Detecting Symmetry in Scalar Fields Using Augmented Extremum Graphs

Thomas, Dilip Mathew; Natarajan, Vijay

doi:10.1109/tvcg.2013.148

Cited by 30 publications

(39 citation statements)

References 41 publications

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“…However, the user could select one of the contours from a region of interest as the query object. It is straightforward to see that this approach may be used to query for symmetric regions within the same dataset, similar to earlier approaches [19,39]. What is more interesting is that the same approach can be extended to search through multiple datasets.…”

Section: Query Contour Driven Explorationmentioning

confidence: 75%

“…Thomas and Natarajan propose topology based methods for symmetry identification and these methods are computationally efficient because they operate on graph representations of the scalar field like the contour tree [38] and the extremum graph [39]. The contour tree based method assumes that the subtrees of the contour tree corresponding to symmetric regions are structurally similar.…”

Section: Topology Based Methodsmentioning

confidence: 99%

“…Query driven exploration is one such paradigm that facilitates navigation through complex data and is gaining popularity over the last few years [1,17]. Symmetric regions in a dataset facilitate query driven exploration of the data [19,39]. A region of interest that is segmented from the domain is employed as the query region and symmetry information is utilized to identify other regions similar to the query.…”

Section: Query Contour Driven Explorationmentioning

confidence: 99%

“…Symmetry is a useful cue in biology for determining growth and development of organs [35]. Since the study of symmetric features is of great interest in scientific data analysis, the problem of detecting symmetry in scalar fields has received consider- able attention among researchers in the recent past [10,13,19,38,39].…”

Section: Introductionmentioning

confidence: 99%

“…Symmetry information in scalar fields has been used for transfer function design, exploration of isosurfaces, selection of cross-section planes and view directions, linked selection and editing, query driven exploration, and visualization of features through dual rendering [10,19,38,39]. We believe that as better techniques for symmetry detection are developed, many more applications will emerge.…”

Section: Introductionmentioning

confidence: 99%

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Multiscale Symmetry Detection in Scalar Fields by Clustering Contours

Thomas

Natarajan

2014

IEEE Trans. Visual. Comput. Graphics

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Fig. 1. Clustering based analysis detects symmetry at different scales in a 3D cryo-electron microscopy image of AMP-activated kinase (EMDB-1897). (left) The three-fold rotational symmetry is apparent from the volume rendering. (center) Contours are represented as points in a high-dimensional shape descriptor space (illustrated in 2D). Symmetric contours form a cluster in the descriptor space and can be easily identified. Three such clusters are shown in gold, blue, and pink. (right) Three symmetric regions of different sizes, highlighted in gold, blue, and pink, detected by the method.Abstract-The complexity in visualizing volumetric data often limits the scope of direct exploration of scalar fields. Isocontour extraction is a popular method for exploring scalar fields because of its simplicity in presenting features in the data. In this paper, we present a novel representation of contours with the aim of studying the similarity relationship between the contours. The representation maps contours to points in a high-dimensional transformation-invariant descriptor space. We leverage the power of this representation to design a clustering based algorithm for detecting symmetric regions in a scalar field. Symmetry detection is a challenging problem because it demands both segmentation of the data and identification of transformation invariant segments. While the former task can be addressed using topological analysis of scalar fields, the latter requires geometry based solutions. Our approach combines the two by utilizing the contour tree for segmenting the data and the descriptor space for determining transformation invariance. We discuss two applications, query driven exploration and asymmetry visualization, that demonstrate the effectiveness of the approach.

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Section: Query Contour Driven Explorationmentioning

confidence: 75%

Section: Topology Based Methodsmentioning

confidence: 99%

Section: Query Contour Driven Explorationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Multiscale Symmetry Detection in Scalar Fields by Clustering Contours

Thomas

Natarajan

2014

IEEE Trans. Visual. Comput. Graphics

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Fast and Accurate Intrinsic Symmetry Detection

Nagar

Raman

2018

Computer Vision – ECCV 2018

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In computer vision and graphics, various types of symmetries are extensively studied since symmetry present in objects is a fundamental cue for understanding the shape and the structure of objects. In this work, we detect the intrinsic reflective symmetry in triangle meshes where we have to find the intrinsically symmetric point for each point of the shape. We establish correspondences between functions defined on the shapes by extending the functional map framework and then recover the point-to-point correspondences. Previous approaches using the functional map for this task find the functional correspondences matrix by solving a non-linear optimization problem which makes them slow. In this work, we propose a closed form solution for this matrix which makes our approach faster. We find the closed-form solution based on our following results. If the given shape is intrinsically symmetric, then the shortest length geodesic between two intrinsically symmetric points is also intrinsically symmetric. If an eigenfunction of the Laplace-Beltrami operator for the given shape is an even (odd) function, then its restriction on the shortest length geodesic between two intrinsically symmetric points is also an even (odd) function. The sign of a low-frequency eigenfunction is the same on the neighboring points. Our method is invariant to the ordering of the eigenfunctions and has the least time complexity. We achieve the best performance on the SCAPE dataset and comparable performance with the state-of-the-art methods on the TOSCA dataset.

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Fast Topology-Based Feature Tracking using a Directed Acyclic Graph

Saikia

Weinkauf

2020

Mathematics and Visualization

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Detecting Symmetry in Scalar Fields Using Augmented Extremum Graphs

Cited by 30 publications

References 41 publications

Multiscale Symmetry Detection in Scalar Fields by Clustering Contours

Multiscale Symmetry Detection in Scalar Fields by Clustering Contours

Fast and Accurate Intrinsic Symmetry Detection

Fast Topology-Based Feature Tracking using a Directed Acyclic Graph

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