- Chinese name
- Minkowski sum, Minkowski addition, expansion
- Foreign name
- Mincowsky sum;Mincowski addition;Dilation
- Discipline
- Topology, manifold, geometry, graphics
Minkowski sum It's two Euclidean space The sum of the point sets of, also known as the expansion sets of these two spaces Minkowski Naming. Minkowski sum of point sets A and B is defined as: For example, there are two triangle , which coordinate A={(1,0), (0,1), (0, - 1)} and B ={(0, 0), (1, 1), (1, − 1)}, then its Minkowski sum is A + B = {(1, 0), (2, 1), (2, −1), (0, 1), (1, 2), (1, 0), (0, −1), (1, 0), (1, −2)}。 If it is extended to the continuous set of manifold, Minkowski sum is the union of the region swept by A set in a continuous motion along the edge of B and B set itself, or it can be the union of the region swept by B in a continuous motion along the edge of A and A itself. According to the definition of Minkowski sum, if the algebraic system of set elements satisfies Abelian group (addition is exchangeable), Minkowski and also meet the exchange law: Barbier Theorem for Proving the Perimeter of Constant Width Graph
Dilation and erosion transformation of image
