Polygonal model fitting

The celebrated minimum inertia line problem is reconsidered: a line is to b e fitted to a planar cloud of points so that the sum of squared distances o f all points to the line becomes minimal. The classical algebraic solution based on the tensor of inertia is complemented by a closed form trigonometr ic solution allowing various generalizations including the fit of elastic p olygons. Proper polygons will be fitted numerically with non-closed partial solutions being reduced to the lowest dimension possible. This is compleme nted by segmentation heuristics for the measurement cloud. The approach allows to solve the robot localization problem with high accur acy for position and orientation to be inferred from distance measurements in a known polygonal environment. The essential feature of the current appr oach is to fit the polygonal geometry as a whole.