Direct Estimation of Optical Flow and of Its Derivatives

Nagel, Hans-Hellmut

doi:10.1007/978-3-642-77840-7_8

Cited by 21 publications

(14 citation statements)

References 31 publications

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“…Numerous numerical algorithms on the optical ow estimation and its applications have been performed. They have clearly shown how the optical ow can be used to recover information about slant and tilt of surface elements, egomotion, shape information, time to collision, etc 31,32,30,34,33,29,28,38,50,24,37,49,27,9,40,41] Almost all these approaches use the classical brightness constancy assumption that relates the gradient of brightness to the components of the local ow to estimate. Because this problem is ill-posed, additional constraints are usually required.…”

Section: Introductionmentioning

confidence: 99%

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A Mathematical Study of the Relaxed Optical Flow Problem in the Space $BV (\Omega)$

Aubert¹,

Kornprobst²

1999

SIAM J. Math. Anal.

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This paper describes a variational approach for estimating a discontinuous optical ow from a sequence of images. De ned as the apparent motion of the image brightness pattern, the optical ow is very important in the computer vision community where its accurate estimation is strongly needed. After a fast overview of existing methods, we present a new variational method that we study in the space of Bounded Variations. We rst present an integral representation of the optical ow problem which appears to be not lower semicontinuous. The relaxed functional is then calculated. We conclude by challenging questions about the possible numerical analysis of the abstract results.

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Section: Introductionmentioning

confidence: 99%

“…Several ideas have been used : working with regions, curves, lines or points. There is also a wide range of methodologies : wavelets, Markov random elds, Fourier analysis and naturally partial di erential equations 29,28,38,50,24,37,49,27,18,40,41]. We refer the interested reader to two (mainly computational) general surveys :…”

Section: Introductionmentioning

confidence: 99%

A Mathematical Study of the Relaxed Optical Flow Problem in the Space $BV (\Omega)$

Aubert¹,

Kornprobst²

1999

SIAM J. Math. Anal.

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“…The first is the application of spatio-temporal filtering schemes [34,44,58,100,113]. The second is the use of improved motion models [10,19,23,42,77,100,111,116] such as the affine model. The fact that these two approaches are actually complementary to each other will become clear as we analyze their individual advantages and disadvantages.…”

Section: Introductionmentioning

confidence: 99%

A general motion model and spatio-temporal filters for 3-D motion interpretations

Liu

1995

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“…(5) with other ones discussed in the literature. In this context, however, it needs to be reiterated that different approaches to estimate OF often turn out to be in fact different ways to define OF [40] even if such differences in definition do not always result in significantly different OFestimates.…”

Section: -G=x;l[ Serves To ( 2 ? R ) 3 / 2~mentioning

confidence: 99%

“…Space limitations prevent a discussion of local approaches towards the estimation of first-order spatiotemporal derivatives of OF, for example [59,39,121, see [40] for a discussion. Non-local features are not likely to result in a densely populated OF-field and will not be treated here.…”

Section: -G=x;l[ Serves To ( 2 ? R ) 3 / 2~mentioning

confidence: 99%

Image sequence evaluation: 30 years and still going strong

Nagel¹

Proceedings 15th International Conference on Pattern Recognition. ICPR-2000

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Over the past thirty years, technical means to record, digitize, store, process, and present video image sequences have multiplied in capacity b y several orders of magnitude. This large quantitative improvement is about t o turn into a qualitative change regarding the research to be pursued within this area in the future. Whereas up to now a n exploratory type of approach has prevailed, the increasingly available technical means for image sequence evaluation facilitate the investigation of large amounts of data. This requires to build encompassing systems and to study their behavior which in t u r n is expected to stimulate theoretical developments: even small effects of a n assumption can be studied in detail within a system environment, thereby enabling stepwise improvements of theoretical approaches underlying the construction of system solutions. The followi n g discussion will emphasize fundamental experimental and theoretical advances rather than details of particular approaches. 149 0-7695-0750-6/00 $10.00 0 2000 IEEE

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Direct Estimation of Optical Flow and of Its Derivatives

Cited by 21 publications

References 31 publications

A Mathematical Study of the Relaxed Optical Flow Problem in the Space $BV (\Omega)$

A Mathematical Study of the Relaxed Optical Flow Problem in the Space $BV (\Omega)$

A general motion model and spatio-temporal filters for 3-D motion interpretations

Image sequence evaluation: 30 years and still going strong

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