Clusters are often defined to be the connected components of a density level set. Unfortunately, this definition depends on a level that needs to be user specified by some means. In this paper we present a simple algorithm that is able to asymptotically determine the optimal level, that is, the level at which there is the first split in the cluster tree of the data generating distribution. We f...

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 ...