DOI: 10.5593/SGEM2016/B23/S11.033

# GEOREFERENCING APPLYING WEIGHTING COEFFICIENTS FOR LEAST SQUARES METHOD ADJUSTMENT

J.Havlicek
Friday 9 September 2016

References: 16th International Multidisciplinary Scientific GeoConference SGEM 2016, www.sgem.org, SGEM2016 Conference Proceedings, ISBN 978-619-7105-60-5 / ISSN 1314-2704, June 28 - July 6, 2016, Book2 Vol. 3, 255-262 pp

ABSTRACT
The article describes one of the problematic aspects of georeferencing old maps. It is the issue of weighting coefficients for ground control points. A certain number of ground control points always enters the transformation calculation. If global transformation methods are used, the adjustment applying the method of least squares is made in the case of a redundant number of ground control points available. The redundant number of ground control points always guarantees the check of the selection of these points. In the case that the standard positional deviation differs by an order, this point is suspicious and it should be eliminated from the calculation after the verification. The remaining ground control points vary by their different standard positional deviation. Ground control points should preferably be evenly distributed throughout the overall map drawing. The points are chosen on clearly identifiable objects on both the local and the reference map. The choice is always easier in urban areas. In rural areas, it mostly falls on road crossings, changes in the vegetation cover on land parcels or the confluence of rivers. These ground control points tend to have worse accuracy. The introduction of weighting coefficients is only suitable for global transformation methods. A source code has been created in the Matlab programme, which first calculates the classical affine or the second order polynomial transformation. At each point, the coordinate and positional difference from the coordinates identified during the collection of ground control points is calculated. Weighting coefficients are selected in two ways. The first way to determine the weighting coefficient is by the inverse absolute value of this coordinate difference. The other option for both coordinates of one control point is the weighting coefficient which equals the inverse of the positional difference. Georeferencing applying weighting coefficients is more appropriate for the result as the map is placed in the reference coordinate system with an emphasis on the ground control point accuracy. The points with a smaller coordinate/positional difference have a greater effect on the calculation, while points with a greater coordinate/positional differences affect the calculation to a lesser extent.

Keywords: georeferencing, transformation, old maps, weighting coefficients.

PAPER DOI: 10.5593/SGEM2016/B23/S11.033, GEOREFERENCING APPLYING WEIGHTING COEFFICIENTS FOR LEAST SQUARES METHOD ADJUSTMENT