88,941 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
Exact Results for Perturbative Chern-Simons Theory with Complex Gauge Group
We develop several methods that allow us to compute all-loop partition
functions in perturbative Chern-Simons theory with complex gauge group G_C,
sometimes in multiple ways. In the background of a non-abelian irreducible flat
connection, perturbative G_C invariants turn out to be interesting topological
invariants, which are very different from finite type (Vassiliev) invariants
obtained in a theory with compact gauge group G. We explore various aspects of
these invariants and present an example where we compute them explicitly to
high loop order. We also introduce a notion of "arithmetic TQFT" and conjecture
(with supporting numerical evidence) that SL(2,C) Chern-Simons theory is an
example of such a theory.Comment: 60 pages, 9 figure
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