| 1. |
- Abrikosov, Alexei I., et al.
(author)
-
Topological analysis of density fields: An evaluation of segmentation methods
- 2021
-
In: Computers & graphics. - : Elsevier. - 0097-8493 .- 1873-7684. ; 98, s. 231-241
-
Journal article (peer-reviewed)abstract
- Topological and geometric segmentation methods provide powerful concepts for detailed field analysis and visualization. However, when it comes to a quantitative analysis that requires highly accurate geometric segmentation, there is a large discrepancy between the promising theory and the available computational approaches. In this paper, we compare and evaluate various segmentation methods with the aim to identify and quantify the extent of these discrepancies. Thereby, we focus on an application from quantum chemistry: the analysis of electron density fields. It is a scalar quantity that can be experimentally measured or theoretically computed. In the evaluation we consider methods originating from the domain of quantum chemistry and computational topology. We apply the methods to the charge density of a set of crystals and molecules. Therefore, we segment the volumes into atomic regions and derive and compare quantitative measures such as total charge and dipole moments from these regions. As a result, we conclude that an accurate geometry determination can be crucial for correctly segmenting and analyzing a scalar field, here demonstrated on the electron density field.
|
|
| 2. |
- Auer, Cornelia, et al.
(author)
-
2D Tensor Field Segmentation
- 2011
-
In: Dagstuhl Follow-Ups. - Dagstuhl, Germany : Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik. - 1868-8977. ; 2, s. 17-35
-
Journal article (peer-reviewed)abstract
- We present a topology-based segmentation as means for visualizing 2D symmetric tensor fields. The segmentation uses directional as well as eigenvalue characteristics of the underlying field to delineate cells of similar (or dissimilar) behavior in the tensor field. A special feature of the resulting cells is that their shape expresses the tensor behavior inside the cells and thus also can be considered as a kind of glyph representation. This allows a qualitative comprehension of important structures of the field. The resulting higher-level abstraction of the field provides valuable analysis. The extraction of the integral topological skeleton using both major and minor eigenvector fields serves as a structural pre-segmentation and renders all directional structures in the field. The resulting curvilinear cells are bounded by tensorlines and already delineate regions of equivalent eigenvector behavior. This pre-segmentation is further adaptively refined to achieve a segmentation reflecting regions of similar eigenvalue and eigenvector characteristics. Cell refinement involves both subdivision and merging of cells achieving a predetermined resolution, accuracy and uniformity of the segmentation. The buildingblocks of the approach can be intuitively customized to meet the demands or different applications. Application to tensor fields from numerical stress simulations demonstrates the effectiveness of our method.
|
|
| 3. |
|
|
| 4. |
- Auer, Cornelia, et al.
(author)
-
Complete Tensor Field Topology on 2D Triangulated Manifolds embedded in 3D
- 2011
-
In: Computer graphics forum (Print). - : Wiley. - 0167-7055 .- 1467-8659. ; 30:3, s. 831-840
-
Journal article (peer-reviewed)abstract
- This paper is concerned with the extraction of the surface topology of tensor fields on 2D triangulated manifoldsembedded in 3D. In scientific visualization topology is a meaningful instrument to get a hold on the structure of agiven dataset. Due to the discontinuity of tensor fields on a piecewise planar domain, standard topology extractionmethods result in an incomplete topological skeleton. In particular with regard to the high computational costs ofthe extraction this is not satisfactory. This paper provides a method for topology extraction of tensor fields thatleads to complete results. The core idea is to include the locations of discontinuity into the topological analysis.For this purpose the model of continuous transition bridges is introduced, which allows to capture the entiretopology on the discontinuous field. The proposed method is applied to piecewise linear three-dimensional tensorfields defined on the vertices of the triangulation and for piecewise constant two or three-dimensional tensor fieldsgiven per triangle, e.g. rate of strain tensors of piecewise linear flow fields.
|
|
| 5. |
|
|
| 6. |
- Behrendt, Benjamin, et al.
(author)
-
Evolutionary Pathlines for Blood Flow Exploration in Cerebral Aneurysms
- 2019
-
In: Eurographics Workshop on Visual Computing for Biology and Medicine. - : The Eurographics Association. - 9783038680819
-
Conference paper (peer-reviewed)abstract
- Blood flow simulations play an important role for the understanding of vascular diseases, such as aneurysms. However, analysis of the resulting flow patterns, especially comparisons across patient groups, are challenging. Typically, the hemodynamic analysis relies on trial and error inspection of the flow data based on pathline visualizations and surface renderings. Visualizing too many pathlines at once may obstruct interesting features, e.g., embedded vortices, whereas with too little pathlines, particularities such as flow characteristics in aneurysm blebs might be missed. While filtering and clustering techniques support this task, they require the pre-computation of pathlines densely sampled in the space-time domain. Not only does this become prohibitively expensive for large patient groups, but the results often suffer from undersampling artifacts. In this work, we propose the usage of evolutionary algorithms to reduce the overhead of computing pathlines that do not contribute to the analysis, while simultaneously reducing the undersampling artifacts. Integrated in an interactive framework, it efficiently supports the evaluation of hemodynamics for clinical research and treatment planning in case of cerebral aneurysms. The specification of general optimization criteria for entire patient groups allows the blood flow data to be batch-processed. We present clinical cases to demonstrate the benefits of our approach especially in presence of aneurysm blebs. Furthermore, we conducted an evaluation with four expert neuroradiologists. As a result, we report advantages of our method for treatment planning to underpin its clinical potential.
|
|
| 7. |
- Boyer, E, et al.
