From basis functions to basis fields: vector field approximation from sparse data

Ferdinando A. Mussa-Ivaldi*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

55 Scopus citations

Abstract

Recent investigations (Poggio and Girosi 1990b) have pointed out the equivalence between a wide class of learning problems and the reconstruction of a real-valued function from a sparse set of data. However, in order to process sensory information and to generate purposeful actions living organisms must deal not only with real-valued functions but also with vector-valued mappings. Examples of such vector-valued mappings range from the optical flow fields associated with visual motion to the fields of mechanical forces produced by neuromuscular activation. In this paper, I discuss the issue of vector-field processing from a broad computational perspective. A variety of vector patterns can be efficiently represented by a combination of linearly independent vector fields that I call "basis fields". Basis fields offer in some cases a better alternative to treating each component of a vector as an independent scalar entity. In spite of its apparent simplicity, such a component-based representation is bound to change with any change of coordinates. In contrast, vector-valued primitives such as basis fields generate vector field representations that are invariant under coordinate transformations.

Original languageEnglish (US)
Pages (from-to)479-489
Number of pages11
JournalBiological Cybernetics
Volume67
Issue number6
DOIs
StatePublished - Oct 1992

ASJC Scopus subject areas

  • Biotechnology
  • Computer Science(all)

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