Computing smooth approzimations of scalar functions with constraints
In engineering, geographical applications, scientific visualization, and bio-informatics, a variety of phenomena is described by a large set of data modeled as the values of a scalar function f: M→R defined on a surface M. A low quality of the discrete representations of the input data, unstable computations, numerical approximations, and noise might produce functions with a high number of critical points. In this context, we propose an algorithmic framework for smoothing an arbitrary scalar function, while simplifying its redundant critical points and preserving those that are mandatory for its description. From our perspective, the critical points of f are a natural choice to guide the approximation scheme; in fact, they usually represent relevant information about the behavior of f or the shape itself. To address the aforementioned aims, we compute a smooth approximation f: M→R of f whose set of critical points contains those that have been preserved by the simplification process. The idea behind the proposed approach is to combine smoothing techniques, critical points, and spectral properties of the Laplacian matrix. Inserting constraints in the smoothing of f allows us to overcome the traditional error-driven approximation of f, which does not provide constraints on the preserved topological features. Finally, the computational cost of the proposed approach is O(n log n), where n is the number of vertices of M.
Signal and function smoothing Critical points Laplacian matriz Shape analysis Morse complez Level sets
Giuseppe Patanè Bianca Falcidieno
Istituto di Matematica Applicata e Tecnologie Informatiche-Consiglio Nazionale delle Ricerche, Genova, Italy
国际会议
IEEE International Conference on Shape Modeling and Applications (SMI)(2009年形状建模国际会议)
北京
英文
399-413
2009-06-26（万方平台首次上网日期，不代表论文的发表时间）