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SPATIOTEMPORAL ANALYSIS WITH ST HELIXES 
Anthony Stefanidis Kristin Eickhorst Peggy Agouris 
Dept. of Spatial Information Science and Engineering 
348 Boardman Hall, University of Maine, USA 
(tony, snoox, peggy } @spatial.maine.edu 
Commission IV, WG IV/1 
KEY WORDS: GIS, Modelling, Management, Database, Query, Multitemporal 
ABSTRACT: 
Efficient modelling of spatiotemporal change as it is depicted in multitemporal imagery is an important step towards the efficient 
analysis and management of large motion imagery (MI) datasets. Furthermore, the development of concise representation schemes 
of MI content is essential for the search, retrieval, interchange, query, and visualization of the information included in MI datasets. 
Towards this goal this paper deals with the concise modelling of spatiotemporal change as it is captured in collections of MI data, 
and the development of spatiotemporal similarity metrics to compare the evolution of different objects. Helixes represent both 
movement and deformation in a single concise model, and are therefore highly suitable to communicate the evolution of phenomena 
as they are captured e.g. in sequences of imagery. This integration of movement and deformation information in a single model is an 
extension of existing solutions, and is highly suitable for the summarization of motion imagery datasets, especially within the 
context of geospatial applications. In this paper we present the spatiotemporal helix model, its use to support spatiotemporal queries, 
and spatiotemporal similarity metrics for the comparison of helixes. These metrics allow us to compare the behavior of different 
objects over time, and express the degree of their similarity. To support these comparisons we have developed a set of mobility state 
transition (MST) cost metrics that express dissimilarity as a function of differences in state. In the full paper we present these models 
in detail, and proceed with experimental results to demonstrate their use in spatiotemporal analysis. 
1. INTRODUCTION The paper is organized as follows. Section 2 of this paper 
details the spatiotemporal helix itself, and section 3 presents 
The image processing community has been dealing with issues metrics for comparing multiple helixes. Helix aggregation is 
of object representation for many years. Of particular interest discussed in section 4. In Section 5 we demonstrate the 
are techniques that model the changes that an object undergoes implementation of the algorithms discussed in previous 
over time. Motion Imagery (MI) analysis makes use of video sections, and present experiments on noise removal, boundary 
feeds or multitemporal sequences of static images, and thus is reconstruction, and computational time for similarity queries. 
typically addressing object tracking over time. Storing such We conclude with our future plans. 
spatiotemporal information imposes obvious challenges related 
to the involved amount of data, and the complexity of 
spatiotemporal variations. Lifelines (Plaisant, Milash et al. 2. THE SPATIOTEMPORAL HELIX 
1996; Hornsby and Egenhofer 2002) and video summarization 
programs (Pope, Kumar et al. 1998; Zhou, Ong et al. 2000) Spatiotemporal (ST) helixes are models of spatiotemporal 
represent some approaches developed in the GIS database and variations. A spatiotemporal helix comprises a central spine and 
image processing communities to model spatiotemporal annotated prongs (Figure 1). More specifically: 
information. 
— The central spine models the spatiotemporal trajectory 
(movement) described by the center of the object as it 
In order to accommodate the particularities of motion imagery ; 
moves during a temporal interval. 
databases we have recently introduced the spatiotemporal (ST) 
helix as a modelling and generalization tool for spatiotemporal — The protruding prongs express expansion or collapse 
information handling (Stefanidis, Agouris et al. 2002; Agouris (deformation) of the object's outline at a specific time 
and Stefanidis 2003). Helixes differ from other approaches in instance. 
that they not only capture the movement of an object's center of 
mass, but also incorporate information about changes in its 
outline. Furthermore, they allow us to identify critical instances 
in an object's history, and support metric analysis. Thus they 
are more than just a visualization mechanism, and incorporate 
databases and data storage techniques that allow the user to 
query for particular object behaviours. In this paper we provide 
an overview of our spatiotemporal helix model, and the ST 
comparison metrics we developed. 
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