Multidimensional reconstruction by set-valued approximations

David Levin

doi:10.1093/imanum/6.2.173

Multidimensional reconstruction by set-valued approximations

David Levin^*

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

Some generalizations of the notion of univariate data interpolation are presented, inducing the concept of set-valued interpolation in a general metric space. Consequently methods for univariate interpolation or smoothing of multidimensional geometrical data are suggested. In particular the application of these methods to 3-D body recognition from cross-sectional data is discussed. Preliminary analysis of the interpolation process is presented and the capability of reconstructing bodies of complex topologies is exemplified.

Original language	English
Pages (from-to)	173-184
Number of pages	12
Journal	IMA Journal of Numerical Analysis
Volume	6
Issue number	2
DOIs	https://doi.org/10.1093/imanum/6.2.173
State	Published - Apr 1986

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10.1093/imanum/6.2.173

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abstract = "Some generalizations of the notion of univariate data interpolation are presented, inducing the concept of set-valued interpolation in a general metric space. Consequently methods for univariate interpolation or smoothing of multidimensional geometrical data are suggested. In particular the application of these methods to 3-D body recognition from cross-sectional data is discussed. Preliminary analysis of the interpolation process is presented and the capability of reconstructing bodies of complex topologies is exemplified.",

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Multidimensional reconstruction by set-valued approximations

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