12,381 research outputs found
Reliability in Constrained Gauss-Markov Models: An Analytical and Differential Approach with Applications in Photogrammetry
This report was prepared by Jackson Cothren, a graduate research associate in the Department of Civil and Environmental Engineering and Geodetic Science at the Ohio State University, under the supervision of Professor Burkhard Schaffrin.This report was also submitted to the Graduate School of the Ohio State University as a dissertation in partial fulfillment of the requirements for the Ph.D. degree.Reliability analysis explains the contribution of each observation in an estimation model
to the overall redundancy of the model, taking into account the geometry of the network
as well as the precision of the observations themselves. It is principally used to design
networks resistant to outliers in the observations by making the outliers more detectible
using standard statistical tests.It has been studied extensively, and principally, in Gauss-
Markov models. We show how the same analysis may be extended to various
constrained Gauss-Markov models and present preliminary work for its use in
unconstrained Gauss-Helmert models. In particular, we analyze the prominent reliability
matrix of the constrained model to separate the contribution of the constraints to the
redundancy of the observations from the observations themselves. In addition, we make
extensive use of matrix differential calculus to find the Jacobian of the reliability matrix
with respect to the parameters that define the network through both the original design
and constraint matrices. The resulting Jacobian matrix reveals the sensitivity of
reliability matrix elements highlighting weak areas in the network where changes in
observations may result in unreliable observations. We apply the analytical framework to
photogrammetric networks in which exterior orientation parameters are directly observed
by GPS/INS systems. Tie-point observations provide some redundancy and even a few
collinear tie-point and tie-point distance constraints improve the reliability of these
direct observations by as much as 33%. Using the same theory we compare networks in
which tie-points are observed on multiple images (n-fold points) and tie-points are
observed in photo pairs only (two-fold points). Apparently, the use of two-fold tiepoints
does not significantly degrade the reliability of the direct exterior observation
observations. Coplanarity constraints added to the common two-fold points do not add
significantly to the reliability of the direct exterior orientation observations. The
differential calculus results may also be used to provide a new measure of redundancy
number stability in networks. We show that a typical photogrammetric network with n-fold
tie-points was less stable with respect to at least some tie-point movement than an
equivalent network with n-fold tie-points decomposed into many two-fold tie-points
Networks for Nonlinear Diffusion Problems in Imaging
A multitude of imaging and vision tasks have seen recently a major
transformation by deep learning methods and in particular by the application of
convolutional neural networks. These methods achieve impressive results, even
for applications where it is not apparent that convolutions are suited to
capture the underlying physics.
In this work we develop a network architecture based on nonlinear diffusion
processes, named DiffNet. By design, we obtain a nonlinear network architecture
that is well suited for diffusion related problems in imaging. Furthermore, the
performed updates are explicit, by which we obtain better interpretability and
generalisability compared to classical convolutional neural network
architectures. The performance of DiffNet tested on the inverse problem of
nonlinear diffusion with the Perona-Malik filter on the STL-10 image dataset.
We obtain competitive results to the established U-Net architecture, with a
fraction of parameters and necessary training data
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