We present a new compressed representation of free trajectories of moving objects. It combines a partial-sums-based structure that retrieves in constant time the position of the object at any instant, with a hierarchical minimum-bounding-boxes representation that allows determining if the object is seen in a certain rectangular area during a time period. Combined with spatial snapshots at regular intervals, the representation is shown to outperform classical ones by orders of magnitude in space, and also to outperform previous compressed representations in time performance, when using the same amount of space.
Spatio-temporal indexes can be classified into three types. The first is a classic multidimensional spatial index, usually the R-tree, augmented with a temporal dimension. For example, the 3DR-tree @cite_5 uses three-dimensional Minimum Bounding Boxes (MBBs), where the third dimension is the time, to index segments of trajectories. A second approach is the multiversion R-trees, which creates an R-tree for each timestamp and a B-tree to select the relevant R-trees. The best known index of this family is the MV3R-tree @cite_18 . The third type of index partitions the space statically, and then a temporal index is built for each of the spatial partitions @cite_7 .
@cite_5 @cite_18 @cite_7
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A spatio-temporal descriptor for representation and recognition of time-varying textures is proposed (binarized statis- tical image features on three orthogonal planes (BSIF-TOP)) in this paper. The descriptor, similar in spirit to the well known local binary patterns on three orthogonal planes approach, estimates histograms of binary coded image sequences on three orthogonal planes corresponding to spatial spatio-temporal dimensions. However, unlike some other methods which generate the code in a heuristic fashion, binary code generation in the BSIF-TOP approach is realized by filtering operations on different regions of spatial spatio-temporal support and by binarizing the filter responses. The filters are learnt via independent component analysis on each of three planes after preprocessing using a whitening transformation. By extending the BSIF-TOP descriptor to a multiresolution scheme, the descriptor is able to capture the spatio-temporal content of an image sequence at multiple scales, improving its representation capacity. In the evaluations on the UCLA, Dyntex, and Dyntex dynamic texture databases, the proposed method achieves very good performance compared to existing approaches. With the recent progress of spatial information technologies and mobile computing technologies, spatio-temporal databases which store information on moving objects including vehicles and mobile users have gained a lot of research in- terests. In this paper, we propose an algorithm to extract mobility statistics from indexed spatio-temporal datasets for the interactive analysis of huge collections of moving object trajectories. We focus on a mobility statistics value called the Markov transition probability, which is based on a cell-based organization of a target space and the Markov chain model. The pro- posed algorithm efficiently computes the specified Markov transition probabilities with the help of a spatial index R-tree. We reduce the statistics computation task to a kind of constraint satisfaction problem that uses a spatial index, and utilize internal This paper describes a generalized axiomatic scale-space theory that makes it possible to derive the notions of linear scale-space, affine Gaussian scale-space and linear spatio-temporal scale-space using a similar set of assumptions (scale-space axioms). The notion of non-enhancement of local extrema is generalized from previous application over discrete and rotationally symmetric kernels to continuous and more general non-isotropic kernels over both spatial and spatio-temporal image domains. It is shown how a complete classification can be given of the linear (Gaussian) scale-space concepts that satisfy these conditions on isotropic spatial, non-isotropic spatial and spatio-temporal domains, which results in a general taxonomy of Gaussian scale-spaces for continuous image data. The resulting theory allows filter shapes to be tuned from specific context information and provides a theoretical foundation for the recently exploited mechanisms of shape adaptation and velocity adaptation, with highly useful applications in computer vision. It is also shown how time-causal spatio-temporal scale-spaces can be derived from similar assumptions. The mathematical structure of these scale-spaces is analyzed in detail concerning transformation properties over space and time, the temporal cascade structure they satisfy over time as well as properties of the resulting multi-scale spatio-temporal derivative operators. It is also shown how temporal derivatives with respect to transformed time can be defined, leading to the formulation of a novel analogue of scale normalized derivatives for time-causal scale-spaces. The kernels generated from these two types of theories have interesting relations to biological vision. We show how filter kernels generated from the Gaussian spatio-temporal scale-space as well as the time-causal spatio-temporal scale-space relate to spatio-temporal receptive field profiles registered from mammalian vision. Specifically, we show that there are close analogies to space-time separable cells in the LGN as well as to both space-time separable and non-separable cells in the striate cortex. We do also present a set of plausible models for complex cells using extended quasi-quadrature measures expressed in terms of scale normalized spatio-temporal derivatives. The theories presented as well as their relations to biological vision show that it is possible to describe a general set of Gaussian and or time-causal scale-spaces using a unified framework, which generalizes and complements previously presented scale-space formulations in this area. Multivariate time series (MTS) classification has gained importance with the increase in the number of temporal datasets in different domains (such as medicine, finance, multimedia, etc.). Similarity-based approaches, such as nearest-neighbor classifiers, are often used for univariate time series, but MTS are characterized not only by individual attributes, but also by their relationships. Here we provide a classifier based on a new symbolic representation for MTS (denoted as SMTS) with several important elements. SMTS considers all attributes of MTS simultaneously, rather than separately, to extract information contained in the relationships. Symbols are learned from a supervised algorithm that does not require pre-defined intervals, nor features. An elementary representation is used that consists of the time index, and the values (and first differences for numerical attributes) of the individual time series as columns. That is, there is essentially no feature extraction (aside from first differences) and the local series values are fused to time position through the time index. The initial representation of raw data is quite simple conceptually and operationally. Still, a tree-based ensemble can detect interactions in the space of the time index and time values and this is exploited to generate a high-dimensional codebook from the terminal nodes of the trees. Because the time index is included as an attribute, each MTS is learned to be segmented by time, or by the value of one of its attributes. The codebook is processed with a second ensemble where now implicit feature selection is exploited to handle the high-dimensional input. The constituent properties produce a distinctly different algorithm. Moreover, MTS with nominal and missing values are handled efficiently with tree learners. Experiments demonstrate the effectiveness of the proposed approach in terms of accuracy and computation times in a large collection multivariate (and univariate) datasets.