A Multigrid Platform for Real-Time Motion Computation with Discontinuity-Preserving Variational Methods

Abstract Variational methods are among the most accurate techniques for estimating the optic flow. They yield dense flow fields and can be designed such that they preserve discontinuities, estimate large displacements correctly and perform well under noise and varying illumination. However, such ada...
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Autor*in:	Bruhn, Andrés [verfasserIn] Weickert, Joachim Kohlberger, Timo Schnörr, Christoph

Format:	Artikel
Sprache:	Englisch

Erschienen:	2006

Schlagwörter:	partial differential equations variational methods optic flow multigrid methods

Anmerkung:	© Springer Science + Business Media, LLC 2006

Übergeordnetes Werk:	Enthalten in: International journal of computer vision - Kluwer Academic Publishers, 1987, 70(2006), 3 vom: Dez., Seite 257-277
Übergeordnetes Werk:	volume:70 ; year:2006 ; number:3 ; month:12 ; pages:257-277

Links:	Volltext

DOI / URN:	10.1007/s11263-006-6616-7

Katalog-ID:	OLC2057741516

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520			\|a Abstract Variational methods are among the most accurate techniques for estimating the optic flow. They yield dense flow fields and can be designed such that they preserve discontinuities, estimate large displacements correctly and perform well under noise and varying illumination. However, such adaptations render the minimisation of the underlying energy functional very expensive in terms of computational costs: Typically one or more large linear or nonlinear equation systems have to be solved in order to obtain the desired solution. Consequently, variational methods are considered to be too slow for real-time performance. In our paper we address this problem in two ways: (i) We present a numerical framework based on bidirectional multigrid methods for accelerating a broad class of variational optic flow methods with different constancy and smoothness assumptions. Thereby, our work focuses particularly on regularisation strategies that preserve discontinuities. (ii) We show by the examples of five classical and two recent variational techniques that real-time performance is possible in all cases—even for very complex optic flow models that offer high accuracy. Experiments show that frame rates up to 63 dense flow fields per second for image sequences of size 160 × 120 can be achieved on a standard PC. Compared to classical iterative methods this constitutes a speedup of two to four orders of magnitude.
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allfields	10.1007/s11263-006-6616-7 doi (DE-627)OLC2057741516 (DE-He213)s11263-006-6616-7-p DE-627 ger DE-627 rakwb eng 004 VZ Bruhn, Andrés verfasserin aut A Multigrid Platform for Real-Time Motion Computation with Discontinuity-Preserving Variational Methods 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science + Business Media, LLC 2006 Abstract Variational methods are among the most accurate techniques for estimating the optic flow. They yield dense flow fields and can be designed such that they preserve discontinuities, estimate large displacements correctly and perform well under noise and varying illumination. However, such adaptations render the minimisation of the underlying energy functional very expensive in terms of computational costs: Typically one or more large linear or nonlinear equation systems have to be solved in order to obtain the desired solution. Consequently, variational methods are considered to be too slow for real-time performance. In our paper we address this problem in two ways: (i) We present a numerical framework based on bidirectional multigrid methods for accelerating a broad class of variational optic flow methods with different constancy and smoothness assumptions. Thereby, our work focuses particularly on regularisation strategies that preserve discontinuities. (ii) We show by the examples of five classical and two recent variational techniques that real-time performance is possible in all cases—even for very complex optic flow models that offer high accuracy. Experiments show that frame rates up to 63 dense flow fields per second for image sequences of size 160 × 120 can be achieved on a standard PC. Compared to classical iterative methods this constitutes a speedup of two to four orders of magnitude. partial differential equations variational methods optic flow multigrid methods Weickert, Joachim aut Kohlberger, Timo aut Schnörr, Christoph aut Enthalten in International journal of computer vision Kluwer Academic Publishers, 1987 70(2006), 3 vom: Dez., Seite 257-277 (DE-627)129354252 (DE-600)155895-X (DE-576)018081428 0920-5691 nnns volume:70 year:2006 number:3 month:12 pages:257-277 https://doi.org/10.1007/s11263-006-6616-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_70 GBV_ILN_100 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2012 GBV_ILN_2244 GBV_ILN_4046 GBV_ILN_4116 GBV_ILN_4700 AR 70 2006 3 12 257-277
