Conversion between the vector and raster data structures using Fuzzy Geographical Entities

Cidália Fonte
Department of Mathematics
Faculty of Sciences and Technology
University of Coimbra, Apartado 3008, 3001 – 454 Coimbra, Portugal
Tel.: + 351 239 791150; Fax: + 351 239 832568
cfonte@mat.uc.pt

Abstract
The conversion of geographical entities between the raster and vector data structures introduces errors in the entities position. The vector to raster conversion results in a loss of information, since, when a Boolean classification of each pixel is used, the entities shape must follow the shape of the pixels. Thus, the information about the position of the entities in the vector data structure is lost with the conversion. This loss can be minimized if, instead of making a Boolean classification of the pixels, a fuzzy classification is performed, building Fuzzy Geographical Entities. These entities keep, for each pixel, the information about the pixel area that was inside the vector entities and therefore only the information about the position of the entities boundaries inside the pixels is lost. The Fuzzy Geographical Entities obtained through the previous conversion may be converted back to the vector data structure. An algorithm was developed to reconstruct the boundaries of the vector geographical entities using the information stored in the raster Fuzzy Geographical Entities. Since the grades of membership represent partial membership of the pixels to the entities, this information is valuable to reconstruct the  entities boundaries in the vector data structure, generating boundaries of the obtained vector entities that are as close as possible to their original position. Even though slight changes on the entities shape and position are expected after the re-conversion to the vector data structure, when Fuzzy Geographical Entities are used, the entities areas are always kept during successive conversions between both structures. Moreover, if the conversion and re-conversion methods are successively applied considering the same pixel, size, origin and orientation, the obtained results are always identical, that is, the positional errors introduce will not propagate indefinitely.

Keywords: vector to raster conversion, raster to vector conversion, fuzzy geographical entities, positional error, error propagation

In: Caetano, M. and Painho, M. (eds). Proceedings of the 7th International Symposium on Spatial Accuracy Assessment in Natural Resources and Environmental Sciences, 5 – 7 July 2006, Lisboa, Instituto Geográfico Português

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