VILSS: Ortho-diffusion decompositions of graph-based representations of images

Adrian Bors, University of York

In this presentation I introduce the ortho-diffusion operator. I consider graph-based data representations where full data interconnectivity is modelled using probability transition matrices. Multi-scale dimensionality reduction at different scales is used in order to extract the meaningful data representations. The QR orthonormal decomposition algorithm, alternating with diffusion and data reduction stages is applied recursively at each scale level for the given data representation. Columns in the ortho-diffusion representation matrix represent characteristic features of the data. Those columns that are not considered essential for the data representation are removed at each scale. The proposed methodology is used to model features extracted from images which are then used for image matching and face recognition. Image matching is applied to optical flow estimation from image sequences. For the face recognition application I consider both global appearance models, based on either the correlation or the covariance of training sets, as well as semantic representations of biometric features. The proposed methodology is shown to be robust in face classification applications when considering image corruption by various noise statistics.