The Topological Effects of Smoothing

The Topological Effects of Smoothing,10.1109/TVCG.2011.74,IEEE Transactions on Visualization and Computer Graphics,Sohail Shafii,Scott E. Dillard,Mari

The Topological Effects of Smoothing  
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OPOLOGICAL analysis is an increasingly important approach for visualization and analysis of scientific data in many fields, with relevance for data sets originating in a broad spectrum of applications, ranging from materials science to medicine. Transfer function design for volume rendering can be viewed as an application of topological characterization, where certain regions of data sets corresponding to ranges of function values are assigned optical properties such as color and opacity. These regions allow a usertoeasilyidentifyanddelineatesignificantstructuresina data set. Transfer function methods based on simple thresholding remain attractive due to their simplicity, reproducibility, and minimal user involvement, but they cannot be usedwhensignificantnoiseispresentinthedata.Inaddition, noise generally leads to isosurfaces that contain many spurious surface components, which complicates queries involving the number, size, and distribution of different regions. When having to process and visualize noisy data, smoothingisalwaysanalluringoption,leadingtoisosurfaces withfewercomponentsandsmootherboundaries.However, smoothing has the potential to drastically alter the data to the point where one draws invalid conclusions. We present a two-stage method to track and visualize the topological changes that occur when smoothing a scalarvalued data set defined over a volumetric, three-dimensional (3D) domain. During the tracking stage, we apply smoothing up to a point where a meaningful interpretation of the data is no longer possible. We track the topological changes that occur, specifically the creation and destruction of extremal points that merge with other topological features that persist. In the visualization stage that follows, the user can select the topological events that affect the original noisy data set by applying labels (or colors) to different portions of the data. To summarize, we have developed a general topological analysis method that requires little input from the user. We first provide an introduction to Morse theory and contour trees in Section 2. We describe the methods used in Section 3 and discuss the results obtained with our methods in Section 4. Future research possibilities are covered in Section 5.
Journal: IEEE Transactions on Visualization and Computer Graphics - TVCG , vol. 18, no. 1, pp. 160-172, 2012
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