1 February 1992 Vector field interpolation using robust statistics
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This paper investigates the problem of interpolating, under physical constraints, 3-D vector fields from sample vectors at irregular positions. This problem arises from analysis of fluid motion, but our results can also be used in such areas as geometric modeling, data approximation, and the analysis of other types of nonrigid motion. The algorithm proposed in this paper combines the generalized multivariate quadratic interpolation and physical constraints into one step to form an over-determined linear equation system. The least squares solution of this system gives the coefficients of interpolation. Since the interpolation is done in one step and is noniterative, it is computationally efficient. We utilize the methods in robust statistics to detect outliers in the sample data so that the result remains stable in the presence of gross errors. Another merit of our scheme is that by incorporating physical constraints into linear equation system, the algorithm takes into account the characteristics of vector field and is much less sensitive to noise. The algorithm is applied to both synthesized and real data representing 3-D fluid vector field. With the application to 3-D fluid flow in mind, we study the applicability of physical constraints in fluid kinematics and analyze the sources of noise from the real data acquisition. A comparison between our algorithm with previous work shows the robustness of our algorithm. The results of interpolating real flow data are presented.
© (1992) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Jialin Zhong, Jialin Zhong, John Juyang Weng, John Juyang Weng, Thomas S. Huang, Thomas S. Huang, } "Vector field interpolation using robust statistics", Proc. SPIE 1610, Curves and Surfaces in Computer Vision and Graphics II, (1 February 1992); doi: 10.1117/12.135134; https://doi.org/10.1117/12.135134

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