Determination of optical flow and its discontinuities using non-linear diffusion

Proesmans, Marc; Gool, Luc J. Van; Pauwels, Eric J.; Oosterlinck, André

doi:10.1007/bfb0028362

Cited by 123 publications

(108 citation statements)

References 7 publications

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“…Equations (18) and (19) become equalities if ▼ and ❍ are linear. In both cases, (18,19) lead to the following new system:…”

Section: Incremental Algorithmmentioning

confidence: 99%

“…If ▼ and ❍ are not linear, equations (20,21,24,25) only produce an approximated solution X b + δX due to the first order Taylor development described in (18) and (19). In this case, the incremental algorithm is applied iteratively until convergence.…”

Section: Incremental Algorithmmentioning

confidence: 99%

“…The advantage of equation (36) is that W can be estimated even for high velocity norms. Equation (37) is an approximation and only well suited for low velocity except if incremental algorithms [12,19] or scale-space methods [1] are considered. In this paper, we choose however to consider the optical flow constraint (37) in order to illustrate the tasks to be applied for going from an ill-posed Image Processing problem to a Data Assimilation system, compare it with state-of-the-art methods, and prove the advantage of Data Assimilation when processing noisy acquisitions including missing data.…”

Section: Application To Optical Flow Estimationmentioning

confidence: 99%

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Solving ill-posed Image Processing problems using Data Assimilation

Béréziat

Herlin

2010

Numer Algor

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Data Assimilation is a mathematical framework used in environmental sciences to improve forecasts performed by meteorological, oceanographic or air quality simulation models. It aims to solve an evolution equation, describing the temporal dynamics, and an observation equation, linking the state vector and observations. In this article we use this framework to study a class of ill-posed Image Processing problems, usually solved by spatial and temporal regularization techniques. An approach is proposed to convert an ill-posed Image Processing problem in terms of a Data Assimilation system, solved by a 4D-Var method. This is illustrated by the estimation of optical flow from a noisy image sequence, with the dynamic model ensuring the temporal regularity of the result. The innovation of the paper concerns first, the extensive description of the tasks to be achieved for going from an image processing problem to a data assimilation description; second, the theoretical analysis of the covariance matrices involved in the algorithm; and third a specific discretisation scheme ensuring the stability of computation for the application on optical flow estimation.

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“…Equations (18) and (19) become equalities if ▼ and ❍ are linear. In both cases, (18,19) lead to the following new system:…”

Section: Incremental Algorithmmentioning

confidence: 99%

Section: Incremental Algorithmmentioning

confidence: 99%

Section: Application To Optical Flow Estimationmentioning

confidence: 99%

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Solving ill-posed Image Processing problems using Data Assimilation

Béréziat

Herlin

2010

Numer Algor

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“…in surveillance) are often filmed with static cameras, whose quality has improved significantly in recent years, so frame differences correspond to actual motions. For more challenging cases where there is slight camera motion, panning, or an increased amount of camera noise, the illumination changes between pairs of frames can be approximated by flow estimates [24], [25] after motion compensation. For simplicity, we refer to either inter-frame illumination differences or optical flow measurements as "illumination changes", denoted as dI(x, y, t):…”

Section: Kurtosis-based Activity Areamentioning

confidence: 99%

Robust Temporal Activity Templates Using Higher Order Statistics

Briassouli

Kompatsiaris

2009

IEEE Trans. on Image Process.

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A robust, theoretically-founded approach for the extraction of temporal templates corresponding to areas of motion in video, is presented. Higher order statistics (kurtosis) are employed to extract Activity Areas, i.e. binary masks indicating which pixels in a video are active. The application of the kurtosis on illumination changes modeled as Gaussians and Mixture of Gaussians is shown to be sensitive to outliers for both models, thus correctly localizing active pixels. Activity Areas are compared to existing, difference-based temporal templates, known as Motion Energy Images, and the robustness of both categories of temporal templates to additive noise is analyzed theoretically. Experiments with numerous real videos with additive noise, both indoors and outdoors, are conducted to compare the robustness of the Activity Areas and Motion Energy Images, and their temporal extensions, the Activity History Areas and Motion History Images. As expected from the theoretical analysis, the kurtosis-based Activity Areas prove to be more robust than the difference-based templates. Challenging videos containing occlusions, varying backgrounds and shadows are also examined, and it is shown that the proposed approach outperforms the difference-based method for these cases as well, consistently providing reliable localization of activity under a wide range of difficult circumstances. The proposed approach provides good results at a very low computational cost, and without requiring prior knowledge about the scene, nor training of any kind.

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“…For this segmentation model, we use optical flow data at the motion layer. The flowfield is obtained via the algorithm proposed in [8], which provides smooth optic flow fields necessary for our MRF model. We then model each motion label by a Gaussian pdf which indicates a normally distributed noise around the mean flow.…”

Section: Motion Layermentioning

confidence: 99%

A Multi-Layer MRF Model for Video Object Segmentation

Kató

Pong

2006

Computer Vision – ACCV 2006

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Abstract.A novel video object segmentation method is proposed which aims at combining color and motion information. The model has a multilayer structure: Each feature has its own layer, called feature layer, where a classical Markov random field (MRF) image segmentation model is defined using only the corresponding feature. A special layer is assigned to the combined MRF model, called combined layer, which interacts with each feature layer and provides the segmentation based on the combination of different features. Unlike previous methods, our approach doesn't assume motion boundaries being part of spatial ones. Therefore a very important property of the proposed method is the ability to detect boundaries that are visible only in the motion feature as well as those visible only in the color one. The method is validated on synthetic and real video sequences.

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Determination of optical flow and its discontinuities using non-linear diffusion

Cited by 123 publications

References 7 publications

Solving ill-posed Image Processing problems using Data Assimilation

Solving ill-posed Image Processing problems using Data Assimilation

Robust Temporal Activity Templates Using Higher Order Statistics

A Multi-Layer MRF Model for Video Object Segmentation

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