spelling	10.1007/s11263-006-6616-7 doi (DE-627)OLC2057741516 (DE-He213)s11263-006-6616-7-p DE-627 ger DE-627 rakwb eng 004 VZ Bruhn, Andrés verfasserin aut A Multigrid Platform for Real-Time Motion Computation with Discontinuity-Preserving Variational Methods 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science + Business Media, LLC 2006 Abstract Variational methods are among the most accurate techniques for estimating the optic flow. They yield dense flow fields and can be designed such that they preserve discontinuities, estimate large displacements correctly and perform well under noise and varying illumination. However, such adaptations render the minimisation of the underlying energy functional very expensive in terms of computational costs: Typically one or more large linear or nonlinear equation systems have to be solved in order to obtain the desired solution. Consequently, variational methods are considered to be too slow for real-time performance. In our paper we address this problem in two ways: (i) We present a numerical framework based on bidirectional multigrid methods for accelerating a broad class of variational optic flow methods with different constancy and smoothness assumptions. Thereby, our work focuses particularly on regularisation strategies that preserve discontinuities. (ii) We show by the examples of five classical and two recent variational techniques that real-time performance is possible in all cases—even for very complex optic flow models that offer high accuracy. Experiments show that frame rates up to 63 dense flow fields per second for image sequences of size 160 × 120 can be achieved on a standard PC. Compared to classical iterative methods this constitutes a speedup of two to four orders of magnitude. partial differential equations variational methods optic flow multigrid methods Weickert, Joachim aut Kohlberger, Timo aut Schnörr, Christoph aut Enthalten in International journal of computer vision Kluwer Academic Publishers, 1987 70(2006), 3 vom: Dez., Seite 257-277 (DE-627)129354252 (DE-600)155895-X (DE-576)018081428 0920-5691 nnns volume:70 year:2006 number:3 month:12 pages:257-277 https://doi.org/10.1007/s11263-006-6616-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_70 GBV_ILN_100 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2012 GBV_ILN_2244 GBV_ILN_4046 GBV_ILN_4116 GBV_ILN_4700 AR 70 2006 3 12 257-277
allfields_unstemmed	10.1007/s11263-006-6616-7 doi (DE-627)OLC2057741516 (DE-He213)s11263-006-6616-7-p DE-627 ger DE-627 rakwb eng 004 VZ Bruhn, Andrés verfasserin aut A Multigrid Platform for Real-Time Motion Computation with Discontinuity-Preserving Variational Methods 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science + Business Media, LLC 2006 Abstract Variational methods are among the most accurate techniques for estimating the optic flow. They yield dense flow fields and can be designed such that they preserve discontinuities, estimate large displacements correctly and perform well under noise and varying illumination. However, such adaptations render the minimisation of the underlying energy functional very expensive in terms of computational costs: Typically one or more large linear or nonlinear equation systems have to be solved in order to obtain the desired solution. Consequently, variational methods are considered to be too slow for real-time performance. In our paper we address this problem in two ways: (i) We present a numerical framework based on bidirectional multigrid methods for accelerating a broad class of variational optic flow methods with different constancy and smoothness assumptions. Thereby, our work focuses particularly on regularisation strategies that preserve discontinuities. (ii) We show by the examples of five classical and two recent variational techniques that real-time performance is possible in all cases—even for very complex optic flow models that offer high accuracy. Experiments show that frame rates up to 63 dense flow fields per second for image sequences of size 160 × 120 can be achieved on a standard PC. Compared to classical iterative methods this constitutes a speedup of two to four orders of magnitude. partial differential equations variational methods optic flow multigrid methods Weickert, Joachim aut Kohlberger, Timo aut Schnörr, Christoph aut Enthalten in International journal of computer vision Kluwer Academic Publishers, 1987 70(2006), 3 vom: Dez., Seite 257-277 (DE-627)129354252 (DE-600)155895-X (DE-576)018081428 0920-5691 nnns volume:70 year:2006 number:3 month:12 pages:257-277 https://doi.org/10.1007/s11263-006-6616-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_70 GBV_ILN_100 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2012 GBV_ILN_2244 GBV_ILN_4046 GBV_ILN_4116 GBV_ILN_4700 AR 70 2006 3 12 257-277
