Applications of Diffusion Wavelets

Diffusion wavelets have been constructed on graphs in order to allow an efficient multiscale representation. This MSc thesis outlines how the diffusion wavelet framework can be
applied to dense and sparse optical fl
ow estimation as well as to the eigendiffusion faces for face recognition and fingerprint authentication. Diffusion wavelets are used for multiscale dimensionality reduction at different scales for feature representation.

Local image features are recorded by the extended bases scale functions at different scales calculated from the graph Laplacian. These features are then used in a dense as well as in a sparse optical
flow estimation algorithm. We also used the same multiscale extended bases method for getting the orthonormalized projections of the covariance matrix of the training set of faces or fingerprints and we called those projections as eigendiffusion faces. By using eigendiffusion faces we calculated the low dimensional space weight components which are used to recognise faces or fingerprints using the minimum Euclidean distance of
the weight vectors.

The proposed methodology was applied on various image sequences such as: Middlebury database, Hamburg taxi sequence, Andrea Hurricane image sequence, Infra-red meteosat image sequence, for image registration in a set of medical images of eye's cornea as well as for the ORL face databases, Yale face database, fingerprint verification competition dataset (FVC2000).