4,124 research outputs found
Improved Maximum Entropy Analysis with an Extended Search Space
The standard implementation of the Maximum Entropy Method (MEM) follows Bryan
and deploys a Singular Value Decomposition (SVD) to limit the dimensionality of
the underlying solution space apriori. Here we present arguments based on the
shape of the SVD basis functions and numerical evidence from a mock data
analysis, which show that the correct Bayesian solution is not in general
recovered with this approach. As a remedy we propose to extend the search basis
systematically, which will eventually recover the full solution space and the
correct solution. In order to adequately approach problems where an
exponentially damped kernel is used, we provide an open-source implementation,
using the C/C++ language that utilizes high precision arithmetic adjustable at
run-time. The LBFGS algorithm is included in the code in order to attack
problems without the need to resort to a particular search space restriction.Comment: 18 pages, 6 figures, v3 includes several changes in text and figures,
t.b.p. in Journal of Computational Physics, source code at
http://www.scicode.org/ExtME
A higher-order active contour model of a `gas of circles' and its application to tree crown extraction
Many image processing problems involve identifying the region in the image
domain occupied by a given entity in the scene. Automatic solution of these
problems requires models that incorporate significant prior knowledge about the
shape of the region. Many methods for including such knowledge run into
difficulties when the topology of the region is unknown a priori, for example
when the entity is composed of an unknown number of similar objects.
Higher-order active contours (HOACs) represent one method for the modelling of
non-trivial prior knowledge about shape without necessarily constraining region
topology, via the inclusion of non-local interactions between region boundary
points in the energy defining the model. The case of an unknown number of
circular objects arises in a number of domains, e.g. medical, biological,
nanotechnological, and remote sensing imagery. Regions composed of an a priori
unknown number of circles may be referred to as a `gas of circles'. In this
report, we present a HOAC model of a `gas of circles'. In order to guarantee
stable circles, we conduct a stability analysis via a functional Taylor
expansion of the HOAC energy around a circular shape. This analysis fixes one
of the model parameters in terms of the others and constrains the rest. In
conjunction with a suitable likelihood energy, we apply the model to the
extraction of tree crowns from aerial imagery, and show that the new model
outperforms other techniques
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