A boundary-line method for pattern recognition on real particles

In this paper, an algorithm based on boundary-line analysis is developed for the first time to directly recognize polygon shapes with or without concaved angles and without any pre-stored shape templates. The algorithm is also capable of quantitatively characterizing an irregular shape by calculating a similarity number between the subject shape and a comparison polygon shape that is automatically constructed based on the subject shape features. The algorithm first generates an r–L curve from the shape boundary line by plotting the distance (r) between a point on the shape boundary line and the shape center as a function of accumulated boundary length (L). The algorithm then performs first and second derivatives on the r-L curve to find all peak/valley positions, peak-to-peak and peak-to-valley distances. Thus, our algorithm can directly recognize a polygon shape, since the number of peaks equals the number of polygon sides and a peak-to-peak distance equals a polygon side length. In addition, the peak height defines the sideʹs relative orientation if there is no valley corresponding to a concaved angle on the shape. If some valleys are at concaved angles, the number of polygon sides equals the number of peaks plus the number of valleys at concaved angles, and the polygon side length equals the peak-to-valley distance for the valley at a concaved angle. Our algorithm identifies convex/concave angles based on the positive or negative value of the bend angle at the valley point. The algorithm is tested satisfactorily using idealized polygons and real particles of salt, sugar and pharmaceutical powders.