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Orthogonal Neighborhood Preserving Projections (ONPP) is a linear dimensionality reduction technique which attempts to preserve both the intrinsic neighborhood geometry of the data samples and the global geometry. The proposed technique constructs a weight ...
The aim of this dissertation is to solve numerically the following problem, denoted by P : given a Riemannian manifold and two points a and b belonging to that manifold, find a tangent vector T at a, such that expa(T) = b, assuming that T exists. This prob ...
Transformation-invariant analysis of signals often requires the computation of the distance from a test pattern to a transformation manifold. In particular, the estimation of the distances between a transformed query signal and several transformation manif ...
Institute of Electrical and Electronics Engineers2011
The characterization of signals and images in manifolds often lead to efficient dimensionality reduction algorithms based on manifold distance computation for analysis or classification tasks. We propose in this paper a method for the discretization of sig ...
We propose a segmentation method based on the geometric representation of images as surfaces embedded in a higher dimensional space, handling naturally multichannel images. The segmentation is based on an active contour embedded in the image manifold, alon ...
Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2011
Transformation invariance is an important property in pattern recognition, where different observations of the same object typically receive the same label. This paper focuses on a transformation invariant distance measure that represents the minimum dista ...
Over the past few decades we have been experiencing a data explosion; massive amounts of data are increasingly collected and multimedia databases, such as YouTube and Flickr, are rapidly expanding. At the same time rapid technological advancements in mobil ...
Transformation manifolds are quite attractive for image analysis applications that require transformation invariance properties. The geometric structure of a transformation manifold has a profound influence on the design of processing algorithm, and the cu ...
This paper addresses the problem of image alignment based on random measurements. Image alignment consists of estimating the relative transformation between a query image and a reference image. We consider the specific problem where the query image is prov ...
The subject of this thesis lies in the intersection of differential geometry and functional analysis, a domain usually called global analysis. A central object in this work is the group Ds(M) of all orientation preserving diffeomorphisms of a compact manif ...
