Robust reorientation of 2D shapes using the orientation indicator index

Shape reorientation is a critical step in many image processing and computer vision applications such as registration, detection, identification, and classification. Shape reorientation is a needed step to restore the correct orientation of a shape when its image is subject to an arbitrary rotation and reflection. In this paper, we present a robust method to determine the standard "normalized" orientation of two-dimensional (2D) shapes in a blind manner, i.e., without any other information other than the given input shape. We introduce a set of orientation indicator indices (OII) that use low order central moments of the shape to monitor the orientational characteristics of the shape. Because these OH's use only low (up to third) order moments, they are robust to noise and errors. We show with examples how we bring consistently a given shape with an unknown arbitrary orientation to its standard normalized orientation using the OII.