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Topology‐based Smoothing of 2D Scalar Fields with C 1 ‐Continuity
Author(s) -
Weinkauf Tino,
Gingold Yotam,
Sorkine Olga
Publication year - 2010
Publication title -
computer graphics forum
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.578
H-Index - 120
eISSN - 1467-8659
pISSN - 0167-7055
DOI - 10.1111/j.1467-8659.2009.01702.x
Subject(s) - smoothing , scalar field , computer science , spurious relationship , scalar (mathematics) , noise (video) , topology (electrical circuits) , noise reduction , topological data analysis , algorithm , artificial intelligence , mathematics , computer vision , machine learning , geometry , image (mathematics) , combinatorics , mathematical physics
Data sets coming from simulations or sampling of real‐world phenomena often contain noise that hinders their processing and analysis. Automatic filtering and denoising can be challenging: when the nature of the noise is unknown, it is difficult to distinguish between noise and actual data features; in addition, the filtering process itself may introduce “artificial” features into the data set that were not originally present. In this paper, we propose a smoothing method for 2D scalar fields that gives the user explicit control over the data features. We define features as critical points of the given scalar function, and the topological structure they induce (i.e., the Morse‐Smale complex). Feature significance is rated according to topological persistence. Our method allows filtering out spurious features that arise due to noise by means of topological simplification, providing the user with a simple interface that defines the significance threshold, coupled with immediate visual feedback of the remaining data features. In contrast to previous work, our smoothing method guarantees a C 1 ‐continuous output scalar field with the exact specified features and topological structures.