3,878 research outputs found
Craquelure as a Graph: Application of Image Processing and Graph Neural Networks to the Description of Fracture Patterns
Cracks on a painting is not a defect but an inimitable signature of an
artwork which can be used for origin examination, aging monitoring, damage
identification, and even forgery detection. This work presents the development
of a new methodology and corresponding toolbox for the extraction and
characterization of information from an image of a craquelure pattern.
The proposed approach processes craquelure network as a graph. The graph
representation captures the network structure via mutual organization of
junctions and fractures. Furthermore, it is invariant to any geometrical
distortions. At the same time, our tool extracts the properties of each node
and edge individually, which allows to characterize the pattern statistically.
We illustrate benefits from the graph representation and statistical features
individually using novel Graph Neural Network and hand-crafted descriptors
correspondingly. However, we also show that the best performance is achieved
when both techniques are merged into one framework. We perform experiments on
the dataset for paintings' origin classification and demonstrate that our
approach outperforms existing techniques by a large margin.Comment: Published in ICCV 2019 Workshop
Finding Induced Subgraphs via Minimal Triangulations
Potential maximal cliques and minimal separators are combinatorial objects
which were introduced and studied in the realm of minimal triangulations
problems including Minimum Fill-in and Treewidth. We discover unexpected
applications of these notions to the field of moderate exponential algorithms.
In particular, we show that given an n-vertex graph G together with its set of
potential maximal cliques Pi_G, and an integer t, it is possible in time |Pi_G|
* n^(O(t)) to find a maximum induced subgraph of treewidth t in G; and for a
given graph F of treewidth t, to decide if G contains an induced subgraph
isomorphic to F. Combined with an improved algorithm enumerating all potential
maximal cliques in time O(1.734601^n), this yields that both problems are
solvable in time 1.734601^n * n^(O(t)).Comment: 14 page
Large induced subgraphs via triangulations and CMSO
We obtain an algorithmic meta-theorem for the following optimization problem.
Let \phi\ be a Counting Monadic Second Order Logic (CMSO) formula and t be an
integer. For a given graph G, the task is to maximize |X| subject to the
following: there is a set of vertices F of G, containing X, such that the
subgraph G[F] induced by F is of treewidth at most t, and structure (G[F],X)
models \phi.
Some special cases of this optimization problem are the following generic
examples. Each of these cases contains various problems as a special subcase:
1) "Maximum induced subgraph with at most l copies of cycles of length 0
modulo m", where for fixed nonnegative integers m and l, the task is to find a
maximum induced subgraph of a given graph with at most l vertex-disjoint cycles
of length 0 modulo m.
2) "Minimum \Gamma-deletion", where for a fixed finite set of graphs \Gamma\
containing a planar graph, the task is to find a maximum induced subgraph of a
given graph containing no graph from \Gamma\ as a minor.
3) "Independent \Pi-packing", where for a fixed finite set of connected
graphs \Pi, the task is to find an induced subgraph G[F] of a given graph G
with the maximum number of connected components, such that each connected
component of G[F] is isomorphic to some graph from \Pi.
We give an algorithm solving the optimization problem on an n-vertex graph G
in time O(#pmc n^{t+4} f(t,\phi)), where #pmc is the number of all potential
maximal cliques in G and f is a function depending of t and \phi\ only. We also
show how a similar running time can be obtained for the weighted version of the
problem. Pipelined with known bounds on the number of potential maximal
cliques, we deduce that our optimization problem can be solved in time
O(1.7347^n) for arbitrary graphs, and in polynomial time for graph classes with
polynomial number of minimal separators
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