TY - GEN
T1 - Robust hypersurface fitting based on random sampling approximations
AU - Fujiki, Jun
AU - Akaho, Shotaro
AU - Hino, Hideitsu
AU - Murata, Noboru
PY - 2012
Y1 - 2012
N2 - This paper considers N - 1-dimensional hypersurface fitting based on L 2 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 L 2 distance in the feature space as a weighted L 2 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.
AB - This paper considers N - 1-dimensional hypersurface fitting based on L 2 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 L 2 distance in the feature space as a weighted L 2 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.
KW - JNLPCA
KW - L PD
KW - L PS
KW - RANSAC
KW - fitting
UR - http://www.scopus.com/inward/record.url?scp=84869051714&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84869051714&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-34487-9_63
DO - 10.1007/978-3-642-34487-9_63
M3 - Conference contribution
AN - SCOPUS:84869051714
SN - 9783642344862
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 520
EP - 527
BT - Neural Information Processing - 19th International Conference, ICONIP 2012, Proceedings
T2 - 19th International Conference on Neural Information Processing, ICONIP 2012
Y2 - 12 November 2012 through 15 November 2012
ER -