289,152 research outputs found
Image registration using finite dimensional lie groups : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Mathematics at Massey University, Palmerston North, New Zealand
D'Arcy Thompson was a biologist and mathematician who, in his 1917 book `On
Growth and Form', posited a `Theory of Transformations', which is based on the observation
that a smooth, global transformation of space may be applied to the shape
of an organism so that its transformed shape corresponds closely to that of a related
organism. Image registration is the computational task of finding such transformations
between pairs of images.
In modern applications in areas such as medical imaging, the transformations are often
chosen from the infinite-dimensional diffieomorphism group. However, this differs from
Thompson's approach where the groups are chosen to be as simple as possible, and
are generally finite-dimensional. The main exception to this is the similarity group
of translation, rotation, and scaling, which is used to pre-align images. In this thesis
the set of planar Lie groups are investigated and applied to image registration of the
types of images that Thompson considered. As these groups are smaller, successful
registration in these groups provides more specifc information about the relationship
between the images than diffeomorphic registration does, as well as providing faster
implementations. We build a lattice of the Lie groups showing which are subgroups of
each other, and the groups are used to perform image registration by minimizing the
L2-norm of the difference between the group-transformed source image and the target
image. A robust, practical, and efficient algorithm for registration in Lie groups is
developed and tested on a variety of image types.
Each successful registration returns a point in a Lie group. Given several related images
(such as the hooves of several animals) it is possible to find smooth curves that pass
through the Lie group elements used to relate the various images. These curves can
then be employed to interpolate points between the set of images or to extrapolate to
new images that have not been seen before. We discuss the mathematics behind this
and demonstrate it on the images that Thompson used, as well as other datasets of
interest.
Finally, we consider using a sequence of the planar Lie groups to perform registration,
with the output from one group being used as the input to the next. We call this multiregistration,
and have identified two types: where the smallest group is a subgroup
of the next smallest, and so on up a chain, and where the groups are not directly
related, i.e., separated on the lattice. We demonstrate experimentally that multiregistration
can provide more information about the relationship between images than
simple registration. In addition, we show that transformations that cannot be obtained
by a single registration in any of the groups considered can be successfully reached
A new strategy for improving vision based tracking accuracy based on utilization of camera calibration information
Abstract— Camera calibration is one of the essential
components of a vision based tracking system where the objective
is to extract three dimensional information from a set of two
dimensional frames. The information extracted from the
calibration process is significant for examining the accuracy of the
vision sensor, and thus further for estimating its effectiveness as a
tracking system in real applications. This paper introduces
another use for this information in which the proper location of
the camera can be predicted. Anew mathematical formula based
on utilizing the extracted calibration information was used for
finding the optimum location for the camera, which provides the
best detection accuracy. Moreover, the calibration information
was also used for selecting the proper image Denoising filter. The
results obtained proved the validity of the proposed formula in
finding the desired camera location where the smallest detection
errors can be produced. Also, results showed that the proper
selection of the filter parameters led to a considerable
enhancement in the overall accuracy of the camera, reducing the
overall detection error by 0.2 mm
Real Time Image Saliency for Black Box Classifiers
In this work we develop a fast saliency detection method that can be applied
to any differentiable image classifier. We train a masking model to manipulate
the scores of the classifier by masking salient parts of the input image. Our
model generalises well to unseen images and requires a single forward pass to
perform saliency detection, therefore suitable for use in real-time systems. We
test our approach on CIFAR-10 and ImageNet datasets and show that the produced
saliency maps are easily interpretable, sharp, and free of artifacts. We
suggest a new metric for saliency and test our method on the ImageNet object
localisation task. We achieve results outperforming other weakly supervised
methods
A geometric approach to archetypal analysis and non-negative matrix factorization
Archetypal analysis and non-negative matrix factorization (NMF) are staples
in a statisticians toolbox for dimension reduction and exploratory data
analysis. We describe a geometric approach to both NMF and archetypal analysis
by interpreting both problems as finding extreme points of the data cloud. We
also develop and analyze an efficient approach to finding extreme points in
high dimensions. For modern massive datasets that are too large to fit on a
single machine and must be stored in a distributed setting, our approach makes
only a small number of passes over the data. In fact, it is possible to obtain
the NMF or perform archetypal analysis with just two passes over the data.Comment: 36 pages, 13 figure
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