We develop fast algorithms for solving regression problems on graphs where one is given the value of a function at some vertices, and must find its smoothest possible extension to all vertices. The extension we compute is the absolutely minimal Lipschitz extension, and is the limit for large p of p-Laplacian regularization. We present an algorithm that computes a minimal Lipschitz extension in ...

We present an extended Mumford-Shah regularization for blind image deconvolution and segmentation in the context of Bayesian estimation for blurred, noisy images or video sequences. The MumfordShah functional is extended to have cost terms for the estimation of blur kernels via a newly introduced prior solution space. This functional is minimized using Γ -convergence approximation in an embedde...

Semi-regular locales are extensions of the classical semiregular spaces. We investigate the conditions such that semi-regularization is a functor. We also investigate the conditions such that semi-regularization is a reflection or coreflection.

Due to the great benefit of rich spectral information, hyperspectral images (HSIs) have been successfully applied in many fields. However, some problems concern also limit their further applications, such as high dimension and expensive labeling. To address these issues, an unsupervised latent low-rank projection learning with graph regularization (LatLRPL) method is presented for feature extra...

Graph convolutional neural networks (GCNNs) have received much attention recently, owing to their capability in handling graph-structured data. Among the existing GCNNs, many methods can be viewed as instances of a message passing motif; features nodes are passed around neighbors, aggregated and transformed produce better nodes’ representations. Nevertheless, these seldom use node transition pr...

rational functions are of great interest to engineers and geoscientists. the rational polynomial coefficient (rpc) model as a generalized sensor model has been introduced as an alternative for the rigorous sensor model of the satellite imaging. numerical instability of normal equations is the only single obstacle to the implementation of these functions. practically, estimating rational functio...

An extension of dimensional regularization to compact dimensions is presented. The procedure keeps the Kaluza-Klein tower structure in tact, but has a regulator specific to the compact dimension. Possible 5 and 4 dimensional divergent and manifest finite contributions of (one-loop) Feynman graphs can be identified easily in this scheme. 1 E-mail: [email protected]