284 research outputs found
Indirect Image Registration with Large Diffeomorphic Deformations
The paper adapts the large deformation diffeomorphic metric mapping framework
for image registration to the indirect setting where a template is registered
against a target that is given through indirect noisy observations. The
registration uses diffeomorphisms that transform the template through a (group)
action. These diffeomorphisms are generated by solving a flow equation that is
defined by a velocity field with certain regularity. The theoretical analysis
includes a proof that indirect image registration has solutions (existence)
that are stable and that converge as the data error tends so zero, so it
becomes a well-defined regularization method. The paper concludes with examples
of indirect image registration in 2D tomography with very sparse and/or highly
noisy data.Comment: 43 pages, 4 figures, 1 table; revise
Diffeomorphic Learning
We introduce in this paper a learning paradigm in which the training data is
transformed by a diffeomorphic transformation before prediction. The learning
algorithm minimizes a cost function evaluating the prediction error on the
training set penalized by the distance between the diffeomorphism and the
identity. The approach borrows ideas from shape analysis where diffeomorphisms
are estimated for shape and image alignment, and brings them in a previously
unexplored setting, estimating, in particular diffeomorphisms in much larger
dimensions. After introducing the concept and describing a learning algorithm,
we present diverse applications, mostly with synthetic examples, demonstrating
the potential of the approach, as well as some insight on how it can be
improved
Deformations of quantum field theories on spacetimes with Killing vector fields
The recent construction and analysis of deformations of quantum field
theories by warped convolutions is extended to a class of curved spacetimes.
These spacetimes carry a family of wedge-like regions which share the essential
causal properties of the Poincare transforms of the Rindler wedge in Minkowski
space. In the setting of deformed quantum field theories, they play the role of
typical localization regions of quantum fields and observables. As a concrete
example of such a procedure, the deformation of the free Dirac field is
studied.Comment: 35 pages, 3 figure
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