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A novel 2-D method for computing the convex hull of a sufficiently dense setof n integer points is introduced. The approach employs a ranking function thatavoids sorting the points directly thus reducing the overall time complexity.The ranked points create a simple polygonal chain from which the Convex Hullcan be found using a suitable O(n) method. The result is achieved by placing abound on the density (or ratio) of points to m, where m is the maximum value ofthe ranking function required to represent the set of points yielding an O(n+m)method. A fast method is then developed based on the bit length, p, of the dataset which reduces this time further. The required conditions are easilysatisfied by image processing methods which determine the Hulls of polygonalregions where the densities are in the range of 3%. Our experiments on a rangeproblem domains show that this is not atypical. Since the complexity of themethod is related to the bit size p for current machines (p=32, p=64) themethod is for all practical purposes O(n). A short proof is provided.

A Rank-based Convex Hull method for Dense Data Sets