A new efficient algorithm for fitting of rectangles and squares

In this paper, we introduce a completely new approach to fitting rectangles and squares to given closed regions using our published ideas in Rothe et al. (1996), Voss and Suesse (1997, 1999). In these papers, we have developed a new region-based fitting method using the method of normalization. There we demonstrate the zero-parametric fitting of lines, triangles, parallelograms, circles and ellipses, and the one-parametric fitting of elliptical segments, circular segments and super-ellipses. In the present paper, we discuss this normalization idea for fitting of closed regions using rectangles and squares. As features we use the area-based low order moments. The main problem is a stable normalization of the rotation. We show that we have to solve only an one-dimensional optimization problem in the case of rectangles. In the case of squares there are no free parameters to determine. The presented algorithm is used in practice for document recognition.