39 research outputs found
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
Image registration via stochastic gradient markov chain monte carlo
We develop a fully Bayesian framework for non-rigid registration of three-dimensional medical images, with a focus on uncertainty quantification. Probabilistic registration of large images along with calibrated uncertainty estimates is difficult for both computational and modelling reasons. To address the computational issues, we explore connections between the Markov chain Monte Carlo by backprop and the variational inference by backprop frameworks in order to efficiently draw thousands of samples from the posterior distribution. Regarding the modelling issues, we carefully design a Bayesian model for registration to overcome the existing barriers when using a dense, high-dimensional, and diffeomorphic parameterisation of the transformation. This results in improved calibration of uncertainty estimates
Image informatics strategies for deciphering neuronal network connectivity
Brain function relies on an intricate network of highly dynamic neuronal connections that rewires dramatically under the impulse of various external cues and pathological conditions. Among the neuronal structures that show morphologi- cal plasticity are neurites, synapses, dendritic spines and even nuclei. This structural remodelling is directly connected with functional changes such as intercellular com- munication and the associated calcium-bursting behaviour. In vitro cultured neu- ronal networks are valuable models for studying these morpho-functional changes. Owing to the automation and standardisation of both image acquisition and image analysis, it has become possible to extract statistically relevant readout from such networks. Here, we focus on the current state-of-the-art in image informatics that enables quantitative microscopic interrogation of neuronal networks. We describe the major correlates of neuronal connectivity and present workflows for analysing them. Finally, we provide an outlook on the challenges that remain to be addressed, and discuss how imaging algorithms can be extended beyond in vitro imaging studies
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Bayesian characterization of uncertainty in intra-subject non-rigid registration
In settings where high-level inferences are made based on registered image data, the registration uncertainty can contain important information. In this article, we propose a Bayesian non-rigid registration framework where conventional dissimilarity and regularization energies can be included in the likelihood and the prior distribution on deformations respectively through the use of Boltzmann’s distribution. The posterior distribution is characterized using Markov Chain Monte Carlo (MCMC) methods with the effect of the Boltzmann temperature hyper-parameters marginalized under broad uninformative hyper-prior distributions. The MCMC chain permits estimation of the most likely deformation as well as the associated uncertainty. On synthetic examples, we demonstrate the ability of the method to identify the maximum a posteriori estimate and the associated posterior uncertainty, and demonstrate that the posterior distribution can be non-Gaussian. Additionally, results from registering clinical data acquired during neurosurgery for resection of brain tumor are provided; we compare the method to single transformation results from a deterministic optimizer and introduce methods that summarize the high-dimensional uncertainty. At the site of resection, the registration uncertainty increases and the marginal distribution on deformations is shown to be multi-modal