18,619 research outputs found
Homological Region Adjacency Tree for a 3D Binary Digital Image via HSF Model
Given a 3D binary digital image I, we define and compute
an edge-weighted tree, called Homological Region Tree (or Hom-Tree,
for short). It coincides, as unweighted graph, with the classical Region
Adjacency Tree of black 6-connected components (CCs) and white 26-
connected components of I. In addition, we define the weight of an edge
(R, S) as the number of tunnels that the CCs R and S “share”. The
Hom-Tree structure is still an isotopic invariant of I. Thus, it provides
information about how the different homology groups interact between
them, while preserving the duality of black and white CCs.
An experimentation with a set of synthetic images showing different
shapes and different complexity of connected component nesting is performed
for numerically validating the method.Ministerio de Economía y Competitividad MTM2016-81030-
Computing the Component-Labeling and the Adjacency Tree of a Binary Digital Image in Near Logarithmic-Time
Connected component labeling (CCL) of binary images is
one of the fundamental operations in real time applications. The adjacency
tree (AdjT) of the connected components offers a region-based
representation where each node represents a region which is surrounded
by another region of the opposite color. In this paper, a fully parallel
algorithm for computing the CCL and AdjT of a binary digital image
is described and implemented, without the need of using any geometric
information. The time complexity order for an image of m × n pixels
under the assumption that a processing element exists for each pixel is
near O(log(m+ n)). Results for a multicore processor show a very good
scalability until the so-called memory bandwidth bottleneck is reached.
The inherent parallelism of our approach points to the direction that
even better results will be obtained in other less classical computing
architectures.Ministerio de Economía y Competitividad MTM2016-81030-PMinisterio de Economía y Competitividad TEC2012-37868-C04-0
Assessing the robustness of parsimonious predictions for gene neighborhoods from reconciled phylogenies
The availability of a large number of assembled genomes opens the way to
study the evolution of syntenic character within a phylogenetic context. The
DeCo algorithm, recently introduced by B{\'e}rard et al. allows the computation
of parsimonious evolutionary scenarios for gene adjacencies, from pairs of
reconciled gene trees. Following the approach pioneered by Sturmfels and
Pachter, we describe how to modify the DeCo dynamic programming algorithm to
identify classes of cost schemes that generates similar parsimonious
evolutionary scenarios for gene adjacencies, as well as the robustness to
changes to the cost scheme of evolutionary events of the presence or absence of
specific ancestral gene adjacencies. We apply our method to six thousands
mammalian gene families, and show that computing the robustness to changes to
cost schemes provides new and interesting insights on the evolution of gene
adjacencies and the DeCo model.Comment: Accepted, to appear in ISBRA - 11th International Symposium on
Bioinformatics Research and Applications - 2015, Jun 2015, Norfolk, Virginia,
United State
On the Topological Disparity Characterization of Square-Pixel Binary Image Data by a Labeled Bipartite Graph
Given an nD digital image I based on cubical n-xel, to fully
characterize the degree of internal topological dissimilarity existing in I
when using different adjacency relations (mainly, comparing 2n or 2n −1
adjacency relations) is a relevant issue in current problems of digital
image processing relative to shape detection or identification. In this
paper, we design and implement a new self-dual representation for a
binary 2D image I, called {4, 8}-region adjacency forest of I ({4, 8}-RAF,
for short), that allows a thorough analysis of the differences between the
topology of the 4-regions and that of the 8-regions of I. This model can
be straightforwardly obtained from the classical region adjacency tree
of I and its binary complement image Ic, by a suitable region label
identification. With these two labeled rooted trees, it is possible: (a) to
compute Euler number of the set of foreground (resp. background) pixels
with regard to 4-adjacency or 8-adjacency; (b) to identify new local and
global measures and descriptors of topological dissimilarity not only for
one image but also between two or more images. The parallelization of
the algorithms to extract and manipulate these structures is complete,
thus producing efficient and unsophisticated codes with a theoretical
computing time near the logarithm of the width plus the height of an
image. Some toy examples serve to explain the representation and some
experiments with gray real images shows the influence of the topological
dissimilarity when detecting feature regions, like those returned by the
MSER (maximally stable extremal regions) method.Ministerio de Economía, Industria y Competitividad PID2019-110455GB-I00 (Par-HoT)Junta de Andalucía US-138107
Maximal Entropy Random Walk: solvable cases of dynamics
We focus on the study of dynamics of two kinds of random walk: generic random
walk (GRW) and maximal entropy random walk (MERW) on two model networks: Cayley
trees and ladder graphs. The stationary probability distribution for MERW is
given by the squared components of the eigenvector associated with the largest
eigenvalue \lambda_0 of the adjacency matrix of a graph, while the dynamics of
the probability distribution approaching to the stationary state depends on the
second largest eigenvalue \lambda_1.
