M.Sc Thesis

M.Sc StudentCohen Aharon
SubjectRobust Shape Collection Matching and Correspondence from
Shape Differences
DepartmentDepartment of Electrical and Computers Engineering
Supervisor ASSOCIATE PROF. Mirela Ben-Chen
Full Thesis textFull thesis text - English Version


Shape collections are widely used in many geometry processing and computer graphics applications. Such collections can be obtained by deforming a given 3D model or by sampling a 3D animation.  Given two shape collections, e.g. two characters in similar poses, often rises the need to match the semantically corresponding shapes. This matching can assist in transferring information between the two collections. For instance, transferring shape annotations in order to allow pose labeling. A more common challenge is to automatically find the pointwise map, also known as correspondence, between non-isometric shapes, e.g. the two different non-isometric shapes from the two collections. In general, it is a very difficult problem, that has been tackled by many different approaches and often requires additional input such as landmarks or descriptors. This pointwise mapping can assist in transferring pointwise data, allowing for example texture transfer between non-isometric shapes.

We propose a method to automatically match two shape collections with a similar shape space structure, and compute the inter-maps between the collections. Given the intra-maps in each collection, which are often easier to compute since the shapes within the collection are isometric, we extract the corresponding shape difference operators, and use them to construct an embedding of the shape space of each collection. We then align the two shape spaces, and use the knowledge gained from the alignment to compute the inter-maps by formulating an appropriate optimization problem.

Unlike existing approaches for collection alignment, our method is applicable to small and large collections alike, and requires no parameter tuning. Furthermore, unlike most approaches for non-isometric correspondence, our method uses solely the variation within the collection to extract the inter-maps, and therefore does not require landmarks, descriptors or any additional input. We demonstrate that we achieve high matching accuracy rates, and compute high quality maps on non-isometric shapes, which compare favorably with automatic state-of-the-art methods for non-isometric shape correspondence. Furthermore, we show that in some cases, it is possible to automatically obtain a high quality map using our method even without requiring a collection, i.e. for two shapes only, by using collection composition.