3.3.2 Similarity Detection

In contrast to symmetry detection, automatic similarity detection is much harder and more time-consuming. Some algorithms for symmetry detection also cover similarity detection [96][98]. A framework for identifying regular and similar shapes in 3D objects was proposed [91]. Other approaches even support transformation functions which are not required to be rigid [20]. The symmetry factored embedding and the symmetry factored distance can be used to analyze symmetries in points sets [140]. A hierarchical approach was proposed for building a graph of all subparts of an object [142]. Usually, all of these algorithms use the surface of the object to sample points and detect local features to find matching similarities [84]. A good overview of symmetry and similarity detection algorithms is given in [99].