323 research outputs found
Discriminative Sliding Preserving Regularization in Medical Image Registration
Sliding effects often occur along tissue/organ boundaries. For instance, it is widely observed that the lung and diaphragm slide against the rib cage and the atria during breathing. Conventional homogeneous smooth registration methods fail to address this issue. Some recent studies preserve motion discontinuities by either using joint registration/segmentation or utilizing robust regularization energy on the motion field. However, allowing all types of discontinuities is not strict enough for physical deformations. In particular, flows that generate local vacuums or mass collisions should be discouraged by the energy functional. In this study, we propose a regularization energy that encodes a discriminative treatment of different types of motion discontinuities. The key idea is motivated by the Helmholtz-Hodge decomposition, and regards the underlying motion flow as a superposition of a solenoidal component, an irrotational component and a harmonic part. The proposed method applies a homogeneous penalty on the divergence, discouraging local volume change caused by the irrotational component, thus avoiding local vacuum or collision; it regularizes the curl field with a robust functional so that the resulting solenoidal component vanishes almost everywhere except on a singular set where the large shear values are preserved. This singularity set corresponds to sliding interfaces. Preliminary tests with both simulated and clinical data showed promising results.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/85988/1/Fessler242.pd
An optimal transport regularized model to image reconstruction problems
Optimal transport problem has gained much attention in image processing
field, such as computer vision, image interpolation and medical image
registration. In this paper, we incorporate optimal transport into linear
inverse problems as a regularization technique. We establish a new variational
model based on Benamou-Brenier energy to regularize the evolution path from a
template to latent image dynamically. The initial state of the continuity
equation can be regarded as a template, which can provide priors for the
reconstructed images. Also, we analyze the existence of solutions of such
variational problem in Radon measure space. Moreover, the first-order
primal-dual algorithm is constructed for solving this general imaging problem
in a special grid strategy. Finally, numerical experiments for undersampled MRI
reconstruction are presented which show that our proposed model can recover
images well with high quality and structure preservation
Disparity and Optical Flow Partitioning Using Extended Potts Priors
This paper addresses the problems of disparity and optical flow partitioning
based on the brightness invariance assumption. We investigate new variational
approaches to these problems with Potts priors and possibly box constraints.
For the optical flow partitioning, our model includes vector-valued data and an
adapted Potts regularizer. Using the notation of asymptotically level stable
functions we prove the existence of global minimizers of our functionals. We
propose a modified alternating direction method of minimizers. This iterative
algorithm requires the computation of global minimizers of classical univariate
Potts problems which can be done efficiently by dynamic programming. We prove
that the algorithm converges both for the constrained and unconstrained
problems. Numerical examples demonstrate the very good performance of our
partitioning method
Signal Processing on Product Spaces
We establish a framework for signal processing on product spaces of
simplicial and cellular complexes. For simplicity, we focus on the product of
two complexes representing time and space, although our results generalize
naturally to products of simplicial complexes of arbitrary dimension. Our
framework leverages the structure of the eigenmodes of the Hodge Laplacian of
the product space to jointly filter along time and space. To this end, we
provide a decomposition theorem of the Hodge Laplacian of the product space,
which highlights how the product structure induces a decomposition of each
eigenmode into a spatial and temporal component. Finally, we apply our method
to real world data, specifically for interpolating trajectories of buoys in the
ocean from a limited set of observed trajectories
Analysis of Crowdsourced Sampling Strategies for HodgeRank with Sparse Random Graphs
Crowdsourcing platforms are now extensively used for conducting subjective
pairwise comparison studies. In this setting, a pairwise comparison dataset is
typically gathered via random sampling, either \emph{with} or \emph{without}
replacement. In this paper, we use tools from random graph theory to analyze
these two random sampling methods for the HodgeRank estimator. Using the
Fiedler value of the graph as a measurement for estimator stability
(informativeness), we provide a new estimate of the Fiedler value for these two
random graph models. In the asymptotic limit as the number of vertices tends to
infinity, we prove the validity of the estimate. Based on our findings, for a
small number of items to be compared, we recommend a two-stage sampling
strategy where a greedy sampling method is used initially and random sampling
\emph{without} replacement is used in the second stage. When a large number of
items is to be compared, we recommend random sampling with replacement as this
is computationally inexpensive and trivially parallelizable. Experiments on
synthetic and real-world datasets support our analysis
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