A Mathematical Model for Simplifying Representations of Objects in a Geographic Information System

The study of operations on representations of objects is well documented in the realm of spatial engineering. However, the mathematical structure and formal proof of these operational phenomena are not thoroughly explored. Other works have often focused on query-based models that seek to order classes and instances of objects in the form of semantic hierarchies or graphs. In some models, nodes of graphs represent objects and are connected by edges that represent different types of coarsening operators. This work, however, studies how the coarsening operator "simplification" can manipulate partitions of finite sets, independent from objects and their attributes. Partitions that are "simplified first have a collection of elements filtered (removed), and then the remaining partition is amalgamated (some sub-collections are unified). Simplification has many interesting mathematical properties. A finite composition of simplifications can also be accomplished with some single simplification. Also, if one partition is a simplification of the other, the simplified partition is defined to be less than the other partition according to the simp relation. This relation is shown to be a partial-order relation based on simplification. Collections of partitions can not only be proven to have a partial- order structure, but also have a lattice structure and are complete. In regard to a geographic information system (GIs), partitions related to subsets of attribute domains for objects are called views. Objects belong to different views based whether or not their attribute values lie in the underlying view domain. Given a particular view, objects with their attribute n-tuple codings contained in the view are part of the actualization set on views, and objects are labeled according to the particular subset of the view in which their coding lies. Though the scope of the work does not mainly focus on queries related directly to geographic objects, it provides verification for the existence of particular views in a system with this underlying structure. Given a finite attribute domain, one can say with mathematical certainty that different views of objects are partially ordered by simplification, and every collection of views has a greatest lower bound and least upper bound, which provides the validity for exploring queries in this regard.

Digital Vertical Aerial Camera System for High-resolution Site Inspections in Conservation Easment Monitoring

A three-level satellite to ground monitoring scheme for conservation easement monitoring has been implemented in which high-resolution imagery serves as an intermediate step for inspecting high priority sites. A digital vertical aerial camera system was developed to fulfill the need for an economical source of imagery for this intermediate step. A method for attaching the camera system to small aircraft was designed, and the camera system was calibrated and tested. To ensure that the images obtained were of suitable quality for use in Level 2 inspections, rectified imagery was required to provide positional accuracy of 5 meters or less to be comparable to current commercially available high-resolution satellite imagery. Focal length calibration was performed to discover the infinity focal length at two lens settings (24mm and 35mm) with a precision of O.1mm. Known focal length is required for creation of navigation points representing locations to be photographed (waypoints). Photographing an object of known size at distances on a test range allowed estimates of focal lengths of 25.lmm and 35.4mm for the 24mm and 35mm lens settings, respectively. Constants required for distortion removal procedures were obtained using analytical plumb-line calibration procedures for both lens settings, with mild distortion at the 24mm setting and virtually no distortion found at the 35mm setting. The system was designed to operate in a series of stages: mission planning, mission execution, and post-mission processing. During mission planning, waypoints were created using custom tools in geographic information system (GIs) software. During mission execution, the camera is connected to a laptop computer with a global positioning system (GPS) receiver attached. Customized mobile GIs software accepts position information from the GPS receiver, provides information for navigation, and automatically triggers the camera upon reaching the desired location. Post-mission processing (rectification) of imagery for removal of lens distortion effects, correction of imagery for horizontal displacement due to terrain variations (relief displacement), and relating the images to ground coordinates were performed with no more than a second-order polynomial warping function. Accuracy testing was performed to verify the positional accuracy capabilities of the system in an ideal-case scenario as well as a real-world case. Using many welldistributed and highly accurate control points on flat terrain, the rectified images yielded median positional accuracy of 0.3 meters. Imagery captured over commercial forestland with varying terrain in eastern Maine, rectified to digital orthophoto quadrangles, yielded median positional accuracies of 2.3 meters with accuracies of 3.1 meters or better in 75 percent of measurements made. These accuracies were well within performance requirements. The images from the digital camera system are of high quality, displaying significant detail at common flying heights. At common flying heights the ground resolution of the camera system ranges between 0.07 meters and 0.67 meters per pixel, satisfying the requirement that imagery be of comparable resolution to current highresolution satellite imagery. Due to the high resolution of the imagery, the positional accuracy attainable, and the convenience with which it is operated, the digital aerial camera system developed is a potentially cost-effective solution for use in the intermediate step of a satellite to ground conservation easement monitoring scheme.