Abstract
We present the BayesBD package providing Bayesian inference for boundaries of noisy images. The BayesBD package implements flexible Gaussian process priors indexed by the circle to recover the boundary in a binary or Gaussian noised image, with the benefits of guaranteed geometric restrictions on the estimated boundary, (nearly) minimax optimal and smoothness adaptive convergence rates, and convenient joint inferences under certain assumptions. The core sampling tasks for our model have linear complexity, and our implementation in c++ using packages Rcpp and RcppArmadillo is computationally efficient. Users can access the full functionality of the package in both Rgui and the corresponding shiny application. Additionally, the package includes numerous utility functions to aid users in data preparation and analysis of results. We compare BayesBD with selected existing packages using both simulations and real data applications, and demonstrate the excellent performance and flexibility of BayesBD even when the observation contains complicated structural information that may violate its assumptions.
Highlights
Boundary estimation is an important problem in image analysis with wide-ranging applications from identifying tumors in medical images (Li et al, 2010), classifying the process of machine wear by analyzing the boundary between normal and worn materials (Yuan et al, 2016), to identifying regions of interest in satellite images, such as the boundary of Scotland’s Lake Menteith (Cucala and Marin, 2014; Marin and Robert, 2014)
We present the R package BayesBD (Syring and Li, 2017) which aims to fill this gap
The developed BayesBD package provides support for analyzing binary images and Gaussian-noised images, which commonly arise in many applications
Summary
Boundary estimation is an important problem in image analysis with wide-ranging applications from identifying tumors in medical images (Li et al, 2010), classifying the process of machine wear by analyzing the boundary between normal and worn materials (Yuan et al, 2016), to identifying regions of interest in satellite images, such as the boundary of Scotland’s Lake Menteith (Cucala and Marin, 2014; Marin and Robert, 2014). There are two functions to draw posterior samples following Algorithm 1 and 2 based on images either simulated or provided by users: fitBinImage for binary images, and fitContImage for Gaussiannoised images These sampling functions take the same arguments, with the exception of the ordering input which is duplicated in fitContImage to allow ordering of the two parameters, i.e., the mean and standard deviation. Following the examples of data simulation for binary and Gaussian-noised images, we can obtain posterior samples via. Our flexibility in choosing between slice and Metropolis-Hastings (MH) sampling algorithms gives users the potential to unlock efficiency gains We highlight these gains below for both binary and Gaussian-noised simulations, and note that the faster MH method suffers little in accuracy.
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