Two-Dimensional Discrete Morphing

In this article we present an algorithm for discrete object deformation. This algorithm is a first step for computing an average shape between two discrete objects and may be used for building a statistical atlas of shapes. The method we develop is based on discrete operators and works only on digital data. We do not compute continuous approximations of objects so that we have neither approximations nor interpolation errors. The first step of our method performs a rigid transformation that aligns the shapes as best as possible and decreases geometrical differences between them. The next step consists in searching the progressive transformations of one object toward the other one, that iteratively adds or suppresses pixels. These operations are based on geodesic distance transformation and lead to an optimal (linear) algorithm.

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