12,928 research outputs found
Streaming Algorithm for Euler Characteristic Curves of Multidimensional Images
We present an efficient algorithm to compute Euler characteristic curves of
gray scale images of arbitrary dimension. In various applications the Euler
characteristic curve is used as a descriptor of an image.
Our algorithm is the first streaming algorithm for Euler characteristic
curves. The usage of streaming removes the necessity to store the entire image
in RAM. Experiments show that our implementation handles terabyte scale images
on commodity hardware. Due to lock-free parallelism, it scales well with the
number of processor cores. Our software---CHUNKYEuler---is available as open
source on Bitbucket.
Additionally, we put the concept of the Euler characteristic curve in the
wider context of computational topology. In particular, we explain the
connection with persistence diagrams
Active Mean Fields for Probabilistic Image Segmentation: Connections with Chan-Vese and Rudin-Osher-Fatemi Models
Segmentation is a fundamental task for extracting semantically meaningful
regions from an image. The goal of segmentation algorithms is to accurately
assign object labels to each image location. However, image-noise, shortcomings
of algorithms, and image ambiguities cause uncertainty in label assignment.
Estimating the uncertainty in label assignment is important in multiple
application domains, such as segmenting tumors from medical images for
radiation treatment planning. One way to estimate these uncertainties is
through the computation of posteriors of Bayesian models, which is
computationally prohibitive for many practical applications. On the other hand,
most computationally efficient methods fail to estimate label uncertainty. We
therefore propose in this paper the Active Mean Fields (AMF) approach, a
technique based on Bayesian modeling that uses a mean-field approximation to
efficiently compute a segmentation and its corresponding uncertainty. Based on
a variational formulation, the resulting convex model combines any
label-likelihood measure with a prior on the length of the segmentation
boundary. A specific implementation of that model is the Chan-Vese segmentation
model (CV), in which the binary segmentation task is defined by a Gaussian
likelihood and a prior regularizing the length of the segmentation boundary.
Furthermore, the Euler-Lagrange equations derived from the AMF model are
equivalent to those of the popular Rudin-Osher-Fatemi (ROF) model for image
denoising. Solutions to the AMF model can thus be implemented by directly
utilizing highly-efficient ROF solvers on log-likelihood ratio fields. We
qualitatively assess the approach on synthetic data as well as on real natural
and medical images. For a quantitative evaluation, we apply our approach to the
icgbench dataset
Reconstruction of three-dimensional porous media using generative adversarial neural networks
To evaluate the variability of multi-phase flow properties of porous media at
the pore scale, it is necessary to acquire a number of representative samples
of the void-solid structure. While modern x-ray computer tomography has made it
possible to extract three-dimensional images of the pore space, assessment of
the variability in the inherent material properties is often experimentally not
feasible. We present a novel method to reconstruct the solid-void structure of
porous media by applying a generative neural network that allows an implicit
description of the probability distribution represented by three-dimensional
image datasets. We show, by using an adversarial learning approach for neural
networks, that this method of unsupervised learning is able to generate
representative samples of porous media that honor their statistics. We
successfully compare measures of pore morphology, such as the Euler
characteristic, two-point statistics and directional single-phase permeability
of synthetic realizations with the calculated properties of a bead pack, Berea
sandstone, and Ketton limestone. Results show that GANs can be used to
reconstruct high-resolution three-dimensional images of porous media at
different scales that are representative of the morphology of the images used
to train the neural network. The fully convolutional nature of the trained
neural network allows the generation of large samples while maintaining
computational efficiency. Compared to classical stochastic methods of image
reconstruction, the implicit representation of the learned data distribution
can be stored and reused to generate multiple realizations of the pore
structure very rapidly.Comment: 21 pages, 20 figure
Fast Solvers for Cahn-Hilliard Inpainting
We consider the efficient solution of the modified Cahn-Hilliard equation for binary image inpainting using convexity splitting, which allows an unconditionally gradient stable time-discretization scheme. We look at a double-well as well as a double obstacle potential. For the latter we get a nonlinear system for which we apply a semi-smooth Newton method combined with a Moreau-Yosida regularization technique. At the heart of both methods lies the solution of large and sparse linear systems. We introduce and study block-triangular preconditioners using an efficient and easy to apply Schur complement approximation. Numerical results indicate that our preconditioners work very well for both problems and show that qualitatively better results can be obtained using the double obstacle potential
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