Shape recognition using eigenvalues of the Dirichlet Laplacian

M. A. Khabou; L. Hermi; M. B.H. Rhouma

doi:10.1016/j.patcog.2006.01.002

Shape recognition using eigenvalues of the Dirichlet Laplacian

M. A. Khabou
, L. Hermi
, M. B.H. Rhouma

Mathematics

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

35 Scopus citations

Abstract

The eigenvalues of the Dirichlet Laplacian are used to generate three different sets of features for shape recognition and classification in binary images. The generated features are rotation-, translation-, and size-invariant. The features are also shown to be tolerant of noise and boundary deformation. These features are used to classify hand-drawn, synthetic, and natural shapes with correct classification rates ranging from 88.9% to 99.2%. The classification was done using few features (only two features in some cases) and simple feedforward neural networks or minimum Euclidian distance.

Original language	English (US)
Pages (from-to)	141-153
Number of pages	13
Journal	Pattern Recognition
Volume	40
Issue number	1
DOIs	https://doi.org/10.1016/j.patcog.2006.01.002
State	Published - Jan 2007

Keywords

Dirichlet boundary condition
Eigenvalues
Fixed membrane problem
Laplacian
Neural networks
Shape recognition

ASJC Scopus subject areas

Software
Signal Processing
Computer Vision and Pattern Recognition
Artificial Intelligence

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10.1016/j.patcog.2006.01.002

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title = "Shape recognition using eigenvalues of the Dirichlet Laplacian",

abstract = "The eigenvalues of the Dirichlet Laplacian are used to generate three different sets of features for shape recognition and classification in binary images. The generated features are rotation-, translation-, and size-invariant. The features are also shown to be tolerant of noise and boundary deformation. These features are used to classify hand-drawn, synthetic, and natural shapes with correct classification rates ranging from 88.9\% to 99.2\%. The classification was done using few features (only two features in some cases) and simple feedforward neural networks or minimum Euclidian distance.",

keywords = "Dirichlet boundary condition, Eigenvalues, Fixed membrane problem, Laplacian, Neural networks, Shape recognition",

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AU - Hermi, L.

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AB - The eigenvalues of the Dirichlet Laplacian are used to generate three different sets of features for shape recognition and classification in binary images. The generated features are rotation-, translation-, and size-invariant. The features are also shown to be tolerant of noise and boundary deformation. These features are used to classify hand-drawn, synthetic, and natural shapes with correct classification rates ranging from 88.9% to 99.2%. The classification was done using few features (only two features in some cases) and simple feedforward neural networks or minimum Euclidian distance.

KW - Dirichlet boundary condition

KW - Eigenvalues

KW - Fixed membrane problem

KW - Laplacian

KW - Neural networks

KW - Shape recognition

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Shape recognition using eigenvalues of the Dirichlet Laplacian

Abstract

Keywords

ASJC Scopus subject areas

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