TY - JOUR
T1 - Shape recognition based on eigenvalues of the Laplacian
AU - Ben Haj Rhouma, Mohamed
AU - Khabou, Mohamed Ali
AU - Hermi, Lotfi
N1 - Funding Information:
The authors thank Dr. Peter Hawkes for his patience and kindness while writing this paper. Part of this work was presented by Lotfi Hermi as a mini-course for the Swiss Doctoral Program, “Shape Recognition Schemes Based on the Spectrum of the Laplacian,” University of Neuchâtel, June 8–12, 2009. We thank Professor Bruno Colbois and the University of Neuchâtel for their hospitality and generosity. We recognize internal financial support for Mohamed Ben Haj Rhouma by Sultan Qaboos University and support for Lotfi Hermi by the Erwin Schrödinger Institute, while performing this work.
Copyright:
Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2011
Y1 - 2011
N2 - 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.
AB - 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.
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U2 - 10.1016/B978-0-12-385985-3.00003-1
DO - 10.1016/B978-0-12-385985-3.00003-1
M3 - Article
AN - SCOPUS:84860196326
VL - 167
SP - 185
EP - 254
JO - Advances in Electronics and Electron Physics
JF - Advances in Electronics and Electron Physics
SN - 1076-5670
ER -