Fusion frames are valuable generalizations of discrete frames. Most concepts of fusion frames are shared by discrete frames. However, the dual setting is so complicated. In particular, unlike discrete frames, two fusion frames are not dual of each other in general. In this paper, we investigate the structure of the duals of fusion frames and discuss the relation between the duals of fusion fram...

We develop a natural generalization of vector-valued frame theory, which we term operator-valued frame theory, using operator-algebraic methods. This extends work of the second author and D. Han which can be viewed as the multiplicity one case and extends to higher multiplicity their dilation approach. We prove several results for operator-valued frames concerning duality, disjointedness, compl...

We propose an innovative, general purpose, method to the selection and hierarchical representation of key frames of a video sequence for video summarization. It is able to create a hierarchical storyboard that the user may easily browse. The method is composed by three different steps. The first removes meaningless key frames, using supervised classification performed by a neural network on the...

In this paper we introduce a block-classified bidirectional motion compensation scheme for our previously developed wavelet-based video codec [24,25], where multiresolution motion estimation is performed in the wavelet domain. The frame classification structure described in this paper is similar to that used in the MPEG standard. Specifically, the I-frames are intraframe coded, the P-frames are...

The aim of this paper is to investigate symmetry properties of tight frames, with a view to constructing tight frames of orthogonal polynomials in several variables which share the symmetries of the weight function, and other similar applications. This is achieved by using representation theory to give methods for constructing tight frames as orbits of groups of unitary transformations acting o...

Linguists have been using different kinds of frame representation since the emergence of the notion “frame”. The main goal of the annotation system described in this paper is to provide an interactive and easy-to-use tool for structuring concept-specific information in linguistic frames for discourse analysis or cultural studies. These frames take into account background or “world” knowledge as...

This paper is a survey of research in discrete expansions over the last 10 years, mainly of functions in L 2 (R). The concept of an orthonormal basis {fn}, allowing every function f ∈ L 2 (R) to be written f = cnfn for suitable coefficients {cn}, is well understood. In separable Hilbert spaces, a generalization known as frames exists, which still allows such a representation. However, the coeff...

In this paper we present an approach for generation and initialization of fuzzy neural networks (FNN) from data. Fuzzy neural networks are concept that integrates some features of the fuzzy logic and the artificial neural networks theory. Based on analysis of several different fuzzy neural networks models, uniform representation method is presented, and two basic types are identified: FNN based...

This paper describes Atlas, a hybrid metrical/topological approach to SLAM that achieves efficient mapping of large-scale environments. The representation is a graph of coordinate frames, with each vertex in the graph representing a local frame, and each edge representing the transformation between adjacent frames. In each frame, we build a map that captures the local environment and the curren...