TY - JOUR

T1 - Laplace spectra as fingerprints for image recognition

AU - Peinecke, Niklas

AU - Wolter, Franz Erich

AU - Reuter, Martin

PY - 2007/6

Y1 - 2007/6

N2 - In the area of image retrieval from data bases and for copyright protection of large image collections there is a growing demand for unique but easily computable fingerprints for images. These fingerprints can be used to quickly identify every image within a larger set of possibly similar images. This paper introduces a novel method to automatically obtain such fingerprints from an image. It is based on a reinterpretation of an image as a Riemannian manifold. This representation is feasible for gray value images and color images. We discuss the use of the spectrum of eigenvalues of different variants of the Laplace operator as a fingerprint and show the usability of this approach in several use cases. Contrary to existing works in this area we do not only use the discrete Laplacian, but also with a particular emphasis the underlying continuous operator. This allows better results in comparing the resulting spectra and deeper insights in the problems arising. We show how the well known discrete Laplacian is related to the continuous Laplace-Beltrami operator. Furthermore, we introduce the new concept of solid height functions to overcome some potential limitations of the method.

AB - In the area of image retrieval from data bases and for copyright protection of large image collections there is a growing demand for unique but easily computable fingerprints for images. These fingerprints can be used to quickly identify every image within a larger set of possibly similar images. This paper introduces a novel method to automatically obtain such fingerprints from an image. It is based on a reinterpretation of an image as a Riemannian manifold. This representation is feasible for gray value images and color images. We discuss the use of the spectrum of eigenvalues of different variants of the Laplace operator as a fingerprint and show the usability of this approach in several use cases. Contrary to existing works in this area we do not only use the discrete Laplacian, but also with a particular emphasis the underlying continuous operator. This allows better results in comparing the resulting spectra and deeper insights in the problems arising. We show how the well known discrete Laplacian is related to the continuous Laplace-Beltrami operator. Furthermore, we introduce the new concept of solid height functions to overcome some potential limitations of the method.

KW - Color images

KW - Copyright protection

KW - Features

KW - Fingerprints

KW - Image data bases

KW - Image recognition

KW - Invariants

KW - Isospectrality

KW - Laplace spectra

KW - Laplace-Beltrami operator

KW - Laplace-Kirchhoff operator

KW - Riemannian manifolds

KW - Spectra

KW - Watermarks

UR - http://www.scopus.com/inward/record.url?scp=34248576574&partnerID=8YFLogxK

U2 - 10.1016/j.cad.2007.01.014

DO - 10.1016/j.cad.2007.01.014

M3 - Article

AN - SCOPUS:34248576574

VL - 39

SP - 460

EP - 476

JO - CAD Computer Aided Design

JF - CAD Computer Aided Design

SN - 0010-4485

IS - 6

ER -