(author)
-
SHREC 2011: Robust Feature Detection and Description Benchmark
- 2011
-
Conference paper (peer-reviewed)abstract
- Feature-based approaches have recently become very popular in computer vision and image analysis applications, and are becoming a promising direction in shape retrieval. SHREC’11 robust feature detection and description benchmark simulates the feature detection and description stages of feature-based shape retrieval algorithms. The benchmark tests the performance of shape feature detectors and descriptors under a wide variety of transformations. The benchmark allows evaluating how algorithms cope with certain classes of transformations and strength of the transformations that can be dealt with. The present paper is a report of the SHREC’11 robust feature detection and description benchmark results.
|
|
| 8. |
- Bujack, Roxana, et al.
(author)
-
Moment Invariants for 2D Flow Fields Using Normalization in Detail
- 2015
-
In: IEEE Transactions on Visualization and Computer Graphics. - 1077-2626 .- 1941-0506. ; 21:8, s. 916-929
-
Journal article (peer-reviewed)abstract
- The analysis of 2D flow data is often guided by the search for characteristic structures with semantic meaning. One way to approach this question is to identify structures of interest by a human observer, with the goal of finding similar structures in the same or other datasets. The major challenges related to this task are to specify the notion of similarity and define respective pattern descriptors. While the descriptors should be invariant to certain transformations, such as rotation and scaling, they should provide a similarity measure with respect to other transformations, such as deformations. In this paper, we propose to use moment invariants as pattern descriptors for flow fields. Moment invariants are one of the most popular techniques for the description of objects in the field of image recognition. They have recently also been applied to identify 2D vector patterns limited to the directional properties of flow fields. Moreover, we discuss which transformations should be considered for the application to flow analysis. In contrast to previous work, we follow the intuitive approach of moment normalization, which results in a complete and independent set of translation, rotation, and scaling invariant flow field descriptors. They also allow to distinguish flow features with different velocity profiles. We apply the moment invariants in a pattern recognition algorithm to a real world dataset and show that the theoretical results can be extended to discrete functions in a robust way.
|
|
| 9. |
- Bujack, Roxana, et al.
(author)
-
Moment Invariants for 2D Flow Fields via Normalization in Detail
- 2014
-
Conference paper (peer-reviewed)abstract
- The analysis of 2D flow data is often guided by the search for characteristic structures with semantic meaning. One way to approach this question is to identify structures of interest by a human observer, with the goal of finding similar structures in the same or other datasets. The major challenges related to this task are to specify the notion of similarity and define respective pattern descriptors. While the descriptors should be invariant to certain transformations, such as rotation and scaling, they should provide a similarity measure with respect to other transformations, such as deformations. In this paper, we propose to use moment invariants as pattern descriptors for flow fields. Moment invariants are one of the most popular techniques for the description of objects in the field of image recognition. They have recently also been applied to identify 2D vector patterns limited to the directional properties of flow fields. Moreover, we discuss which transformations should be considered for the application to flow analysis. In contrast to previous work, we follow the intuitive approach of moment normalization, which results in a complete and independent set of translation, rotation, and scaling invariant flow field descriptors. They also allow to distinguish flow features with different velocity profiles. We apply the moment invariants in a pattern recognition algorithm to a real world dataset and show that the theoretical results can be extended to discrete functions in a robust way.
|
|
| 10. |
- Bujack, Roxana, et al.
(author)
-
State of the Art in Time-Dependent Flow Topology: Interpreting Physical Meaningfulness Through Mathematical Properties
- 2020
-
In: Computer graphics forum (Print). - : WILEY. - 0167-7055 .- 1467-8659. ; 39:3, s. 811-835
-
Journal article (peer-reviewed)abstract
- We present a state-of-the-art report on time-dependent flow topology. We survey representative papers in visualization and provide a taxonomy of existing approaches that generalize flow topology from time-independent to time-dependent settings. The approaches are classified based upon four categories: tracking of steady topology, reference frame adaption, pathline classification or clustering, and generalization of critical points. Our unique contributions include introducing a set of desirable mathematical properties to interpret physical meaningfulness for time-dependent flow visualization, inferring mathematical properties associated with selective research papers, and utilizing such properties for classification. The five most important properties identified in the existing literature include coincidence with the steady case, induction of a partition within the domain, Lagrangian invariance, objectivity, and Galilean invariance.
|
|
