Affine-Invariant Triangulation of Spatio-Temporal Data with an Application to Image Retrieval

In the geometric data model for spatio-temporal data, introduced by Chomicki and Revesz , spatio-temporal data are modelled as a finite collection of triangles that are transformed by time-dependent affinities of the plane. To facilitate querying and animation of spatio-temporal data, we present a normal form for data in the geometric data model. We propose an algorithm for constructing this normal form via a spatio-temporal triangulation of geometric data objects. This triangulation algorithm generates new geometric data objects that partition the given objects both in space and in time. A particular property of the proposed partition is that it is invariant under time-dependent affine transformations, and hence independent of the particular choice of coordinate system used to describe the spatio-temporal data in. We can show that our algorithm works correctly and has a polynomial time complexity (of reasonably low degree in the number of input triangles and the maximal degree of the polynomial functions that describe the transformation functions). We also discuss several possible applications of this spatio-temporal triangulation. The application of our affine-invariant spatial triangulation method to image indexing and retrieval is discussed and an experimental evaluation is given in the context of bird images

Detection and Generalization of Spatio-temporal Trajectories for Motion Imagery

In today\u27s world of vast information availability users often confront large unorganized amounts of data with limited tools for managing them. Motion imagery datasets have become increasingly popular means for exposing and disseminating information. Commonly, moving objects are of primary interest in modeling such datasets. Users may require different levels of detail mainly for visualization and further processing purposes according to the application at hand. In this thesis we exploit the geometric attributes of objects for dataset summarization by using a series of image processing and neural network tools. In order to form data summaries we select representative time instances through the segmentation of an object\u27s spatio-temporal trajectory lines. High movement variation instances are selected through a new hybrid self-organizing map (SOM) technique to describe a single spatio-temporal trajectory. Multiple objects move in diverse yet classifiable patterns. In order to group corresponding trajectories we utilize an abstraction mechanism that investigates a vague moving relevance between the data in space and time. Thus, we introduce the spatio-temporal neighborhood unit as a variable generalization surface. By altering the unit\u27s dimensions, scaled generalization is accomplished. Common complications in tracking applications that include occlusion, noise, information gaps and unconnected segments of data sequences are addressed through the hybrid-SOM analysis. Nevertheless, entangled data sequences where no information on which data entry belongs to each corresponding trajectory are frequently evident. A multidimensional classification technique that combines geometric and backpropagation neural network implementation is used to distinguish between trajectory data. Further more, modeling and summarization of two-dimensional phenomena evolving in time brings forward the novel concept of spatio-temporal helixes as compact event representations. The phenomena models are comprised of SOM movement nodes (spines) and cardinality shape-change descriptors (prongs). While we focus on the analysis of MI datasets, the framework can be generalized to function with other types of spatio-temporal datasets. Multiple scale generalization is allowed in a dynamic significance-based scale rather than a constant one. The constructed summaries are not just a visualization product but they support further processing for metadata creation, indexing, and querying. Experimentation, comparisons and error estimations for each technique support the analyses discussed

Concepts for the Representation, Storage, and Retrieval of Spatio-Temporal Objects in 3D/4D Geo-Informations-Systems

The quickly increasing number of spatio-temporal applications in fields like environmental management or geology is a new challenge to the development of database systems. This thesis addresses three areas of the problem of integrating spatio-temporal objects into databases. First, a new representational model for continuously changing, spatial 3D objects is introduced and transferred into a small system of classes within an object-oriented database framework. The model extends simplicial cell complexes to the spatio-temporal setting. The problem of closure under certain operations is investigated. Second, internal data structures are introduced that represent instances of the (user-level) spatio-temporal classes. A new technique provides a compromise between compact storage and efficient retrieval of spatio-temporal objects. These structures correspond to temporal graphs and support updates as well as the maintainance of connected components over time. Third, it is shown how to realise further operations on the new type of objects. Among these operations are range queries, intersection tests, and the Euclidean distance function

A Geometric Framework for Specifying Spatiotemporal Objects

We present a framework for specifying spatiotemporal objects using spatial and temporal objects, and a geometric transformation. We define a number of classes of spatiotemporal objects and study their closure properties. 1 Introduction Many natural or man-made phenomena have both a spatial and a temporal extent. Consider for example, a forest fire or property histories in a city. To store information about such phenomena in a database one needs appropriate data modeling constructs. We claim that a new concept, spatiotemporal object, is necessary. In this paper, we introduce a very general framework for specifying spatiotemporal objects. To define a spatiotemporal object we need a spatial object, a temporal object, and a continuous geometric transformation (specified using a parametric representation) that determines the image of the spatial object at different time instants belonging to the temporal object. In this framework, a number of classes of spatiotemporal objects arise quite ..