A signal processing approach to fair surface design
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Implicit fairing of irregular meshes using diffusion and curvature flow
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Computer Aided Geometric Design
Molecular shape analysis based upon the morse-smale complex and the connolly function
Proceedings of the nineteenth annual symposium on Computational geometry
Bilateral Filtering for Gray and Color Images
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Fair morse functions for extracting the topological structure of a surface mesh
ACM SIGGRAPH 2004 Papers
Simplifying Flexible Isosurfaces Using Local Geometric Measures
VIS '04 Proceedings of the conference on Visualization '04
Proceedings of the 2006 ACM symposium on Solid and physical modeling
Proceedings of the 4th international conference on Computer graphics and interactive techniques in Australasia and Southeast Asia
Vector Field Editing and Periodic Orbit Extraction Using Morse Decomposition
IEEE Transactions on Visualization and Computer Graphics
Generalized surface flows for mesh processing
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Constraint-based fairing of surface meshes
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
A Practical Approach to Morse-Smale Complex Computation: Scalability and Generality
IEEE Transactions on Visualization and Computer Graphics
Separatrix persistence: extraction of salient edges on surfaces using topological methods
SGP '09 Proceedings of the Symposium on Geometry Processing
A topological hierarchy for functions on triangulated surfaces
IEEE Transactions on Visualization and Computer Graphics
SMI 2012: Short Dimension-independent multi-resolution Morse complexes
Computers and Graphics
Empirical mode decomposition on surfaces
Graphical Models
Smooth Shape-Aware Functions with Controlled Extrema
Computer Graphics Forum
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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 C1-continuous output scalar field with the exact specified features and topological structures.