Enhanced Way for Computing Smallest Convex Polygon and Euler Number

A convex hull is a polygon which encloses all given set of points.Euler number or Euler characteristic of an image has proven to be an important feature in many image analyses and visual inspection applications. This paper presents an algorithm for fast computing the convex hull of a planar scattered point set, which pre-strike an initial convex hull boundary, remove internal points in the boundary which cannot be the minimum convex hull vertex points, improve the efficiency of computing the convex hull. Experimental analysis and comparison show that the algorithm has better time complexity and efficiency of obtaining the minimum convex hull. We present an algorithm for finding the convex hull of a sorted planar point set. This algorithm uses graham-scan for recognizing those points computing the smallest convex polygon and bresenham method to represent the computed smallest convex polygon. In this paper, we have also calculated the Euler number by using the concept of convexity and concavity. Convexity (or the convex number) N2 + (X, α) is defined as the number of first entries in a given direction α.Concavity (or the concave number) N2 -