Decomposing the Laplacian

M. Ann Piech

doi:10.1109/34.57673

Decomposing the Laplacian

M. Ann Piech

Mathematics

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

5 Scopus citations

Abstract

We correct and give an elementary derivation of Clark’s decomposition of the Laplacian ∇2/(x, y) into a second directional derivative in the gradient direction of f, and a product of gradient magnitude by curvature of the level curve through f (x, y).

Original language	English
Pages (from-to)	830-831
Number of pages	2
Journal	IEEE Transactions on Pattern Analysis and Machine Intelligence
Volume	12
Issue number	8
DOIs	https://doi.org/10.1109/34.57673
State	Published - Aug 1990

Keywords

Laplacian
Laplacian decomposition

Access to Document

10.1109/34.57673

Cite this

@article{9476fce8593a4ca38c7e1c1ea40fe5bf,

title = "Decomposing the Laplacian",

abstract = "We correct and give an elementary derivation of Clark{\textquoteright}s decomposition of the Laplacian ∇2/(x, y) into a second directional derivative in the gradient direction of f, and a product of gradient magnitude by curvature of the level curve through f (x, y).",

keywords = "Laplacian, Laplacian decomposition",

author = "Piech, \{M. Ann\}",

year = "1990",

month = aug,

doi = "10.1109/34.57673",

language = "English",

volume = "12",

pages = "830--831",

journal = "IEEE Transactions on Pattern Analysis and Machine Intelligence",

issn = "0162-8828",

publisher = "IEEE Computer Society",

number = "8",

}

TY - JOUR

T1 - Decomposing the Laplacian

AU - Piech, M. Ann

PY - 1990/8

Y1 - 1990/8

N2 - We correct and give an elementary derivation of Clark’s decomposition of the Laplacian ∇2/(x, y) into a second directional derivative in the gradient direction of f, and a product of gradient magnitude by curvature of the level curve through f (x, y).

AB - We correct and give an elementary derivation of Clark’s decomposition of the Laplacian ∇2/(x, y) into a second directional derivative in the gradient direction of f, and a product of gradient magnitude by curvature of the level curve through f (x, y).

KW - Laplacian

KW - Laplacian decomposition

UR - https://www.scopus.com/pages/publications/0025472565

U2 - 10.1109/34.57673

DO - 10.1109/34.57673

M3 - Article

AN - SCOPUS:0025472565

SN - 0162-8828

VL - 12

SP - 830

EP - 831

JO - IEEE Transactions on Pattern Analysis and Machine Intelligence

JF - IEEE Transactions on Pattern Analysis and Machine Intelligence

IS - 8

ER -

Decomposing the Laplacian

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this