield><subfield code="g">64(2021), 3 vom: 23. Dez., Seite 223-242</subfield><subfield code="w">(DE-627)271179465</subfield><subfield code="w">(DE-600)1479363-5</subfield><subfield code="x">1573-7683</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:64</subfield><subfield code="g">year:2021</subfield><subfield code="g">number:3</subfield><subfield code="g">day:23</subfield><subfield code="g">month:12</subfield><subfield code="g">pages:223-242</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">https://dx.doi.org/10.1007/s10851-021-01057-9</subfield><subfield code="z">kostenfrei</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_SPRINGER</subfield></datafield><datafield tag="912" 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