M.Sc Student | Omer Bar |
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Subject | Non-Linear Transformations between Cartographic Maps: A Model for a Continuous Correction Surface |

Department | Department of Civil and Environmental Engineering |

Supervisor | Professor Emeritus Doytsher Yerach |

Full Thesis text |

This research studies the mutual-geo-registration between two maps, one of which has a fully known coordinate-system, while the other lacks its coordinate-system parameters. In order to register one map to the other a coordinate transformation must be available; which holds the parameters enclosed in the coordinate-systems of both maps (Datum and Projection types and parameters). Since one of the maps in this study lacks some of its coordinate-system parameters, a full mathematical coordinate transformation is impossible to create; thus the position transformation between the maps relies on cartographic points of interest on those maps, for example: junctions, historic landmarks, etc.

In order to re-register the map without full coordinate-system parameters an image registration process is used. The traditional image registration process is executed by pairing two datasets of homological interest points extracted from the images. Matching the homological points from two datasets is preformed in this research using Triangular Irregular Network (TIN) created from the points' datasets. The matching of triangles is more geometrically stable than matching points, especially when noise has to be detected and removed from the datasets.

Matching the triangles is conducted using an iterative process, which is based upon two similarity measurements: (1) Hausdorff Distances, and (2) “Euler numbers” for geometric similarity index. The iterative process helps to remove any noise existing in the point datasets, using an affine transformation between the points' datasets. Noise points are identified as “lonely”, meaning that they have no neighbor in the transformed-dataset.

Using the TIN matching, two interpolation surfaces are computed to obtain a position transformation from one point dataset to the other. The interpolation surfaces for position-transformation (one for easting and another for northing ordinates) result from the position differences of the points matched through the TIN matching process.

These interpolation surfaces have distinct bi-cubic interpolation properties: continuous, and the first order derivative is continuous as well. Bi-cubic interpolation is executed on gridded data; a modification was made to the traditional algorithm, to enable bi-cubic interpolation to run upon triangles (scattered) and not a grid.

A test case conducted in the research upon maps printed by Survey of Israel (2000) and British authorities (2004), showed a good connectivity to the registered map, with junctions’ position and roads extending on the same location. Nevertheless, errors occur in the resampling process from various cartographic issues, such as a fold in the middle of one map.