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Multidimensional directional steerable filters — Theory and application to 3D flow estimation.

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Title: Multidimensional directional steerable filters — Theory and application to 3D flow estimation.
Authors: Alexiadis, Dimitrios S.1 dalexiad@iti.gr, Mitianoudis, Nikolaos1, Stathaki, Tania2
Source: Image & Vision Computing. Mar2018, Vol. 71, p38-67. 30p.
Subjects: Probability theory, Relevance logic, Mathematical analysis, Estimation theory, Efficient market theory
Abstract: In this paper, a thorough theoretical analysis on the construction of multi-dimensional directional steerable filters is given. Steerable filters have been constructed for up to three dimensions. We extend the relevant theory to multiple dimensions and construct multi-dimensional steerable filters, as well as quadrature pairs of such filters. Formulating the multi-dimensional motion estimation problem in the spatiotemporal frequency domain, it is shown that motion manifests itself as energy concentration along “motion hyper-planes” in that domain. Subsequently, using the constructed multi-dimensional filters, we formulate the “hyper-donut” mechanism, i.e. a mechanism to efficiently “measure” the “motion energy” on a “motion hyper-plane”. On top of that, rigorous mathematical analysis on the use of the constructed filters in the dense flow estimation task is given. Based on the theoretical developments, a steerable filter-based algorithm is formulated, in its simplest possible form, for estimating 3D flow in sequences of volumetric or point-cloud data. Experimental results on simulated and real-world data verify the validity of our arguments and the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]
Copyright of Image & Vision Computing is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
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  Data: In this paper, a thorough theoretical analysis on the construction of multi-dimensional directional steerable filters is given. Steerable filters have been constructed for up to three dimensions. We extend the relevant theory to multiple dimensions and construct multi-dimensional steerable filters, as well as quadrature pairs of such filters. Formulating the multi-dimensional motion estimation problem in the spatiotemporal frequency domain, it is shown that motion manifests itself as energy concentration along “motion hyper-planes” in that domain. Subsequently, using the constructed multi-dimensional filters, we formulate the “hyper-donut” mechanism, i.e. a mechanism to efficiently “measure” the “motion energy” on a “motion hyper-plane”. On top of that, rigorous mathematical analysis on the use of the constructed filters in the dense flow estimation task is given. Based on the theoretical developments, a steerable filter-based algorithm is formulated, in its simplest possible form, for estimating 3D flow in sequences of volumetric or point-cloud data. Experimental results on simulated and real-world data verify the validity of our arguments and the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Image & Vision Computing is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1016/j.imavis.2018.01.002
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        Text: English
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        Type: general
      – SubjectFull: Relevance logic
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      – SubjectFull: Mathematical analysis
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      – SubjectFull: Estimation theory
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      – SubjectFull: Efficient market theory
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              Text: Mar2018
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