Combinatorial optimization for fitting of digital line and plane

Abstract : We present a method for fitting a digital line/plane from a given set of 2D/3D grid points. In the framework of discrete geometry, a digital line or plane is defined as a set of grid points located between two parallel lines or planes separated by a small distance. Our purpose is to identify such a pair of Euclidean lines/planes that represents a given set of points. This problem is formulated as a mixed integer/linear programming problem, with the objective to maximize the number of points between the two lines/planes.