



Mathematical frameworks supporting conflation problems
BAA Number NMA40102BAA0002
NIMA University Research Initiative (NURI)
Area 1: Mathematical Support to Data Conflation Issues
Secondary Areas:
Geospatial Data Integration
Image processing
Principal Investigator
Dr. Boris Kovalerchuk
Dept. of Computer Science
ABSTRACT
The primary objective of this project is the development of mathematical frameworks for characterizing the quality of conflated data relative to a given problem. This includes consideration of tasks related to NIMA's future operating environment such as: growing geospatial data from multiple sources, a variety of techniques for data generation, a variety of requested data combinations, and emerging data types. Specifically, this proposal will describe two mathematical frameworks. The algebraic invariants framework is the development of a new methodology along with a corresponding implementation that automates the correlation/registration of large satellite images at high speeds, giving them common scales and coordinates. The visual correlation framework offers multidimensional measures of the correctness of conflation with a visual presentation. The project concentrates on improving geospatial data representations by investigating methodologies and algorithms for conflation of disparate elevations, features, and image data sets.
The mathematical theory of algebraic invariants is a powerful new tool for combining and deconflicting geospatial data sets. It is ideally suited for integrating small patches of higher resolution elevation, digital terrain and urban site data with lower resolution digital terrain information, providing a common , fully coregistered coordinate system. When data sets contain conflicting information, algebraic invariants can quantify the differences and suggest possible resolutions.
The algebraic invariant framework also serves well as a core mathematical mechanism for the design of measures of data quality. Since there are no rigorous ways to conflate disparate data universally for all possible tasks, reliable measures of uncertainty are essential. For some tasks, distortion of data during conflation is acceptable, but for others the same distortion can prove disastrous. Appropriate taskspecific mathematical measures can serve as guardians for preserving attributes most critical for the problem at hand. When mathematical quality measures indicate that a conflation or combination is contradictory for a given task, a visual correlation framework can be used to make the contradictions clear and guide further investigation.
Our team of mathematicians, computer scientists, and geographical information specialists address these issues by:
 Developing and implementing a methodology for combining multisource and multiresolution spatial objects using the mathematical theory of algebraic invariants.
 Developing and implementing a methodology for deconflicting multisource geospatial data with disparate terrain elevations, locations, topologies, geospatial shapes, and feature classifications. A methodology will be developed and implemented for the two complimentary situations when extensive auxiliary quality information is available and for the case when little or no auxiliary quality information is available.
 Developing and implementing a me thodology for characterizing the quality of conflated data relative to a taskspecific problem by introducing measures of the correctness for the combination of geospatial data using algebraic invariants, integrating statistical and fuzzy logic measures, and providing a visual correlation framework to resolve ambiguities.
The algebraic theory and methods of visual correlation are described in detail and their specific relevance to the problems of combining/deconflicting geospatial data is illustrated with several examples.
