Complex Representations For Learning Statistical Shape Priors

Parametrisation of the shape of deformable objects is of paramount importance in many computer vision applications. Many state-of-the-art statistical deformable models perform landmark localisation via optimising an objective function over a certain parametrisation of the object's shape. Arguably, the most popular way is by employing statistical techniques. The points of shape samples of an object lie in a 2D lattice and they are normally represented by concatenating the 2D coordinates into a vector. As the 2D coordinates can be naturally represented as a complex number, in this paper we study statistical complex number representations of an object's shape. In particular, we show that the real representation provides a similar statistical prior as the widely linear complex model, while the circular complex representation results in a much more condensed encoding.