Summary: THE 2D ORIENTATION IS UNIQUE THROUGH PRINCIPAL MOMENTS ANALYSIS
Jo~ao F. P. Crespo, Pedro M. Q. Aguiar
Institute for Systems and Robotics / IST, Lisboa, Portugal
When comparing 2D shapes, a key issue is their normalization.
Translation and scale are easily taken care of by removing the mean
and normalizing the energy. However, defining and computing the
orientation of a 2D shape is not so simple. In fact, although for
elongated shapes the principal axis can be used to define one of two
possible orientations, there is not such a tool for general shapes.
As we show in the paper, previous approaches fail to compute the
orientation of even noiseless observations of simple shapes. We
address this problem. In the paper, we show how to uniquely define
the orientation of an arbitrary 2D shape, in terms of what we call its
principal moments. We further propose a new method to efficiently
compute the shape orientation: Principal Moments Analysis. Be-
sides the theoretical proof of correctness, we describe experiments
demonstrating robustness to noise and illustrating with real images.
Index Terms-- Image shape analysis, Moment methods