Mass Density Laplace-Spectra for Image Recognition

Abstract

Modern multimedia applications generate vast amounts of image data. With the availability of cheap photo hardware and affordable rendering software even more such data is being collected. In order to manage huge collections of image data one needs short representations of the data sets, or to be more precise invariant features being appropriate to identify a specific voxel data set using just a few numbers. This paper describes a variation of a method introduced by Reuter, Wolter and Peinecke based on the computation of the spectrum of the Laplace operator for the image for generating an invariant feature vector - a fingerprint. Oppose to previous techniques interpreting the image as a height function we make use of the representation of the image as a density function. We discuss the use of the spectrum of eigenvalues of the Laplace mass density operator as a fingerprint and show the usability of this approach in several cases. Instead of using the discrete Laplace-Kirchhoff operator the approach presented in this paper is based on the continuous Laplace operator allowing better results in comparing the resulting spectra and deeper insights into the problems arising when comparing two spectra generated using discrete Laplacians.