Abstract
This paper investigates the problem of interpolating, under physical constraints, 3D 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 non-iterative, 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 3D fluid vector field. With the application to 3D 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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 58-67 |
| Number of pages | 10 |
| Journal | Proceedings of SPIE - The International Society for Optical Engineering |
| Volume | 1610 |
| DOIs | |
| State | Published - Feb 1 1992 |
| Event | Curves and Surfaces in Computer Vision and Graphics II 1991 - Boston, United States Duration: Nov 14 1991 → Nov 15 1991 |
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ASJC Scopus subject areas
- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics
- Computer Science Applications
- Applied Mathematics
- Electrical and Electronic Engineering
Cite this
Vector field interpolation using robust statistics. / Zhong, Jialin; Weng, Juyang; Huang, Thomas S.
In: Proceedings of SPIE - The International Society for Optical Engineering, Vol. 1610, 01.02.1992, p. 58-67.Research output: Contribution to journal › Conference article
}
TY - JOUR
T1 - Vector field interpolation using robust statistics
AU - Zhong, Jialin
AU - Weng, Juyang
AU - Huang, Thomas S.
PY - 1992/2/1
Y1 - 1992/2/1
N2 - This paper investigates the problem of interpolating, under physical constraints, 3D 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 non-iterative, 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 3D fluid vector field. With the application to 3D 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.
AB - This paper investigates the problem of interpolating, under physical constraints, 3D 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 non-iterative, 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 3D fluid vector field. With the application to 3D 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.
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U2 - 10.1117/12.135134
DO - 10.1117/12.135134
M3 - Conference article
AN - SCOPUS:85075640652
VL - 1610
SP - 58
EP - 67
JO - Proceedings of SPIE - The International Society for Optical Engineering
JF - Proceedings of SPIE - The International Society for Optical Engineering
SN - 0277-786X
ER -