Recursive filters for optical flow

Fleet, David J.; Langley, Keith

doi:10.1109/34.368151

Cited by 105 publications

(61 citation statements)

References 17 publications

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“…Based on one-dimensional scale-space kernels, which guarantee non-creation of local extrema with increasing scales and respect the time direction as causal (Lindeberg 1990), (Lindeberg & Fagerström 1996) expressed a strictly time-recursive temporal scale-space model, in which temporal derivatives are computed from differences between temporal channels at different scales. A similar computation of temporal derivatives has been proposed by (Fleet & Langley 1995). The spatio-temporal scale-space model presented here has several qualitative similarities to these previously presented models when projected onto a pure temporal domain.…”

Section: Relations To Previous Workmentioning

confidence: 48%

“…Then, he applied Gaussian smoothing in the transformed domain, thus avoiding violations of temporal causality. Based on a classification of continuous and discrete scalespace kernels in (Lindeberg 1994), (Lindeberg & Fagerström 1996) presented another set of time-causal scale-space kernels based on cascaded recursive filters for discrete time and first-order integrators in the case of continuous time, with close relations to an earlier approach for estimating optical flow (Fleet & Langley 1995). Follow-up works based on Koenderinks logarithmic mapping of the time axis have then been presented by (Florack 1997 and (Lindeberg 2001).…”

Section: Smoothed -Warpingmentioning

confidence: 99%

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Linear spatio-temporal scale-space

Lindeberg

1997

Scale-Space Theory in Computer Vision

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This article shows how a linear scale-space formulation previously expressed for spatial domains extends to spatio-temporal data. Starting from the main assumptions that: (i) the scale-space should be generated by convolution with a semi-group of filter kernels and that (ii) local extrema must not be enhanced when the scale parameter increases, a complete taxonomy is given of the linear scale-space concepts that satisfy these conditions on spatial, temporal and spatio-temporal domains, including the cases with continuous as well as discrete data.Key aspects captured by this theory include that: (i) time-causal scale-space kernels must not extend into the future, (ii) filter shapes can be tuned from specific context information, permitting mechanisms such local shifting, shape adaptation and velocity adaptation, all expressed in terms of local diffusion operations.Receptive field profiles generated by the proposed theory show high qualitative similarities to receptive field profiles recorded from biological vision.£ Earlier versions of this manuscript have been presented at

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Section: Relations To Previous Workmentioning

confidence: 48%

Section: Smoothed -Warpingmentioning

confidence: 99%

Linear spatio-temporal scale-space

Lindeberg

1997

Scale-Space Theory in Computer Vision

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“…Gaussian 0.5 accuracy will be low due to increased noise levels. The recursive filter is known to be less accurate on synthetic image sequences than the Gaussian 1.5 filter [7]. Of interest is how accuracy effects on-board performance.…”

Section: Accuracymentioning

confidence: 99%

“…Docking comparisons examine performances when flow is not constant, but exhibiting increasing levels of divergence. The temporal filters for comparison are: Gaussian filtering with central differencing, Simoncelli's matched-pair derivative filters [15], and Fleet and Langley's recursive temporal filter [7]. These are applied with Lucas and Kanade's gradient-based optical flow method [9], chosen on the basis of strong performances in [11].…”

Section: Introductionmentioning

confidence: 99%

Comparison of Temporal Filters for Optical Flow Estimation in Continuous Mobile Robot Navigation

McCarthy

Barnes

2006

Springer Tracts in Advanced Robotics

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Abstract. We present our complete study involving comparisons of three spatio-temporal filters used in the estimation of optical flow for continuous mobile robot navigation. Previous comparisons of optical flow and associated techniques have compared performance in terms of accuracy and/or efficiency, and only in isolation. These comparisons are inadequate for addressing applicability to continuous, real-time operation as part of a robot control loop. In recent work [11], we presented a comparison of optical flow techniques for corridor navigation through two biologically inspired behaviours: corridor centring and visual odometry. In that study, flow was predominantly constant. In this paper we give new results from comparisons for flow-divergence based docking, where flow is non-constant. Results for traditionally used Gaussian filters indicate that long latencies significantly impede performance for real-time tasks in the control loop.

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“…For this domain, we can consider two basic use cases: For offline analysis of pre-recorded video, one may take the liberty of accessing the virtual future in relation to any pre-recorded time moment and make use of symmetric filtering over the temporal domain based on the non-causal Gaussian spatio-temporal scale-space theory [61,67,70]. For online analysis of real-time video streams on the other hand, the future cannot be accessed and we will base the analysis on a fully time-causal and time-recursive spatiotemporal scale-space concept for real-time image streams that only requires access to information from the present moment and a very compact buffer of what has occurred in the past [75] and which constitutes an extension of previous temporal scale-space and multi-scale models [23,27,45,81,110]. Specifically, for performing spatio-temporal feature detection in the latter time-causal scenario, we will build upon a recently developed theory for temporal scale selection in a time-causal scale-space representation [77] and extend that theory to spatio-temporal scale selection for features that are computed based on a time-causal spatio-temporal scalespace representation.…”

Section: Fig 4 the First-and Second-order Temporal Derivatives Of Thmentioning

confidence: 99%

Spatio-Temporal Scale Selection in Video Data

Lindeberg

2017

J Math Imaging Vis

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This work presents a theory and methodology for simultaneous detection of local spatial and temporal scales in video data. The underlying idea is that if we process video data by spatio-temporal receptive fields at multiple spatial and temporal scales, we would like to generate hypotheses about the spatial extent and the temporal duration of the underlying spatio-temporal image structures that gave rise to the feature responses. For two types of spatio-temporal scale-space representations, (i) a non-causal Gaussian spatio-temporal scale space for offline analysis of pre-recorded video sequences and (ii) a time-causal and timerecursive spatio-temporal scale space for online analysis of real-time video streams, we express sufficient conditions for spatio-temporal feature detectors in terms of spatio-temporal receptive fields to deliver scale-covariant and scale-invariant feature responses. We present an in-depth theoretical analysis of the scale selection properties of eight types of spatio-temporal interest point detectors in terms of either: (i)-(ii) the spatial Laplacian applied to the first-and secondorder temporal derivatives, (iii)-(iv) the determinant of the spatial Hessian applied to the first-and second-order temporal derivatives, (v) the determinant of the spatio-temporal Hessian matrix, (vi) the spatio-temporal Laplacian and (vii)-(viii) the first-and second-order temporal derivatives of the determinant of the spatial Hessian matrix. It is shown that seven of these spatio-temporal feature detectors allow for provable scale covariance and scale invariance. Then, we describe a time-causal and time-recursive algorithm for detecting sparse spatio-temporal interest points from video streams and show that it leads to intuitively reasonable results. An experimental quantification of the accuracy of the spatio-temporal scale estimates and the amount of temporal delay obtained from these spatio-temporal interest point detectors is given, showing that: (i) the spatial and temporal scale selection properties predicted by the continuous theory are well preserved in the discrete implementation and (ii) the spatial Laplacian or the determinant of the spatial Hessian applied to the first-and second-order temporal derivatives leads to much shorter temporal delays in a timecausal implementation compared to the determinant of the spatio-temporal Hessian or the first-and second-order temporal derivatives of the determinant of the spatial Hessian matrix.

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Recursive filters for optical flow

Cited by 105 publications

References 17 publications

Linear spatio-temporal scale-space

Linear spatio-temporal scale-space

Comparison of Temporal Filters for Optical Flow Estimation in Continuous Mobile Robot Navigation

Spatio-Temporal Scale Selection in Video Data

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