Abstract
Sometimes it is necessary to know the transformation to apply to a mapping shape in order to locate its true place. Such an operation can be computed if a corresponding reference object exists and we can identify corresponding points in both shapes. Nevertheless our approach does not need to match any corresponding point beforehand. The method proposed defines a polygon in the frequency domain—two periodic functions are derived from a polygonal or polygon. According to the theory of elliptic Fourier descriptors those two periodic functions can be expressed by Fourier expansions. The transformation can be computed using the coefficients of the harmonics from the corresponding shapes without taking into account where each polygon vertex is placed in the spatial domain. The transformation parameters will be derived by a least squares approach. The geomatics and geosciences applications of this method go from photogrammetry, geographic information system, computer vision, to cadaster and real estates.
Highlights
Transformation operations are usual in geomatic and geosciences, in mapping and survey fields
Transformation operations applied to a mapping shape is a frequent task in geosciences and geomatic fields
In this paper we have focused on the case of two corresponding polygons, which have small differences in their shapes they are more or less similar
Summary
Transformation operations are usual in geomatic and geosciences, in mapping and survey fields. Most GIS (Geographical Information Systems) incorporate functions to compute transformation between planar shapes (vector format) and images (raster format). Such transformations depends on the applications requirements and they might involve similarity, affine or projective parameters computation. Digital photogrammetry is a field where matching techniques have been studied most intensively—from shape based stereo-matching [5,6], to features point-based matching [7]; interesting are the geometrical transformations applications shown in Reference [8], which implies an important remark in photogrammetry. Some methods based on moment and correlation for measuring shape change have been developed and applied to images [9,10]
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