DETECTION OF ROTATIONALLY SYMMETRICAL SHAPE ORIENTATIONS BY FOLD-INVARIANT SHAPE-SPECIFIC POINTS

Abstract

Two new types of shape-specific points, called fold-invariant centroid (FIC) and fold-invariant radius weighted mean (FIRWM), are introduced for detecting the orientations of rotationally symmetric shapes. A given rotationally symmetric shape is first transformed into a new fold-invariant shape. The centroid and the radius weighted mean of the new shape are then transformed back to obtain the proposed FIC and FIRWM, respectively. FIC and FIRWM points are proved to be invariant to translation, rotation and scaling, and so can be used for matching rotationally symmetric shapes. Using the proposed fold-invariant shape-specific points to detect the orientations of rotationally symmetric shapes is easier to implement than that of using the fold principal axes. Some illustrative examples and a method to avoid the case where the proposed fold-invariant shape-specific points are too close to the centroid are also given.