Discrete Average of Two-Dimensional Shapes

In this article we present an algorithm for computing discrete average of n two-dimensional shapes. Our previous work was limited to two shapes, we generalize it to an arbitrary number of objects with consideration of increasing inter-individual variability. The first step of our approach performs a rigid transformation that aligns the shapes as best as possible. The next step consists in searching the progressive metamorphosis of one object toward the other one, that iteratively adds or suppresses pixels. This process is then iterated between the last average shape obtained and the new object from the set according to weighting consideration. It considers the rank in which each shape is added and gives criteria of optimization in variability and global topology preservation. The basic operations are based on geodesic distance transformations and lead to an optimal (linear) algorithm.