Details
| Original language | English |
|---|---|
| Pages (from-to) | 460-476 |
| Number of pages | 17 |
| Journal | CAD Computer Aided Design |
| Volume | 39 |
| Issue number | 6 |
| Early online date | 3 Feb 2007 |
| Publication status | Published - Jun 2007 |
Abstract
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.
Keywords
- Color images, Copyright protection, Features, Fingerprints, Image data bases, Image recognition, Invariants, Isospectrality, Laplace spectra, Laplace-Beltrami operator, Laplace-Kirchhoff operator, Riemannian manifolds, Spectra, Watermarks
ASJC Scopus subject areas
- Computer Science(all)
- Computer Science Applications
- Computer Science(all)
- Computer Graphics and Computer-Aided Design
- Engineering(all)
- Industrial and Manufacturing Engineering
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In: CAD Computer Aided Design, Vol. 39, No. 6, 06.2007, p. 460-476.
Research output: Contribution to journal › Article › Research › peer review
}
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 -