Habermas' Method: Rational Reconstruction

Protos - a Rational Reconstruction

Eecient Rational Number Reconstruction

The paper presents an eecient algorithm for reconstructing a rational number from its residue modulo a given integer. The algorithm is based on a double-digit version of Lehmer's multi-precision extended Euclidean algorithm. While asymptotic complexity remains quadratic in the length of the input, experiments with an implementation show that for small inputs the new algorithm is more than 3 tim...

Efficient Rational Number Reconstruction

Vector Rational Number Reconstruction

The final step of some algebraic algorithms is to reconstruct the common denominator d of a collection of rational numbers (ni/d)1≤i≤n from their images (ai)1≤i≤n modulo M , subject to the condition 0 < d ≤ N and |ni| ≤ N for a given magnitude bound N . Using elementwise rational reconstruction requires that M > 2N2. We present an algorithm, based on lattice basis reduction, which can perform t...

Rational Supershapes for Surface Reconstruction

Simple representation of complex 3D data sets is a fundamental problem in computer vision. From a quality control perspective, it is crucial to use efficient and simple techniques do define a reference model for further recognition or comparison tasks. In this paper, we focus on reverse engineering 3D data sets by recovering rational supershapes to build an implicit function to represent mechan...