allfieldsGer	10.1007/s11263-006-6616-7 doi (DE-627)OLC2057741516 (DE-He213)s11263-006-6616-7-p DE-627 ger DE-627 rakwb eng 004 VZ Bruhn, Andrés verfasserin aut A Multigrid Platform for Real-Time Motion Computation with Discontinuity-Preserving Variational Methods 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science + Business Media, LLC 2006 Abstract Variational methods are among the most accurate techniques for estimating the optic flow. They yield dense flow fields and can be designed such that they preserve discontinuities, estimate large displacements correctly and perform well under noise and varying illumination. However, such adaptations render the minimisation of the underlying energy functional very expensive in terms of computational costs: Typically one or more large linear or nonlinear equation systems have to be solved in order to obtain the desired solution. Consequently, variational methods are considered to be too slow for real-time performance. In our paper we address this problem in two ways: (i) We present a numerical framework based on bidirectional multigrid methods for accelerating a broad class of variational optic flow methods with different constancy and smoothness assumptions. Thereby, our work focuses particularly on regularisation strategies that preserve discontinuities. (ii) We show by the examples of five classical and two recent variational techniques that real-time performance is possible in all cases—even for very complex optic flow models that offer high accuracy. Experiments show that frame rates up to 63 dense flow fields per second for image sequences of size 160 × 120 can be achieved on a standard PC. Compared to classical iterative methods this constitutes a speedup of two to four orders of magnitude. partial differential equations variational methods optic flow multigrid methods Weickert, Joachim aut Kohlberger, Timo aut Schnörr, Christoph aut Enthalten in International journal of computer vision Kluwer Academic Publishers, 1987 70(2006), 3 vom: Dez., Seite 257-277 (DE-627)129354252 (DE-600)155895-X (DE-576)018081428 0920-5691 nnns volume:70 year:2006 number:3 month:12 pages:257-277 https://doi.org/10.1007/s11263-006-6616-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_70 GBV_ILN_100 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2012 GBV_ILN_2244 GBV_ILN_4046 GBV_ILN_4116 GBV_ILN_4700 AR 70 2006 3 12 257-277
allfieldsSound	10.1007/s11263-006-6616-7 doi (DE-627)OLC2057741516 (DE-He213)s11263-006-6616-7-p DE-627 ger DE-627 rakwb eng 004 VZ Bruhn, Andrés verfasserin aut A Multigrid Platform for Real-Time Motion Computation with Discontinuity-Preserving Variational Methods 2006 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science + Business Media, LLC 2006 Abstract Variational methods are among the most accurate techniques for estimating the optic flow. They yield dense flow fields and can be designed such that they preserve discontinuities, estimate large displacements correctly and perform well under noise and varying illumination. However, such adaptations render the minimisation of the underlying energy functional very expensive in terms of computational costs: Typically one or more large linear or nonlinear equation systems have to be solved in order to obtain the desired solution. Consequently, variational methods are considered to be too slow for real-time performance. In our paper we address this problem in two ways: (i) We present a numerical framework based on bidirectional multigrid methods for accelerating a broad class of variational optic flow methods with different constancy and smoothness assumptions. Thereby, our work focuses particularly on regularisation strategies that preserve discontinuities. (ii) We show by the examples of five classical and two recent variational techniques that real-time performance is possible in all cases—even for very complex optic flow models that offer high accuracy. Experiments show that frame rates up to 63 dense flow fields per second for image sequences of size 160 × 120 can be achieved on a standard PC. Compared to classical iterative methods this constitutes a speedup of two to four orders of magnitude. partial differential equations variational methods optic flow multigrid methods Weickert, Joachim aut Kohlberger, Timo aut Schnörr, Christoph aut Enthalten in International journal of computer vision Kluwer Academic Publishers, 1987 70(2006), 3 vom: Dez., Seite 257-277 (DE-627)129354252 (DE-600)155895-X (DE-576)018081428 0920-5691 nnns volume:70 year:2006 number:3 month:12 pages:257-277 https://doi.org/10.1007/s11263-006-6616-7 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_70 GBV_ILN_100 GBV_ILN_2004 GBV_ILN_2006 GBV_ILN_2012 GBV_ILN_2244 GBV_ILN_4046 GBV_ILN_4116 GBV_ILN_4700 AR 70 2006 3 12 257-277
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title_sort	a multigrid platform for real-time motion computation with discontinuity-preserving variational methods
title_auth	A Multigrid Platform for Real-Time Motion Computation with Discontinuity-Preserving Variational Methods
