2 research outputs found
A Geometric Flow Approach for Segmentation of Images with Inhomongeneous Intensity and Missing Boundaries
Image segmentation is a complex mathematical problem, especially for images
that contain intensity inhomogeneity and tightly packed objects with missing
boundaries in between. For instance, Magnetic Resonance (MR) muscle images
often contain both of these issues, making muscle segmentation especially
difficult. In this paper we propose a novel intensity correction and a
semi-automatic active contour based segmentation approach. The approach uses a
geometric flow that incorporates a reproducing kernel Hilbert space (RKHS) edge
detector and a geodesic distance penalty term from a set of markers and
anti-markers. We test the proposed scheme on MR muscle segmentation and compare
with some state of the art methods. To help deal with the intensity
inhomogeneity in this particular kind of image, a new approach to estimate the
bias field using a fat fraction image, called Prior Bias-Corrected Fuzzy
C-means (PBCFCM), is introduced. Numerical experiments show that the proposed
scheme leads to significantly better results than compared ones. The average
dice values of the proposed method are 92.5%, 85.3%, 85.3% for quadriceps,
hamstrings and other muscle groups while other approaches are at least 10%
worse.Comment: Presented at CVIT 2023 Conference. Accepted to Journal of Image and
Graphic
Applications of ML-Based Surrogates in Bayesian Approaches to Inverse Problems
Neural networks have become a powerful tool as surrogate models to provide
numerical solutions for scientific problems with increased computational
efficiency. This efficiency can be advantageous for numerically challenging
problems where time to solution is important or when evaluation of many similar
analysis scenarios is required. One particular area of scientific interest is
the setting of inverse problems, where one knows the forward dynamics of a
system are described by a partial differential equation and the task is to
infer properties of the system given (potentially noisy) observations of these
dynamics. We consider the inverse problem of inferring the location of a wave
source on a square domain, given a noisy solution to the 2-D acoustic wave
equation. Under the assumption of Gaussian noise, a likelihood function for
source location can be formulated, which requires one forward simulation of the
system per evaluation. Using a standard neural network as a surrogate model
makes it computationally feasible to evaluate this likelihood several times,
and so Markov Chain Monte Carlo methods can be used to evaluate the posterior
distribution of the source location. We demonstrate that this method can
accurately infer source-locations from noisy data.Comment: 5 pages, 2 figures, submitted to NeurIPS Workshop on Machine Learning
for Physical Science