Polygon interior point query and applications

In computer vision and image processing, when dealing with image segmentation, edge detection, shape detection and particularly for pattern recognition, it is sometimes interesting and even necessary to know whether a given point is inside or outside a closed polygon. This will enable us to detect objects (or shapes) that are enclosed within a given closed contour. But this is not a trivial task and since we are, generally, concerned with discrete contours, the solution and its performance are dependant on the connectness of the vertices of the contour and on their number. In this paper, we present two new methods for interior point query: the first one is based on Cauchy´s theorem of closed curves in the complex plan. The second proposed method, the “point insertion” method, is a heuristic approach. The proposed solutions are evaluated based on practical applications like polygon filling, polygons intersection detection and freeform cropping of images. Experimental results indicate that the proposed methods yield interesting performance. For low mean distance between consecutive vertices, both methods are equivalent in terms of polygon filling performance but the method of “point insertion” is faster. When this distance increases, the method based on Cauchy´s theorem outperforms with almost zero error.