We propose a method for achieving a novel concise graph-based representation for retrieval of objects from large video data. The emphasis in this paper is towards achieving a compact representation of video data for faster retrieval. Specifically, we use information available from scripts and subtitles in order to group all occurrences of an object in video data, which provides a separate repre...

We discuss the concepts of pseudo-dual frames and approximately dual frames, and illuminate their relationship to classical frames. Approximately dual frames are easier to construct than the classical dual frames, and might be tailored to yield almost perfect reconstruction. For approximately dual frames constructed via perturbation theory, we provide a bound on the deviation from perfect recon...

This paper is concerned with the construction of atomic decompositions and Banach frames for subspaces of certain Banach spaces consisting of elements which are invariant under some symmetry group. These Banach spaces – called coorbit spaces – are related to an integrable group representation. The construction is established via a generalization of the well-established Feichtinger-Gröchenig the...

In this paper, we show how frames can be employed in the analysis 5 of genitive constructions. We model the main approaches in the discussion about 6 genitive constructions, i.e. the argument-only approach, the modifier-only approach 7 and the split approach. Of these three, the split approach is modeled most naturally 8 in frames. Thus, if frames are considered a cognitively adequate represent...

We have implemented a novel approach for robust ontology design from natural language texts by combining Discourse Representation Theory (DRT), linguistic frame semantics, and ontology design patterns. We show that DRT-based frame detection is feasible by conducting a comparative evaluation of our approach and existing tools. Furthermore, we define a mapping between DRT and RDF/OWL for the prod...

We present a comprehensive analysis of the convergence properties of the frame operators of Weyl-Heisenberg systems and shift-invariant systems, and relate these to the convergence of the Walnut representation. We give a deep analysis of necessary conditions and sufficient conditions for convergence of the frame operator. We show that symmetric, norm and unconditional convergence of the Walnut ...

In this paper we generalize the method of sweeping, which may be used for both object representation and object visualization, to objects in E 4. The generalized sweeping method involves a trajectory in E 4 , and a three-dimensional cross-section orthogonal to the trajectory. Three alternatives are considered for specifying the relationship between the trajectory and the cross-section, namely t...

In this paper, an efficient video content representation is proposed using optimal extraction of characteristic frames and scenes. This representation, apart from providing browsing capabilities to digital video databases, also allows more efficient content-based queries and indexing. For performing the frame/scene extraction, a feature vector formulation of the images is proposed based on colo...

In this paper, we introduce a unified theory of tight wavelet frames on non-flat domains in both continuum setting, i.e. on manifolds, and discrete setting, i.e. on graphs; discuss how fast tight wavelet frame transforms can be computed and how they can be effectively used to process graph data. We start from defining multiresolution analysis (MRA) generated by a single generator on manifolds, ...