We construct a unique weak solution of the nonlinear PDE which asserts each level set evolves in time according to its mean curvature. This weak solution allows us then to define for any compact set Γo a unique generalized motion by mean curvature, existing for all time. We investigate the various geometric properties and pathologies of this evolution.

Tree-structured partitions provide a natural framework for rapid and accurate extraction of the level sets of a multivariate function f from noisy data. In general, a level set is the set S on which f exceeds some critical value (e.g., S = {x : f(x) ≥ γ}). Boundaries of level sets typically constitute manifolds embedded in the high-dimensional observation space. The identification of these boun...

In this paper, we consider reinitializing level functions through equation /tþ sgnð/Þðkr/k 1Þ 1⁄4 0 [16]. The method of Russo and Smereka [11] is taken in the spatial discretization of the equation. The spatial discretization is, simply speaking, the second order ENO finite difference with subcell resolution near the interface. Our main interest is on the temporal discretization of the equation...

Implicit representations of geometry have found applications in shape modeling, simulation, and other graphics pipelines. These representations, however, do not provide information about the paths of individual points as shapes move and undergo deformation. For this reason, we reconsider the problem of tracking points on level set surfaces, with the goal of designing an algorithm that — unlike ...

We tackle the problem of estimation level sets Lf(λ) density f a random vector X supported on smooth manifold M⊂Rd, from an iid sample X. To do that we introduce kernel-based estimator fˆn,h, which is slightly modified version one proposed in Rodríguez-Casal and Saavedra-Nieves (2014) proves its a.s. uniform convergence to f. Then, propose two estimators Lf(λ), first plug-in: Lfˆn,h(λ), proven ...