Describing Complicated Objects by Implicit Polynomials

Daniel Keren; David Kooper

doi:10.1109/34.273718

Describing Complicated Objects by Implicit Polynomials

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

Abstract

This paper introduces and focuses on two problems. First is the representation power of closed implicit polynomials of modest degree for curves in 2-D images and surfaces in 3-D range data. Super quadrics are a small subset of object boundaries that are well fitted by these polynomials. The second problem is the stable computationally efficient fitting of noisy data by closed implicit polynomial curves and surfaces. The attractive features of these polynomials for Vision is discussed.

Original language	English
Pages (from-to)	38-53
Number of pages	16
Journal	IEEE Transactions on Pattern Analysis and Machine Intelligence
Volume	16
Issue number	1
DOIs	https://doi.org/10.1109/34.273718
State	Published - Jan 1994
Externally published	Yes

Bibliographical note

Funding Information:
Manuscript received February 3, 1992; revised October 20, 1992. This work was supported by NSF Grant IRI-8715774 and NSF-DARPA Grant IRI-8905436. Recommended for acceptance by Associate Editor R. Nevatia.

ASJC Scopus subject areas

Software
Computer Vision and Pattern Recognition
Computational Theory and Mathematics
Artificial Intelligence
Applied Mathematics

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10.1109/34.273718

Cite this

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abstract = "This paper introduces and focuses on two problems. First is the representation power of closed implicit polynomials of modest degree for curves in 2-D images and surfaces in 3-D range data. Super quadrics are a small subset of object boundaries that are well fitted by these polynomials. The second problem is the stable computationally efficient fitting of noisy data by closed implicit polynomial curves and surfaces. The attractive features of these polynomials for Vision is discussed.",

author = "Daniel Keren and David Kooper",

note = "Funding Information: Manuscript received February 3, 1992; revised October 20, 1992. This work was supported by NSF Grant IRI-8715774 and NSF-DARPA Grant IRI-8905436. Recommended for acceptance by Associate Editor R. Nevatia.",

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Describing Complicated Objects by Implicit Polynomials

Abstract

Bibliographical note

ASJC Scopus subject areas

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