2022
Bujack, Roxana; Zhang, Xinhua; Suk, Tomáš; Rogers, David
Systematic generation of moment invariant bases for 2D and 3D tensor fields Journal Article
In: Pattern Recognition, vol. 123, pp. 108313, 2022, ISSN: 0031-3203.
Abstract | Links | BibTeX | Tags: Basis, Flexible, Generator approach, moment invariants, pattern detection, Rotation invariant, Tensor, Vector
@article{BUJACK2022108313,
title = {Systematic generation of moment invariant bases for 2D and 3D tensor fields},
author = {Roxana Bujack and Xinhua Zhang and Tomáš Suk and David Rogers},
url = {https://www.sciencedirect.com/science/article/pii/S0031320321004933},
doi = {https://doi.org/10.1016/j.patcog.2021.108313},
issn = {0031-3203},
year = {2022},
date = {2022-01-01},
urldate = {2022-01-01},
journal = {Pattern Recognition},
volume = {123},
pages = {108313},
abstract = {Moment invariants have been successfully applied to pattern detection tasks in 2D and 3D scalar, vector, and matrix valued data. However so far no flexible basis of invariants exists, i.e., no set that is optimal in the sense that it is complete and independent for every input pattern. In this paper, we prove that a basis of moment invariants can be generated that consists of tensor contractions of not more than two different moment tensors each under the conjecture of the set of all possible tensor contractions to be complete. This result allows us to derive the first generator algorithm that produces flexible bases of moment invariants with respect to orthogonal transformations by selecting a single non-zero moment to pair with all others in these two-factor products. Since at least one non-zero moment can be found in every non-zero pattern, this approach always generates a complete set of descriptors.},
keywords = {Basis, Flexible, Generator approach, moment invariants, pattern detection, Rotation invariant, Tensor, Vector},
pubstate = {published},
tppubtype = {article}
}
Moment invariants have been successfully applied to pattern detection tasks in 2D and 3D scalar, vector, and matrix valued data. However so far no flexible basis of invariants exists, i.e., no set that is optimal in the sense that it is complete and independent for every input pattern. In this paper, we prove that a basis of moment invariants can be generated that consists of tensor contractions of not more than two different moment tensors each under the conjecture of the set of all possible tensor contractions to be complete. This result allows us to derive the first generator algorithm that produces flexible bases of moment invariants with respect to orthogonal transformations by selecting a single non-zero moment to pair with all others in these two-factor products. Since at least one non-zero moment can be found in every non-zero pattern, this approach always generates a complete set of descriptors.
2018
Bujack, Roxana; Rogers, David; Ahrens, James
Reducing Occlusion in Cinema Databases through Feature-Centric Visualizations Proceedings Article
In: Leipzig Symposium on Visualization In Applications (LEVIA), 2018.
Abstract | Links | BibTeX | Tags: cinema, feature, image space, in situ, moment invariants, occlusion, pattern detection
@inproceedings{bujack2018reducing,
title = {Reducing Occlusion in Cinema Databases through Feature-Centric Visualizations},
author = {Roxana Bujack and David Rogers and James Ahrens},
url = {https://datascience.dsscale.org/wp-content/uploads/2019/01/ReducingOcclusioninCinemaDatabasesthroughFeature-CentricVisualizations.pdf},
year = {2018},
date = {2018-01-01},
booktitle = {Leipzig Symposium on Visualization In Applications (LEVIA)},
abstract = {In modern supercomputer architectures, the I/O capabilities do not keep up with the computational speed. Image-based techniques are one very promising approach to a scalable output format for visual analysis, in which a reduced output that corresponds to the visible state of the simulation is rendered in-situ and stored to disk. These techniques can support interactive exploration of the data through image compositing and other methods, but automatic methods of highlighting data and reducing clutter can make these methods more effective. In this paper, we suggest a method of assisted exploration through the combination of feature-centric analysis with image space techniques and show how the reduction of the data to features of interest reduces occlusion in the output for a set of example applications.},
keywords = {cinema, feature, image space, in situ, moment invariants, occlusion, pattern detection},
pubstate = {published},
tppubtype = {inproceedings}
}
In modern supercomputer architectures, the I/O capabilities do not keep up with the computational speed. Image-based techniques are one very promising approach to a scalable output format for visual analysis, in which a reduced output that corresponds to the visible state of the simulation is rendered in-situ and stored to disk. These techniques can support interactive exploration of the data through image compositing and other methods, but automatic methods of highlighting data and reducing clutter can make these methods more effective. In this paper, we suggest a method of assisted exploration through the combination of feature-centric analysis with image space techniques and show how the reduction of the data to features of interest reduces occlusion in the output for a set of example applications.
