Robust hypersurface fitting based on random sampling approximations

Jun Fujiki, Shotaro Akaho, Hideitsu Hino, Noboru Murata

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

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.

Original languageEnglish
Title of host publicationNeural Information Processing - 19th International Conference, ICONIP 2012, Proceedings
Pages520-527
Number of pages8
EditionPART 3
DOIs
Publication statusPublished - 2012 Nov 19
Event19th International Conference on Neural Information Processing, ICONIP 2012 - Doha, Qatar
Duration: 2012 Nov 122012 Nov 15

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 3
Volume7665 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference19th International Conference on Neural Information Processing, ICONIP 2012
CountryQatar
CityDoha
Period12/11/1212/11/15

Keywords

  • JNLPCA
  • L PD
  • L PS
  • RANSAC
  • fitting

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Fingerprint Dive into the research topics of 'Robust hypersurface fitting based on random sampling approximations'. Together they form a unique fingerprint.

  • Cite this

    Fujiki, J., Akaho, S., Hino, H., & Murata, N. (2012). Robust hypersurface fitting based on random sampling approximations. In Neural Information Processing - 19th International Conference, ICONIP 2012, Proceedings (PART 3 ed., pp. 520-527). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7665 LNCS, No. PART 3). https://doi.org/10.1007/978-3-642-34487-9_63