Template-based 3D model fitting using dual-domain relaxation.

We introduce a template fitting method for 3D surface meshes. A given template mesh is deformed to closely approximate the input 3D geometry. The connectivity of the deformed template model is automatically adjusted to facilitate the geometric fitting and to ascertain high quality of the mesh elements. The template fitting process utilizes a specially tailored Laplacian processing framework, where in the first, coarse fitting stage we approximate the input geometry with a linearized biharmonic surface (a variant of LS-mesh), and then the fine geometric detail is fitted further using iterative Laplacian editing with reliable correspondence constraints and a local surface flattening mechanism to avoid foldovers. The latter step is performed in the dual mesh domain, which is shown to encourage near-equilateral mesh elements and significantly reduces the occurrence of triangle foldovers, a well-known problem in mesh fitting. To experimentally evaluate our approach, we compare our method with relevant state-of-the-art techniques and confirm significant improvements of results. In addition, we demonstrate the usefulness of our approach to the application of consistent surface parameterization (also known as cross-parameterization).

On linear variational surface deformation methods.

This survey reviews the recent advances in linear variational mesh deformation techniques. These methods were developed for editing detailed high-resolution meshes, like those produced by scanning real-world objects. The challenge of manipulating such complex surfaces is three-fold: the deformation technique has to be sufficiently fast, robust, and intuitive and easy to control to be useful for interactive applications. An intuitive, and thus predictable, deformation tool should provide physically plausible and aesthetically pleasing surface deformations, which in particular requires its geometric details to be preserved. The methods we survey generally formulate surface deformation as a global variational optimization problem that addresses the differential properties of the edited surface. Efficiency and robustness are achieved by linearizing the underlying objective functional, such that the global optimization amounts to solving a sparse linear system of equations. We review the different deformation energies and detail preservation techniques that were proposed in the recent years, together with the various techniques to rectify the linearization artifacts. Our goal is to provide the reader with a systematic classification and comparative description of the different techniques, revealing the strengths and weaknesses of each approach in common editing scenarios.

Geometry-aware bases for shape approximation.

We introduce a new class of shape approximation techniques for irregular triangular meshes. Our method approximates the geometry of the mesh using a linear combination of a small number of basis vectors. The basis vectors are functions of the mesh connectivity and of the mesh indices of a number of anchor vertices. There is a fundamental difference between the bases generated by our method and those generated by geometry-oblivious methods, such as Laplacian-based spectral methods. In the latter methods, the basis vectors are functions of the connectivity alone. The basis vectors of our method, in contrast, are geometry-aware since they depend on both the connectivity and on a binary tagging of vertices that are "geometrically important" in the given mesh (e.g., extrema). We show that, by defining the basis vectors to be the solutions of certain least-squares problems, the reconstruction problem reduces to solving a single sparse linear least-squares problem. We also show that this problem can be solved quickly using a state-of-the-art sparse-matrix factorization algorithm. We show how to select the anchor vertices to define a compact effective basis from which an approximated shape can be reconstructed. Furthermore, we develop an incremental update of the factorization of the least-squares system. This allows a progressive scheme where an initial approximation is incrementally refined by a stream of anchor points. We show that the incremental update and solving the factored system are fast enough to allow an online refinement of the mesh geometry.