Computing correspondences or maps between shapes is one of the oldest problems in
Computer Graphics and Geometry Processing with a wide range of applications from
deformation transfer, statistical shape analysis, to co-segmentation and exploration among
a myriad others. A good map is supposed to be continuous, as-bijective-as-possible, accurate
if there are ground-truth corresponding landmarks given, and lowdistortionw.r.t.
different measures, for example as-conformal-as-possible to preserve the angles. This
thesis contributes to the area of non-rigid shape matching and map space exploration
in Geometry Processing. Specifically, we consider the discrete setting, where the shapes
are discretized as amesh structure consisting of vertices, edges, and polygonal faces. In
the simplest case, we only consider the graph structure with vertices and edges only.
In this thesis, we design algorithms to compute soft correspondences between discrete
shapes. Specifically, (1)we propose different regularizers, including orientation-preserving
operator and the Resolvent Laplacian Commutativity operator, to promote the shape
correspondences in the functional map framework. (2) We propose two refinement
methods, namely BCICP and ZoomOut, to improve the accuracy, continuity, bijectivity
and the coverage of given point-wisemaps. (3)We propose a tree structure and an enumeration
algorithm to explore the map space between a pair of shapes that can update
multiple high-quality dense correspondences.
| Identifer | oai:union.ndltd.org:kaust.edu.sa/oai:repository.kaust.edu.sa:10754/670353 |
| Date | 29 July 2021 |
| Creators | Ren, Jing |
| Contributors | Wonka, Peter, Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division, Ovsjanikov, Maks, Ghanem, Bernard, Pottmann, Helmut, Solomon, Justin |
| Source Sets | King Abdullah University of Science and Technology |
| Language | English |
| Detected Language | English |
| Type | Dissertation |
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