Geometric data fitting

José L. Martínez-Morales

Abstract and Applied Analysis, 2004, vol. 2004, 1-50

Abstract:

Given a dense set of points lying on or near an embedded submanifold M 0 ⊂ ℝ n of Euclidean space, the manifold fitting problem is to find an embedding F : M → ℝ n that approximates M 0 in the sense of least squares. When the dataset is modeled by a probability distribution, the fitting problem reduces to that of finding an embedding that minimizes E d [ F ] , the expected square of the distance from a point in ℝ n to F ( M ) . It is shown that this approach to the fitting problem is guaranteed to fail because the functional E d has no local minima. This problem is addressed by adding a small multiple k of the harmonic energy functional to the expected square of the distance. Techniques from the calculus of variations are then used to study this modified functional.

Date: 2004
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/AAA/2004/209367.pdf (application/pdf)
http://downloads.hindawi.com/journals/AAA/2004/209367.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:209367

DOI: 10.1155/S1085337504401043

Access Statistics for this article

More articles in Abstract and Applied Analysis from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().