Representing surfaces in local, rather than global, coordinate systems proves to be useful for various geometry processing applications. In particular, we have been investigating surface representations based on differential coordinates, constructed using the Laplacian operator and discrete forms. Unlike global Cartesian coordinates, that only represent the spatial locations of points on the su...

This paper addresses the problem of determining suitable mask values and sizes for the discrete implementation of the Laplacian of Gaussian edge operator. This is achieved by providing a theoretical connection between the mask size and the edge detection error introduced by truncation of the operator. Additionally, the importance of introducing a bias correction within the finite approximation ...

In this paper, we prove the invariance of the spectrum of the basic Dirac operator defined on a Riemannian foliation (M,F) with respect to a change of bundle-like metric. We then establish new estimates for its eigenvalues on spin flows in terms of the O’Neill tensor and the first eigenvalue of the Dirac operator on M . We discuss examples and also define a new version of the basic Laplacian wh...

We study two quantization schemes for compact symplectic manifolds with almost complex structures. The first of these is the Spinc quantization. We prove the analog of Kodaira vanishing for the Spinc Dirac operator, which shows that the index space of this operator provides an honest (not virtual) vector space semiclassically. We also introduce a new quantization scheme, based on a rescaled Lap...

In this paper, we prove the invariance of the spectrum of the basic Dirac operator defined on a Riemannian foliation (M,F) with respect to a change of bundle-like metric. We then establish new estimates for its eigenvalues on spin flows in terms of the O’Neill tensor and the first eigenvalue of the Dirac operator on M . We discuss examples and also define a new version of the basic Laplacian wh...