Monge–Ampère boundary measures

Stability of boundary measures

Boundary Measures for Geometric Inference

We study the boundary measures of compact subsets of the d-dimensional Euclidean space, which are closely related to Federer’s curvature measures. We show that they can be computed efficiently for point clouds and suggest that these measures can be used for geometric inference. The main contribution of this work is the proof of a quantitative stability theorem for boundary measures using tools ...

Adaptive Region Growing Based on Boundary Measures

Weak boundary contrast, inhomogeneous background and overlapped intensity distributions of the object and background are main causes that may lead to failure of boundary detection for many image segmentation methods. An adaptive region growing method based on multiple boundary measures is presented. It consists of region expansion and boundary selection processes. During the region expansion pr...

Carleson measures and elliptic boundary value

In this article, we highlight the role of Carleson measures in elliptic boundary value prob5 lems, and discuss some recent results in this theory. The focus here is on the Dirichlet problem, with 6 measurable data, for second order elliptic operators in divergence form. We illustrate, through selected 7 examples, the various ways Carleson measures arise in characterizing those classes of operat...

Combining Behavioral Measures and Brain Potentials to Study Categorical Prosodic Boundary Perception and Relative Boundary Strength

Two controversial issues in speech prosody research concern (i) the traditional notion of categorical boundary perception (i.e., intermediate phrase [ip] boundaries versus intonation phrase boundaries [IPh]), and (ii) the suggestion that the relative strength of competing boundaries (rather than the mere presence of boundaries) may account for prosody effects on sentences interpretation. An alt...