M.Sc Thesis

M.Sc StudentShoham Meged
SubjectHierarchical Functional Maps between Subdivision
DepartmentDepartment of Electrical and Computers Engineering
Supervisor ASSOCIATE PROF. Mirela Ben-Chen
Full Thesis textFull thesis text - English Version


Subdivision surfaces are a common and popular shape representation for 3D modelling and designing. As so, they are abundantly used in the pipeline of graphics artists. OpenSubdiv, an open source code package released recently by Pixar Studios, is an evidence of the usefulness of subdivision surfaces. A common modeling pipeline includes the design of a simple base mesh, with a small number of control polygons. The base mesh is subdivided several times, producing a smoother mesh. The smooth model is then sculpted artistically, yielding a finely detailed shape.

We propose a novel approach for computing correspondences between subdivision surfaces with different control polygons. Our main observation is that the multiresolution spectral basis functions that are often used for computing a functional correspondence can be compactly represented on subdivision surfaces, and therefore can be efficiently computed. Furthermore, the reconstruction of a pointwise map from a functional correspondence also greatly benefits from the subdivision structure. Leveraging these observations, we suggest a hierarchical pipeline for functional map inference, allowing us to compute correspondences between surfaces at fine subdivision levels, with hundreds of thousands of polygons, an order of magnitude faster than existing correspondence methods. We demonstrate the applicability of our results by transferring high-resolution sculpting displacement maps and textures between subdivision models.