Shape recognition based on eigenvalues of the Laplacian

Mohamed Ben Haj Rhouma, Mohamed Ali Khabou, Lotfi Hermi

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

This chapter offers a theoretical overview of the characteristics of the eigenvalues of four well-known linear operators and assess their usefulness as reliable tools for shape recognition. A shape recognition technique can also be classified as either information-preserving or non-preserving depending on whether full recovery of the shape being analyzed is possible from the extracted feature vectors. The boundary conditions in Saito's problem emerge by requiring the Laplacian to commute with the expression of Green's function for free space. Rather than providing a comprehensive review of methods of computation of the eigenvalues of the membrane problem and the other associated problems described previously, we mention the techniques that were most prominent recently and others that provide future hope. A total of 288 hand-drawn images of disks, triangles, rectangles, ellipses, diamonds, and squares of different sizes and orientations were scanned into the compute.

Original languageEnglish (US)
Pages (from-to)185-254
Number of pages70
JournalAdvances in Imaging and Electron Physics
Volume167
DOIs
StatePublished - 2011

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Green's function
Diamonds
eigenvalues
Boundary conditions
Membranes
Recovery
linear operators
rectangles
ellipses
triangles
preserving
Green's functions
recovery
diamonds
boundary conditions
membranes

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Condensed Matter Physics
  • Nuclear and High Energy Physics

Cite this

Shape recognition based on eigenvalues of the Laplacian. / Ben Haj Rhouma, Mohamed; Khabou, Mohamed Ali; Hermi, Lotfi.

In: Advances in Imaging and Electron Physics, Vol. 167, 2011, p. 185-254.

Research output: Contribution to journalArticle

Ben Haj Rhouma, Mohamed ; Khabou, Mohamed Ali ; Hermi, Lotfi. / Shape recognition based on eigenvalues of the Laplacian. In: Advances in Imaging and Electron Physics. 2011 ; Vol. 167. pp. 185-254.
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