Name
Abstract | ||
|---|---|---|
Representing 2D and 3D data sets with implicit polynomials (IPs) has been attractive because of its applicability to various computer vision issues. Therefore, many IP fitting methods have already been proposed. However, the existing fitting methods can be and need to be improved with respect to computational cost for deciding on the appropriate degree of the IP representation and to fitting accuracy, while still maintaining the stability of the fit. We propose a stable method for accurate fitting that automatically determines the moderate degree required. Our method increases the degree of IP until a satisfactory fitting result is obtained. The incrementability of QR decomposition with Gram-Schmidt orthogonalization gives our method computational efficiency. Furthermore, since the decomposition detects the instability element precisely, our method can selectively apply ridge regression-based constraints to that element only. As a result, our method achieves computational stability while maintaining fitting accuracy. Experimental results demonstrate the effectiveness of our method compared with prior methods. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1109/TPAMI.2009.189 | IEEE Trans. Pattern Anal. Mach. Intell. |
Keywords | Field | DocType |
fitting accuracy,satisfactory fitting result,prior method,gram-schmidt orthogonalization,fitting methods,ip representation,implicit shape representation.,method computational efficiency,2d data sets,implicit polynomials,curve fitting,stable method,ip fitting method,ridge regression-based constraints,implicit polynomial (ip),appropriate degree,accurate fitting,computer vision,fitting algebraic curves and surfaces,computational stability,fitting implicit polynomial curves,existing fitting method,polynomials,3d data sets,implicit polynomial curves,ridge regression,stability,gram schmidt orthogonalization,algebraic curve,spline,shape,image recognition,qr decomposition | Spline (mathematics),Gram–Schmidt process,Polynomial,Curve fitting,Computer science,Artificial intelligence,QR decomposition,Mathematical optimization,Pattern recognition,Polynomial interpolation,Matrix decomposition,Algorithm,Orthogonalization | Journal |
Volume | Issue | ISSN |
32 | 3 | 1939-3539 |
Citations | PageRank | References |
23 | 0.97 | 30 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Bo Zheng | 1 | 159 | 13.62 |
| Jun Takamatsu | 2 | 280 | 51.47 |
| Katsushi Ikeuchi | 3 | 4651 | 881.49 |