Name
Abstract | ||
|---|---|---|
This paper considers N−1-dimensional hypersurface fitting based on L2 distance in N-dimensional input space. The problem is usually reduced to hyperplane fitting in higher dimension. However, because feature mapping is generally a nonlinear mapping, it does not preserve the order of lengthes, and this derives an unacceptable fitting result. To avoid it, JNLPCA is introduced. JNLPCA defines the L2 distance in the feature space as a weighted L2 distance to reflect the metric in the input space. In the fitting, random sampling approximation of least k-th power deviation, and least α-percentile of squares are introduced to make estimation robust. The proposed hypersurface fitting method is evaluated by quadratic curve fitting and quadratic curve segments extraction from artificial data and a real image. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1007/978-3-642-34487-9_63 | ICONIP (3) |
Keywords | Field | DocType |
feature mapping,input space,quadratic curve fitting,random sampling approximation,l2 distance,1-dimensional hypersurface fitting,robust hypersurface fitting,unacceptable fitting result,feature space,n-dimensional input space,proposed hypersurface fitting method,nonlinear mapping,fitting,ransac | Applied mathematics,Nonlinear system,Hypersurface,Artificial intelligence,Hyperplane,Topology,Feature vector,Pattern recognition,RANSAC,Quadratic function,Sampling (statistics),Real image,Mathematics | Conference |
Volume | ISSN | Citations |
7665 | 0302-9743 | 1 |
PageRank | References | Authors |
0.36 | 9 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jun Fujiki | 1 | 33 | 10.33 |
| Shotaro Akaho | 2 | 650 | 79.46 |
| Hideitsu Hino | 3 | 99 | 25.73 |
| Noboru Murata | 4 | 855 | 170.36 |