abstract	Abstract Variational methods are among the most accurate techniques for estimating the optic flow. They yield dense flow fields and can be designed such that they preserve discontinuities, estimate large displacements correctly and perform well under noise and varying illumination. However, such adaptations render the minimisation of the underlying energy functional very expensive in terms of computational costs: Typically one or more large linear or nonlinear equation systems have to be solved in order to obtain the desired solution. Consequently, variational methods are considered to be too slow for real-time performance. In our paper we address this problem in two ways: (i) We present a numerical framework based on bidirectional multigrid methods for accelerating a broad class of variational optic flow methods with different constancy and smoothness assumptions. Thereby, our work focuses particularly on regularisation strategies that preserve discontinuities. (ii) We show by the examples of five classical and two recent variational techniques that real-time performance is possible in all cases—even for very complex optic flow models that offer high accuracy. Experiments show that frame rates up to 63 dense flow fields per second for image sequences of size 160 × 120 can be achieved on a standard PC. Compared to classical iterative methods this constitutes a speedup of two to four orders of magnitude. © Springer Science + Business Media, LLC 2006
abstractGer	Abstract Variational methods are among the most accurate techniques for estimating the optic flow. They yield dense flow fields and can be designed such that they preserve discontinuities, estimate large displacements correctly and perform well under noise and varying illumination. However, such adaptations render the minimisation of the underlying energy functional very expensive in terms of computational costs: Typically one or more large linear or nonlinear equation systems have to be solved in order to obtain the desired solution. Consequently, variational methods are considered to be too slow for real-time performance. In our paper we address this problem in two ways: (i) We present a numerical framework based on bidirectional multigrid methods for accelerating a broad class of variational optic flow methods with different constancy and smoothness assumptions. Thereby, our work focuses particularly on regularisation strategies that preserve discontinuities. (ii) We show by the examples of five classical and two recent variational techniques that real-time performance is possible in all cases—even for very complex optic flow models that offer high accuracy. Experiments show that frame rates up to 63 dense flow fields per second for image sequences of size 160 × 120 can be achieved on a standard PC. Compared to classical iterative methods this constitutes a speedup of two to four orders of magnitude. © Springer Science + Business Media, LLC 2006
abstract_unstemmed	Abstract Variational methods are among the most accurate techniques for estimating the optic flow. They yield dense flow fields and can be designed such that they preserve discontinuities, estimate large displacements correctly and perform well under noise and varying illumination. However, such adaptations render the minimisation of the underlying energy functional very expensive in terms of computational costs: Typically one or more large linear or nonlinear equation systems have to be solved in order to obtain the desired solution. Consequently, variational methods are considered to be too slow for real-time performance. In our paper we address this problem in two ways: (i) We present a numerical framework based on bidirectional multigrid methods for accelerating a broad class of variational optic flow methods with different constancy and smoothness assumptions. Thereby, our work focuses particularly on regularisation strategies that preserve discontinuities. (ii) We show by the examples of five classical and two recent variational techniques that real-time performance is possible in all cases—even for very complex optic flow models that offer high accuracy. Experiments show that frame rates up to 63 dense flow fields per second for image sequences of size 160 × 120 can be achieved on a standard PC. Compared to classical iterative methods this constitutes a speedup of two to four orders of magnitude. © Springer Science + Business Media, LLC 2006
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container_issue	3
title_short	A Multigrid Platform for Real-Time Motion Computation with Discontinuity-Preserving Variational Methods
url	https://doi.org/10.1007/s11263-006-6616-7
remote_bool	false
author2	Weickert, Joachim Kohlberger, Timo Schnörr, Christoph
author2Str	Weickert, Joachim Kohlberger, Timo Schnörr, Christoph
ppnlink	129354252
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doi_str	10.1007/s11263-006-6616-7
up_date	2024-07-03T16:07:22.133Z
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