Rectangle fitting via quadratic programming

This paper investigates rectangle fitting via optimization approaches. We summarize two basic requirements for rectangular fitting, leading to a basic model that are non-convex and difficult to attack. To avoid potential trapping of local minima, we extend the basic model with centroid and orientation constraints into a quadratic programming. To achieve reliable fitting from noisy points, slack variables are introduced to soften hard constraints. The scalability to problem size are further addressed by careful selecting only a small fraction of slack variables. Results on clean dataset, noisy dataset, and practical data show that our method is able to reliably fit rectangles for various kinds of data.