Firstly, we give analytic solutions for Cayley trees with arbitrary branching
number, root degree, and number of generations. We determine three regimes of a
tree structure that result in different statics and dynamics of MERW, which are
due to strongly, critically, and weakly branched roots. We show how the
relaxation times, generically shorter for MERW than for GRW, scale with the
graph size.
Secondly, we give numerical results for ladder graphs with symmetric defects.
MERW shows a clear exponential growth of the relaxation time with the size of
defective regions, which indicates trapping of a particle within highly
entropic intact region and its escaping that resembles quantum tunneling
through a potential barrier. GRW shows standard diffusive dependence
irrespective of the defects.Comment: 13 pages, 6 figures, 24th Marian Smoluchowski Symposium on
Statistical Physics (Zakopane, Poland, September 17-22, 2011
A graph-based mathematical morphology reader
This survey paper aims at providing a "literary" anthology of mathematical
morphology on graphs. It describes in the English language many ideas stemming
from a large number of different papers, hence providing a unified view of an
active and diverse field of research
Graph Refinement based Airway Extraction using Mean-Field Networks and Graph Neural Networks
Graph refinement, or the task of obtaining subgraphs of interest from
over-complete graphs, can have many varied applications. In this work, we
extract trees or collection of sub-trees from image data by, first deriving a
graph-based representation of the volumetric data and then, posing the tree
extraction as a graph refinement task. We present two methods to perform graph
refinement. First, we use mean-field approximation (MFA) to approximate the
posterior density over the subgraphs from which the optimal subgraph of
interest can be estimated. Mean field networks (MFNs) are used for inference
based on the interpretation that iterations of MFA can be seen as feed-forward
operations in a neural network. This allows us to learn the model parameters
using gradient descent. Second, we present a supervised learning approach using
graph neural networks (GNNs) which can be seen as generalisations of MFNs.
Subgraphs are obtained by training a GNN-based graph refinement model to
directly predict edge probabilities. We discuss connections between the two
classes of methods and compare them for the task of extracting airways from 3D,
low-dose, chest CT data. We show that both the MFN and GNN models show
significant improvement when compared to one baseline method, that is similar
to a top performing method in the EXACT'09 Challenge, and a 3D U-Net based
airway segmentation model, in detecting more branches with fewer false
positives.Comment: Accepted for publication at Medical Image Analysis. 14 page
Cluster adjacency beyond MHV
We explore further the notion of cluster adjacency, focussing on non-MHV
amplitudes. We extend the notion of adjacency to the BCFW decomposition of
tree-level amplitudes. Adjacency controls the appearance of poles, both
physical and spurious, in individual BCFW terms. We then discuss how this
notion of adjacency is connected to the adjacency already observed at the level
of symbols of scattering amplitudes which controls the appearance of branch cut
singularities. Poles and symbols become intertwined by cluster adjacency and we
discuss the relation of this property to the -equation which imposes
constraints on the derivatives of the transcendental functions appearing in
loop amplitudes.Comment: 51 pages, 25 figures, 4 table
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