We propose learning a depth covariance function with applications to geometric vision tasks. Given RGB images as input, the covariance function can be flexibly used to define priors over depth functions, predictive distributions given observations, and methods for active point selection. We leverage these techniques for a selection of downstream tasks: depth completion, bundle adjustment, and monocular dense visual odometry.

Cited by 17

Estimation of low-rank covariance function

Vladimir Koltchinskii, Karim Lounici, A. B. Tsybakov · Stochastic Processes and their Applications · 2016

Cited by 0Open access

Covariance function of space-time series

Vendula Tetíková · Digital Repository (National Repository of Grey Literature) · 2006

Space-time series and their covariance function are very important in areas such as meteorology, hydrology and evolutionary biology. This diploma thesis concentrates on space-time covariance functions and on the way how this covariance functions describe space-time interaction. It focuses mainly on stationary nonseparable covariance functions but also on separable ones. The aim is to introduce main methods of creation covariance functions. In practice the estimating of covariance function is different, therefore there are, at the conclusion, examples of solutions and their comparison.

Cited by 0

Nonparametric estimation of isotropic covariance function

Yiming Wang, Sujit K. Ghosh · Journal of nonparametric statistics · 2022

A nonparametric model using a sequence of Bernstein polynomials is constructed to approximate arbitrary isotropic covariance functions valid in R∞ and related approximation properties are investigated using the popular L∞ norm and L2 norms. A computationally efficient sieve maximum likelihood (sML) estimation is then developed to nonparametrically estimate the unknown isotropic covariance function valid in R∞. Consistency of the proposed sieve ML estimator is established under increasing domain regime. The proposed methodology is compared numerically with couple of existing nonparametric as well as with commonly used parametric methods. Numerical results based on simulated data show that our approach outperforms the parametric methods in reducing bias due to model misspecification and also the nonparametric methods in terms of having significantly lower values of expected L∞ and L2 norms. Application to precipitation data is illustrated to showcase a real case study. Additional technical details and numerical illustrations are also made available.

Cited by 1

Covariance function of vector self-similar processes

Lavancier, Frédéric, Philippe, Anne, Surgailis, Donatas · RePEc: Research Papers in Economics

The paper obtains the general form of the cross-covariance function of vector fractional Brownian motions with correlated components having different self-similarity indices.

Cited by 0

Covariance function of vector self-similar processes

Frédéric Lavancier, Anne Philippe, Донатас Сургайлис · Statistics & Probability Letters · 2009

Cited by 47Open access

The time-covariance function : Properties and application

Hawawini, Gabriel A. · RePEc: Research Papers in Economics

Cited by 0

Modelling the global topographic-isostatic covariance function

Hussein A. Abd-Elmotaal · Manuscripta geodetica. · 1991

Cited by 0

Covariance function diagnostics for spatial linear models

Ronald Christensen, Wesley O. Johnson, Larry M. Pearson · Mathematical Geology · 1993

Cited by 22

Wavelet Estimation of Nonstationary Spatial Covariance Function

Yangyang Chen, Pedro A. Morettin, Ronaldo Dias et al. · 2024

Cited by 0

GeneralizedWendland: Fully Parameterized Generalized Wendland Covariance Function

Thomas Fischer, Reinhard Furrer, Josef Stocker · 2022

A fully parameterized Generalized Wendland covariance function for use in Gaussian process models, as well as multiple methods for approximating it via covariance interpolation. The available methods are linear interpolation, polynomial interpolation, and cubic spline interpolation. Moreno Bevilacqua and Reinhard Furrer and Tarik Faouzi and Emilio Porcu (2019) <url:<<a href="https://projecteuclid.org/journalArticle/Download?urlId=10.1214%2F17-AOS1652" target="_top">https://projecteuclid.org/journalArticle/Download?urlId=10.1214%2F17-AOS1652</a>>>. Moreno Bevilacqua and Christian Caamaño-Carrillo and Emilio Porcu (2022) <<a href="https://doi.org/10.48550%2FarXiv.2008.02904" target="_top">doi:10.48550/arXiv.2008.02904</a>>. Reinhard Furrer and Roman Flury and Florian Gerber (2022) <url:<<a href="https://CRAN.R-project.org/package=spam" target="_top">https://CRAN.R-project.org/package=spam</a>>>.

Cited by 2Open access