Selection of Optimal Stopping Time for Nonlinear Difusion Filtering

Mrázek, Pavel

doi:10.1007/3-540-47778-0_26

Cited by 69 publications

(110 citation statements)

References 6 publications

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“…Image processing and computer vision algorithms utilizing diffusion equations require estimating stopping time [60]; this is called the termination problem [56]. Reaction-diffusion algorithms with a nonlinear reaction such as the FitzHugh-Nagumo type do not require solving the termination problem, if they can spend sufficient duration of time for their processing, as shown in Figs.…”

Section: Discussionmentioning

confidence: 99%

Stereo Algorithm with Anisotropic Reaction-Diffusion Systems

Nomura¹,

Okada²,

Miike³

et al. 2012

Current Advancements in Stereo Vision

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Section: Discussionmentioning

confidence: 99%

Stereo Algorithm with Anisotropic Reaction-Diffusion Systems

Nomura¹,

Okada²,

Miike³

et al. 2012

Current Advancements in Stereo Vision

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“…The magnitude values of det H (x,y,t) L have been stretched by the monotone function φ(z) = (sign z) √ |z| (image size: 320 × 172 pixels of original 320 × 240 pixels; frame 90 of 226 frames at 25 frames/s) human-computer interaction, biometrics and robotics. Alternative approaches for spatial scale selection in other problem domains have also been proposed [7,8,10,19,28,29,31,[38][39][40]54,55,66,82,83,85,91,92,105,109,115].…”

Section: The Determinant Of the Spatial Hessian Of The Second-order Tmentioning

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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“…In the case of a small variance θ 0 of the additive noise, Eq. (5) reduces to 'decorrelation' between the estimated noise and the model output' [8]. Fig.…”

Section: Evidence-maximizing Stoppingmentioning

confidence: 99%

Optimal Stopping and Constraints for Diffusion Models of Signals with Discontinuities

Girdziušas

Laaksonen

2005

Machine Learning: ECML 2005

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Abstract. Gaussian process regression models can be utilized in recovery of discontinuous signals. Their computational complexity is linear in the number of observations if applied with the covariance functions of nonlinear diffusion. However, such processes often result in hard-tocontrol jumps of the signal value. Synthetic examples presented in this work indicate that Bayesian evidence-maximizing stopping and knowledge whether signal values are discrete help to outperform the steady state solutions of nonlinear diffusion filtering.

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Selection of Optimal Stopping Time for Nonlinear Difusion Filtering

Cited by 69 publications

References 6 publications

Stereo Algorithm with Anisotropic Reaction-Diffusion Systems

Stereo Algorithm with Anisotropic Reaction-Diffusion Systems

Spatio-Temporal Scale Selection in Video Data

Optimal Stopping and Constraints for Diffusion Models of Signals with Discontinuities

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