Optimal consensus set for digital line and plane fitting

This paper presents a method for fitting a digital line (resp. plane) to a given set of points in a 2D (resp. 3D) image in the presence of outliers. One of the most widely used methods is Random Sample Consensus (RANSAC). However it is also known that RANSAC has a drawback: as maximum iteration number must be set, the solution may not be optimal. To overcome this problem, we present a new method that uses a digital geometric model for lines and planes in a discrete space. Such a digital model allows us to efficiently examine all possible consensus sets, which guarantees the solution optimality and exactness.