2017
Bujack, Roxana; Flusser, Jan
Flexible Moment Invariant Bases for 2D Scalar and Vector Fields Proceedings Article
In: Proceedings of International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision (WSCG), 2017, (LA-UR-17-20144).
Abstract | Links | BibTeX | Tags: moment invariants, pattern detection, vector fields
@inproceedings{bujack2017flexible,
title = {Flexible Moment Invariant Bases for 2D Scalar and Vector Fields},
author = {Roxana Bujack and Jan Flusser},
url = {http://datascience.dsscale.org/wp-content/uploads/2017/09/LA-UR-17-20144.pdf},
year = {2017},
date = {2017-01-01},
booktitle = {Proceedings of International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision (WSCG)},
abstract = {Complex moments have been successfully applied to pattern detection tasks in two-dimensional real, complex, and vector valued functions.
In this paper, we review the different bases of rotational moment invariants based on the generator approach with complex monomials. We analyze their properties with respect to independence, completeness, and existence and present superior bases that are optimal with respect to all three criteria for both scalar and vector fields.},
note = {LA-UR-17-20144},
keywords = {moment invariants, pattern detection, vector fields},
pubstate = {published},
tppubtype = {inproceedings}
}
Complex moments have been successfully applied to pattern detection tasks in two-dimensional real, complex, and vector valued functions.
In this paper, we review the different bases of rotational moment invariants based on the generator approach with complex monomials. We analyze their properties with respect to independence, completeness, and existence and present superior bases that are optimal with respect to all three criteria for both scalar and vector fields.
In this paper, we review the different bases of rotational moment invariants based on the generator approach with complex monomials. We analyze their properties with respect to independence, completeness, and existence and present superior bases that are optimal with respect to all three criteria for both scalar and vector fields.
: . .
1.
Bujack, Roxana; Zhang, Xinhua; Suk, Tomáš; Rogers, David
Systematic generation of moment invariant bases for 2D and 3D tensor fields Journal Article
In: Pattern Recognition, vol. 123, pp. 108313, 2022, ISSN: 0031-3203.
@article{BUJACK2022108313,
title = {Systematic generation of moment invariant bases for 2D and 3D tensor fields},
author = {Roxana Bujack and Xinhua Zhang and Tomáš Suk and David Rogers},
url = {https://www.sciencedirect.com/science/article/pii/S0031320321004933},
doi = {https://doi.org/10.1016/j.patcog.2021.108313},
issn = {0031-3203},
year = {2022},
date = {2022-01-01},
urldate = {2022-01-01},
journal = {Pattern Recognition},
volume = {123},
pages = {108313},
abstract = {Moment invariants have been successfully applied to pattern detection tasks in 2D and 3D scalar, vector, and matrix valued data. However so far no flexible basis of invariants exists, i.e., no set that is optimal in the sense that it is complete and independent for every input pattern. In this paper, we prove that a basis of moment invariants can be generated that consists of tensor contractions of not more than two different moment tensors each under the conjecture of the set of all possible tensor contractions to be complete. This result allows us to derive the first generator algorithm that produces flexible bases of moment invariants with respect to orthogonal transformations by selecting a single non-zero moment to pair with all others in these two-factor products. Since at least one non-zero moment can be found in every non-zero pattern, this approach always generates a complete set of descriptors.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Moment invariants have been successfully applied to pattern detection tasks in 2D and 3D scalar, vector, and matrix valued data. However so far no flexible basis of invariants exists, i.e., no set that is optimal in the sense that it is complete and independent for every input pattern. In this paper, we prove that a basis of moment invariants can be generated that consists of tensor contractions of not more than two different moment tensors each under the conjecture of the set of all possible tensor contractions to be complete. This result allows us to derive the first generator algorithm that produces flexible bases of moment invariants with respect to orthogonal transformations by selecting a single non-zero moment to pair with all others in these two-factor products. Since at least one non-zero moment can be found in every non-zero pattern, this approach always generates a complete set of descriptors.
