Surface fitting and registration of point clouds using approximations of the unsigned distance function

Many problems in computer aided geometric design and geometry processing are stated as least-squares optimizations. Least-squares problems are well studied and widely used but exhibit immanent drawbacks such as high sensitivity to outliers. For this reason, we consider techniques for the registration of point clouds and surface fitting to point sets based on the l1-norm. We develop algorithms to solve l1-registration and l1-fitting problems and explore the emerging non-smooth minimization problems. We describe efficient ways to solve the optimization programs and present results for various applications.