We introduce observation frames as an extension of ordinary frames. The aim is to give an abstract representation of a mapping from observable predicates to all predicates of a specific system. A full subcategory of the category of observation frames is shown to be dual to the category of F! topological spaces. The notions we use generalize those in the adjunction between frames and topological...

We are interested here in wavelet frames and their construction via multiresolution analysis (MRA); of particular interest to us are tight wavelet frames. The redundant representation offered by wavelet frames has already been put to good use for signal denoising, and is currently explored for image compression. Motivated by these and other applications, we explore in this article the theory of...

Current work on sentiment analysis is characterized by approaches with a pragmatic focus, which use shallow techniques in the interest of robustness but often rely on ad-hoc creation of data sets and methods. We argue that progress towards deep analysis depends on a) enriching shallow representations with linguistically motivated, rich information, and b) focussing different branches of researc...

This paper proposes a novel memory-based online video representation that is efficient, accurate and predictive. This is in contrast to prior works that often rely on computationally heavy 3D convolutions, ignore actual motion when aligning features over time, or operate in an off-line mode to utilize future frames. In particular, our memory (i) holds the feature representation, (ii) is spatial...

Wavelet packets provide a flexible representation of data, which has been proved to be very useful in a lot of applications in signal, image and video processing. In particular, in image and video coding, their ability to best capture the input content features can be exploited by designing appropriate optimization criteria. In this paper, we introduce joint wavelet packets for groups of frames...

This paper is concerned with the construction of generalized Banach frames on homogeneous spaces. The major tool is a unitary group representation which is square integrable modulo a certain subgroup. By means of this representation, generalized coorbit spaces can be defined. Moreover, we can construct a specific reproducing kernel which, after a judicious discretization, gives rise to atomic d...

A framework for video content representation is proposed in this paper for extracting limited, but meaningful, information of video data directly from MPEG compressed domain. First, the traditional frame-based representation is transformed to a feature-based one. Then, all features are gathered together using a fuzzy formulation and extraction of several key frames is performed for each shot in...

partial frames provide a rich context in which to do pointfree structured and unstructured topology. a small collection of axioms of an elementary nature allows one to do much traditional pointfree topology, both on the level of frames or locales, and that of uniform or metric frames. these axioms are sufficiently general to include as examples bounded distributive lattices, $sigma$-frames, $ka...

Reference frames are important for understanding sensory processing in the cortex. Previous work showed that vestibular heading signals in the ventral intraparietal area (VIP) are represented in body-centered coordinates. In contrast, vestibular heading tuning in the medial superior temporal area (MSTd) is approximately head centered. We considered the hypothesis that visual heading signals (fr...