7 papers
Compensated Convex Based Transforms for Image Processing and Shape Interrogation
Antonio Orlando, Elaine Crooks, Kewei Zhang
This paper reviews some recent applications of the theory of the compensated convex transforms or of the proximity hull as developed by the authors to image processing and shape in…
A variational asymmetric phase-field model of quasi-brittle fracture: Energetic solutions and their computation
Mariela Luege, Antonio Orlando
We derive the variational formulation of a gradient damage model by applying the energetic formulation of rate-independent processes and obtain a regularized formulation of fractur…
Compensated Convexity on Bounded Domains, Mixed Moreau Envelopes and Computational Methods
Kewei Zhang, Antonio Orlando, Elaine Crooks
Compensated convex transforms have been introduced for extended real-valued functions defined over . In their application to image processing, interpolation, and shap…
Compensated Convexity Methods for Approximations and Interpolations of Sampled Functions in Euclidean Spaces: Applications to Contour Lines, Sparse Data and Inpainting
Kewei Zhang, Elaine Crooks, Antonio Orlando
This paper is concerned with applications of the theory of approximation and interpolation based on compensated convex transforms developed in [K. Zhang, E. Crooks, A. Orlando, Com…
Compensated Convex Transforms and Geometric Singularity Extraction from Semiconvex Functions
Kewei Zhang, Elaine Crooks, Antonio Orlando
We apply upper and lower compensated convex transforms, which are `tight' one-sided approximations of a given function, to the extraction of fine geometric singularities from semic…
Compensated Convexity Methods for Approximations and Interpolations of Sampled Functions in Euclidean Spaces: Theoretical Foundations
Kewei Zhang, Elaine Crooks, Antonio Orlando
We introduce Lipschitz continuous and geometric approximation and interpolation methods for sampled bounded uniformly continuous functions over compact sets and over comp…
Compensated Convexity, Multiscale Medial Axis Maps and Sharp Regularity of the Squared Distance Function
Kewei Zhang, Elaine Crooks, Antonio Orlando
We introduce a new stable mathematical model for locating and measuring the medial axis of geometric objects, called the quadratic multiscale medial axis map of scale , and prov…