Variational Barycentric Coordinates
SessionVisual Perception
DescriptionWe propose a variational technique to optimize for generalized barycentric coordinates that offers additional artistic control compared to existing models. Prior work represents barycentric coordinates using meshes or closed-form formulae, in practice limiting the choice of objective function. In contrast, we directly parameterize the continuous function that maps any coordinate in a polytope's interior to its barycentric coordinates using a neural field. This formulation is enabled by our theoretical characterization of barycentric coordinates, which allows us to construct neural fields that parameterize the entire function class of valid coordinates. We demonstrate the flexibility of our model using a variety of objective functions, including multiple smoothness and deformation-aware energies; as a side contribution, we also present mathematically-justified means of measuring and minimizing objectives like total variation on discontinuous neural fields. We offer a practical acceleration strategy, present a thorough validation of our algorithm, and demonstrate several applications.
Event Type
Technical Papers
TimeFriday, 15 December 20239:10am - 9:25am 
LocationMeeting Room C4.11, Level 4 (Convention Centre)
