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Picture polynomial math depends on regarding a picture as raised as convex polygons (2d) or convex polyhedrons (3d). A generalized formula for the generation of total number of convex polygons and polyhedrons and total no of G-filters for a given structuring elements is explained in this paper.

Let P, where |P| ≥ 2, be a set of points in d-dimensional space with a given metric ρ. For a point p ∈ P, let rp be the distance of p with respect to ρ from its nearest neighbour in P. Let B(p, rp) be the open ball with respect to ρ centered at p and having the radius rp. We define the sphere-of-influence graph (SIG) of P as the intersection graph of the… (More)

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