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 ...

Machine learning can extract desired knowledge and ease the development bottleneck in building expert systems. Among the proposed approaches, deriving classification rules from training examples is the most common. Given a set of examples, a learning program tries to induce rules that describe each class. The rough-set theory has served as a good mathematical tool for dealing with data classifi...

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 ...