2.
Bujack, Roxana; Rogers, David; Ahrens, James
Reducing Occlusion in Cinema Databases through Feature-Centric Visualizations Proceedings Article
In: Leipzig Symposium on Visualization In Applications (LEVIA), 2018.
@inproceedings{bujack2018reducing,
title = {Reducing Occlusion in Cinema Databases through Feature-Centric Visualizations},
author = {Roxana Bujack and David Rogers and James Ahrens},
url = {https://datascience.dsscale.org/wp-content/uploads/2019/01/ReducingOcclusioninCinemaDatabasesthroughFeature-CentricVisualizations.pdf},
year = {2018},
date = {2018-01-01},
booktitle = {Leipzig Symposium on Visualization In Applications (LEVIA)},
abstract = {In modern supercomputer architectures, the I/O capabilities do not keep up with the computational speed. Image-based techniques are one very promising approach to a scalable output format for visual analysis, in which a reduced output that corresponds to the visible state of the simulation is rendered in-situ and stored to disk. These techniques can support interactive exploration of the data through image compositing and other methods, but automatic methods of highlighting data and reducing clutter can make these methods more effective. In this paper, we suggest a method of assisted exploration through the combination of feature-centric analysis with image space techniques and show how the reduction of the data to features of interest reduces occlusion in the output for a set of example applications.},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
In modern supercomputer architectures, the I/O capabilities do not keep up with the computational speed. Image-based techniques are one very promising approach to a scalable output format for visual analysis, in which a reduced output that corresponds to the visible state of the simulation is rendered in-situ and stored to disk. These techniques can support interactive exploration of the data through image compositing and other methods, but automatic methods of highlighting data and reducing clutter can make these methods more effective. In this paper, we suggest a method of assisted exploration through the combination of feature-centric analysis with image space techniques and show how the reduction of the data to features of interest reduces occlusion in the output for a set of example applications.
3.
Bujack, Roxana; Flusser, Jan
Flexible Moment Invariant Bases for 2D Scalar and Vector Fields Proceedings Article
In: Proceedings of International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision (WSCG), 2017, (LA-UR-17-20144).
@inproceedings{bujack2017flexible,
title = {Flexible Moment Invariant Bases for 2D Scalar and Vector Fields},
author = {Roxana Bujack and Jan Flusser},
url = {http://datascience.dsscale.org/wp-content/uploads/2017/09/LA-UR-17-20144.pdf},
year = {2017},
date = {2017-01-01},
booktitle = {Proceedings of International Conference in Central Europe on Computer Graphics, Visualization and Computer Vision (WSCG)},
abstract = {Complex moments have been successfully applied to pattern detection tasks in two-dimensional real, complex, and vector valued functions.
In this paper, we review the different bases of rotational moment invariants based on the generator approach with complex monomials. We analyze their properties with respect to independence, completeness, and existence and present superior bases that are optimal with respect to all three criteria for both scalar and vector fields.},
note = {LA-UR-17-20144},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
Complex moments have been successfully applied to pattern detection tasks in two-dimensional real, complex, and vector valued functions.
In this paper, we review the different bases of rotational moment invariants based on the generator approach with complex monomials. We analyze their properties with respect to independence, completeness, and existence and present superior bases that are optimal with respect to all three criteria for both scalar and vector fields.
In this paper, we review the different bases of rotational moment invariants based on the generator approach with complex monomials. We analyze their properties with respect to independence, completeness, and existence and present superior bases that are optimal with respect to all three criteria for both scalar and vector fields.