22,997 research outputs found
Multicut Algorithms for Neurite Segmentation
Correlation clustering, or multicut partitioning is widely used for image segmentation
and graph partitioning. Given an undirected edge weighted graph with positive and
negative weights, correlation clustering partitions the graph such that the sum of
cut edge weights is minimized. Since the optimal number of clusters is automatically
chosen, multicut partitioning is well suited for clustering neural structures in EM
connectomics datasets where the optimal number of clusters is unknown a-priori. Due
to the NP-hardness of optimizing the multicut objective, exact solvers do not scale
and approximative solvers often give unsatisfactory results.
In chapter 2 we investigate scalable methods for correlation clustering. To this end
we define fusion moves for the multicut objective function which iteratively fuses
the current and a proposed partitioning and monotonously improves the partitioning.
Fusion moves scale to larger datasets, give near optimal solutions and at the same
time show state of the art anytime performance.
In chapter 3 we generalize the fusion moves frameworks for the lifted multicut ob-
jective, a generalization of the multicut objective which can penalize or reward all
decompositions of a graph for which any given pair of nodes are in distinct compo-
nents. The proposed framework scales well to large datasets and has a cutting edge
anytime performance.
In chapter 4 we propose a framework for automatic segmentation of neural structures
in 3D EM connectomics data where a membrane probability is predicted for each
pixel with a neural network and superpixels are computed based on this probability
map. Finally the superpixels are merged to neurites using the techniques described
in chapter 3. The proposed pipeline is validated with an extensive set of experiments
and a detailed lesion study. This work substantially narrows the accuracy gap between
humans and computers for neurite segmentation.
In chapter 5 we summarize the software written for this thesis. The provided imple-
mentations for algorithms and techniques described in chapters 2 to 4 and many other
algorithms resulted in a software library for graph partitioning, image segmentation
and discrete optimization
Exploring the assortativity-clustering space of a network's degree sequence
Nowadays there is a multitude of measures designed to capture different
aspects of network structure. To be able to say if the structure of certain
network is expected or not, one needs a reference model (null model). One
frequently used null model is the ensemble of graphs with the same set of
degrees as the original network. In this paper we argue that this ensemble can
be more than just a null model -- it also carries information about the
original network and factors that affect its evolution. By mapping out this
ensemble in the space of some low-level network structure -- in our case those
measured by the assortativity and clustering coefficients -- one can for
example study how close to the valid region of the parameter space the observed
networks are. Such analysis suggests which quantities are actively optimized
during the evolution of the network. We use four very different biological
networks to exemplify our method. Among other things, we find that high
clustering might be a force in the evolution of protein interaction networks.
We also find that all four networks are conspicuously robust to both random
errors and targeted attacks
A Message Passing Algorithm for the Minimum Cost Multicut Problem
We propose a dual decomposition and linear program relaxation of the NP -hard
minimum cost multicut problem. Unlike other polyhedral relaxations of the
multicut polytope, it is amenable to efficient optimization by message passing.
Like other polyhedral elaxations, it can be tightened efficiently by cutting
planes. We define an algorithm that alternates between message passing and
efficient separation of cycle- and odd-wheel inequalities. This algorithm is
more efficient than state-of-the-art algorithms based on linear programming,
including algorithms written in the framework of leading commercial software,
as we show in experiments with large instances of the problem from applications
in computer vision, biomedical image analysis and data mining.Comment: Added acknowledgment
Thermalization, Error-Correction, and Memory Lifetime for Ising Anyon Systems
We consider two-dimensional lattice models that support Ising anyonic
excitations and are coupled to a thermal bath. We propose a phenomenological
model for the resulting short-time dynamics that includes pair-creation,
hopping, braiding, and fusion of anyons. By explicitly constructing topological
quantum error-correcting codes for this class of system, we use our
thermalization model to estimate the lifetime of the quantum information stored
in the encoded spaces. To decode and correct errors in these codes, we adapt
several existing topological decoders to the non-Abelian setting. We perform
large-scale numerical simulations of these two-dimensional Ising anyon systems
and find that the thresholds of these models range between 13% to 25%. To our
knowledge, these are the first numerical threshold estimates for quantum codes
without explicit additive structure.Comment: 34 pages, 9 figures; v2 matches the journal version and corrects a
misstatement about the detailed balance condition of our Metropolis
simulations. All conclusions from v1 are unaffected by this correctio
Automatic Segmentation of Fluorescence Lifetime Microscopy Images of Cells Using Multi-Resolution Community Detection
We have developed an automatic method for segmenting fluorescence lifetime
(FLT) imaging microscopy (FLIM) images of cells inspired by a multi-resolution
community detection (MCD) based network segmentation method. The image
processing problem is framed as identifying segments with respective average
FLTs against a background in FLIM images. The proposed method segments a FLIM
image for a given resolution of the network composed using image pixels as the
nodes and similarity between the pixels as the edges. In the resulting
segmentation, low network resolution leads to larger segments and high network
resolution leads to smaller segments. Further, the mean-square error (MSE) in
estimating the FLT segments in a FLIM image using the proposed method was found
to be consistently decreasing with increasing resolution of the corresponding
network. The proposed MCD method outperformed a popular spectral clustering
based method in performing FLIM image segmentation. The spectral segmentation
method introduced noisy segments in its output at high resolution. It was
unable to offer a consistent decrease in MSE with increasing resolution.Comment: 21 pages, 6 figure
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