Least squares regression model for generalization of multiple lines (Case study: Zerivar Lake)

The most basic linear regression model, also known as the base model for Linear Regression, is LS (Least Squares) Regression. LS regression is a statistical technique for minimizing the sum of square differences between observed and predicted values. With the help of LS, it is possible to fit the best line to the features in the field of feature generalization. The aim of this summarization is to maintain the geometry and area while reducing the details. In this research, the least squares regression was used to generalize multiple lines with the aim of minimizing the distance from the main line. In order to study the proposed model, after its implementation on different shapes, the multi-lines of Zerivar Lake were summarized and the results of the proposed model were compared with the common Douglas-Poker and Viswalingam methods. To evaluate the results, the indices of area differences, mean curvature similarity, similarity of the angle changes, and the corrected median Hausdorff distances were used. Based on the first three metrics, the proposed model performed around ۱۲ to ۱۴ percent better. However, the corrected Hasdroff distance index shows that it performed about ۵ meters worse than the other approaches, which is indicative of the fact that it did not depend on the feature's initial points.

کلیدواژه ها:

LS ، Cartography ، Generalization ، Summarization