Results 1 
4 of
4
Multiscale Symmetry Detection in Scalar Fields by Clustering Contours
"... Fig. 1. Clustering based analysis detects symmetry at different scales in a 3D cryoelectron microscopy image of AMPactivated kinase (EMDB1897). (left) The threefold rotational symmetry is apparent from the volume rendering. (center) Contours are represented as points in a highdimensional shape ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
(Show Context)
Fig. 1. Clustering based analysis detects symmetry at different scales in a 3D cryoelectron microscopy image of AMPactivated kinase (EMDB1897). (left) The threefold rotational symmetry is apparent from the volume rendering. (center) Contours are represented as points in a highdimensional 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 highdimensional transformationinvariant 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. Index Terms—Scalar field visualization, symmetry detection, contour tree, data exploration. 1
Extended Branch Decomposition Graphs: Structural Comparison of Scalar Data
"... We present a method to find repeating topological structures in scalar data sets. More precisely, we compare all subtrees of two merge trees against each other – in an efficient manner exploiting redundancy. This provides pairwise distances between the topological structures defined by sub/superlev ..."
Abstract
 Add to MetaCart
(Show Context)
We present a method to find repeating topological structures in scalar data sets. More precisely, we compare all subtrees of two merge trees against each other – in an efficient manner exploiting redundancy. This provides pairwise distances between the topological structures defined by sub/superlevel sets, which can be exploited in several applications such as finding similar structures in the same data set, assessing periodic behavior in timedependent data, and comparing the topology of two different data sets. To do so, we introduce a novel data structure called the extended branch decomposition graph, which is composed of the branch decompositions of all subtrees of the merge tree. Based on dynamic programming, we provide two highly efficient algorithms for computing and comparing extended branch decomposition graphs. Several applications attest to the utility of our method and its robustness against noise. 1.
Approved by the Guidance Committee:
, 2015
"... Microfilm or other copies of this dissertation are obtainable from ..."
(Show Context)
U.S. Geological Survey
"... Species distribution models (SDM) are used to help understand what drives the distribution of various plant and animal species. These models are typically high dimensional scalar functions, where the dimensions of the domain correspond to predictor variables of the model algorithm. Understanding an ..."
Abstract
 Add to MetaCart
(Show Context)
Species distribution models (SDM) are used to help understand what drives the distribution of various plant and animal species. These models are typically high dimensional scalar functions, where the dimensions of the domain correspond to predictor variables of the model algorithm. Understanding and exploring the differences between models help ecologists understand areas where their data or understanding of the system is incomplete and will help guide further investigation in these regions. These differences can also indicate an important source of model to model uncertainty. However, it is cumbersome and often impractical to perform this analysis using existing tools, which allows for manual exploration of the models usually as 1dimensional curves. In this paper, we propose a topologybased framework to help ecologists explore the differences in various SDMs directly in the high dimensional domain. In order to accomplish this, we introduce the concept of maximum topology matching that computes a localityaware correspondence between similar extrema of two scalar functions. The matching is then used to compute the similarity between two functions. We also design a visualization interface that allows ecologists to explore SDMs using their topological features and to study the differences between pairs of models found using maximum topological matching. We demonstrate the utility of the proposed framework through several use cases using different data sets and report the feedback obtained from ecologists.