Efficient Visualization Of Multivariate Simulation Data

With the advancement of technology and the enhancement of computing power,many complex models have been developed in different domains,such as computational fluid dynamics,climate research and combustion simulation.These simulations often create multiple variables describing different physical/chemical properties within the same spatial domain.Thus,the simulation is usually large-scale,high-resolution and multivariate.Visualizing multivariate data sets effectively is an important part of simulation.The potential features and hidden relationships in multivariate data can be displayed directly using visualization,and this is expected to assist scientists to gain an in-depth understanding of a scientific process,verify hypothesis and further discover new physical phenomenons and rules.Large-scale data calls for proper data representation to reduce the data size and maintain the key information.Complex interactive relationships need effective correlation models and visualization methods to extract and express the similarity relationship and distinctive relationship between variables.In order to enable visualization to be a promising tool to assist the exploration and analysis of large-scale multivariate spatial data,there are still many challenges need to be conquer,that is,the huge amount of data size,the complexity of internal structures of data,the hidden of relationships between variables.In this dissertation,we consider 3D multivariate simulation data as the main object of our study and focus on data representation methods,correlation modeling,multivariate feature definition and relationship establishment.The main research results of this dissertation are summarized as follows:·We propose a novel distribution-based representation based on value-position joint cluster-ing.Distribution-based representations preserve the data's statistical properties well and reduce the size of the data significantly,thus are widely used in different applications.In this work,we take the inherent spatial data coherency into consideration to further improve the accuracy and effectiveness of the data representation.First,the original volume is split into non-overlapping block regions,and then the voxels in the data block are clustered according to their values and positions to hold the value distribution.The value-based spatial distribution in a cluster is represented using the Gaussian Mixture Model.An adaptive scheme is used to determine the number of Gaussian components needed for each GMM to make the storage overhead small.Based on Bayes' rule,we combine the value distribution and spatial distribution to compute the probability density function of clusters at any location.The value of a position is determined by using Monte Carlo sampling.·We propose a co-analysis framework based on feature subspaces to interactively explore different relationships in multivariate data set.In this work,we first extract all feature subspaces automatically,each of which only contains voxels with a similar scalar-value pattern over a subset of variables.To permit users to sift through an exponential number of feature subspace,we introduce a mechanism to deal with feature subspace redundancy by grouping them based on their corresponding variate sets and by hierarchically clustering them based on their similarity.In order to visually explore feature subspaces,we design several coordinated views and an analytical pipeline.The variable relationship is represented in an association matrix between variables and groups of feature subspaces.The user can specify one variable set to further analyze its feature subspaces.After selection,its feature subspaces are visually encoded in the scatter plot to show the similarities between feature subspaces.When one cluster or feature subspace is selected,an enhanced parallel coordinate is designed to show the correlation of scalar values in the variable set.·We present a visual analytic approach for interactively exploring features and their relation-ships in multivariate volume data.The relationship between features from different fields can intuitively reveal the correlation and difference between fields.In this work,Major features of each variable are extracted based on the merge tree,which provides the nesting relationship of contours in a tree structure.Associated features are identified based on an application associated feature correlation measurement.FeatureNet is derived by matching the tree structures of interested fields based on the associated features.We also develop a novel layout algorithm to present FeatureNet,which highlights associated features while maintaining the nesting relationship in each field.Several coordinate views with well-suited interactions make FeatureNet possible to serve as a navigation tool to guide data exploration.