Colocalization structures and eigenvalue spectra for colour image comparison

摘要

Eigenvalue spectra of the Laplace-Beltrami operator have successfully been employed as fingerprints for shape and image comparison. Especially notable in this context is the work of Peinecke on Laplace spectrum fingerprinting for image data. Recently, new research on greyscale images by Berger et al. introduces the idea of attributing individual eigenfunctions to image parts and describes a mechanism for controlling their localisation. These parts are separated by sufficiently strong variations of grey value, giving the originally global fingerprint a semi-local character. This paper provides an approach to extend this idea to colour images so that not only gradients of brightness but also gradients of hue or chroma lead to localisation of eigenfunctions. This is accomplished by generalising the eigenfunctions to -valued functions and mapping the colours to symmetric -matrices. The resulting matrix field is then used to modify the Laplacian. Finally, we present a distance function for comparing eigenvalue-based fingerprints that makes use of eigenfunction colocalization information.