7,892 research outputs found
Three variants of three Stage Optimal Memetic Exploration for handling non-separable fitness landscapes
The file attached to this record is the authors final peer reviewed version. The publisher's final version can be found by following the DOI link.Three Stage Optimal Memetic Exploration (3SOME) is a recently proposed algorithmic framework which sequentially perturbs a single solution by means of three operators. Although 3SOME proved to be extremely successful at handling high-dimensional multi-modal landscapes, its application to non-separable fitness functions present some flaws. This paper proposes three possible variants of the original 3SOME algorithm aimed at improving its performance on non-separable problems. The first variant replaces one of the 3SOME operators, namely the middle distance exploration, with a rotation-invariant Differential Evolution (DE) mutation scheme, which is applied on three solutions sampled in a progressively shrinking search space. In the second proposed mechanism, a micro-population rotation-invariant DE is integrated within the algorithmic framework. The third approach employs the search logic (1+1)-Covariance Matrix Adaptation Evolution Strategy, aka (1+1)-CMA-ES. In the latter scheme, a Covariance Matrix adapts to the landscape during the optimization in order to determine the most promising search directions. Numerical results show that, at the cost of a higher complexity, the three approaches proposed are able to improve upon 3SOME performance for non-separable problems without an excessive performance deterioration in the other problems
Doctor of Philosophy in Computing
dissertationAn important area of medical imaging research is studying anatomical diffeomorphic shape changes and detecting their relationship to disease processes. For example, neurodegenerative disorders change the shape of the brain, thus identifying differences between the healthy control subjects and patients affected by these diseases can help with understanding the disease processes. Previous research proposed a variety of mathematical approaches for statistical analysis of geometrical brain structure in three-dimensional (3D) medical imaging, including atlas building, brain variability quantification, regression, etc. The critical component in these statistical models is that the geometrical structure is represented by transformations rather than the actual image data. Despite the fact that such statistical models effectively provide a way for analyzing shape variation, none of them have a truly probabilistic interpretation. This dissertation contributes a novel Bayesian framework of statistical shape analysis for generic manifold data and its application to shape variability and brain magnetic resonance imaging (MRI). After we carefully define the distributions on manifolds, we then build Bayesian models for analyzing the intrinsic variability of manifold data, involving the mean point, principal modes, and parameter estimation. Because there is no closed-form solution for Bayesian inference of these models on manifolds, we develop a Markov Chain Monte Carlo method to sample the hidden variables from the distribution. The main advantages of these Bayesian approaches are that they provide parameter estimation and automatic dimensionality reduction for analyzing generic manifold-valued data, such as diffeomorphisms. Modeling the mean point of a group of images in a Bayesian manner allows for learning the regularity parameter from data directly rather than having to set it manually, which eliminates the effort of cross validation for parameter selection. In population studies, our Bayesian model of principal modes analysis (1) automatically extracts a low-dimensional, second-order statistics of manifold data variability and (2) gives a better geometric data fit than nonprobabilistic models. To make this Bayesian framework computationally more efficient for high-dimensional diffeomorphisms, this dissertation presents an algorithm, FLASH (finite-dimensional Lie algebras for shooting), that hugely speeds up the diffeomorphic image registration. Instead of formulating diffeomorphisms in a continuous variational problem, Flash defines a completely new discrete reparameterization of diffeomorphisms in a low-dimensional bandlimited velocity space, which results in the Bayesian inference via sampling on the space of diffeomorphisms being more feasible in time. Our entire Bayesian framework in this dissertation is used for statistical analysis of shape data and brain MRIs. It has the potential to improve hypothesis testing, classification, and mixture models
On-Manifold Preintegration for Real-Time Visual-Inertial Odometry
Current approaches for visual-inertial odometry (VIO) are able to attain
highly accurate state estimation via nonlinear optimization. However, real-time
optimization quickly becomes infeasible as the trajectory grows over time, this
problem is further emphasized by the fact that inertial measurements come at
high rate, hence leading to fast growth of the number of variables in the
optimization. In this paper, we address this issue by preintegrating inertial
measurements between selected keyframes into single relative motion
constraints. Our first contribution is a \emph{preintegration theory} that
properly addresses the manifold structure of the rotation group. We formally
discuss the generative measurement model as well as the nature of the rotation
noise and derive the expression for the \emph{maximum a posteriori} state
estimator. Our theoretical development enables the computation of all necessary
Jacobians for the optimization and a-posteriori bias correction in analytic
form. The second contribution is to show that the preintegrated IMU model can
be seamlessly integrated into a visual-inertial pipeline under the unifying
framework of factor graphs. This enables the application of
incremental-smoothing algorithms and the use of a \emph{structureless} model
for visual measurements, which avoids optimizing over the 3D points, further
accelerating the computation. We perform an extensive evaluation of our
monocular \VIO pipeline on real and simulated datasets. The results confirm
that our modelling effort leads to accurate state estimation in real-time,
outperforming state-of-the-art approaches.Comment: 20 pages, 24 figures, accepted for publication in IEEE Transactions
on Robotics (TRO) 201
A Comprehensive Introduction of Visual-Inertial Navigation
In this article, a tutorial introduction to visual-inertial navigation(VIN)
is presented. Visual and inertial perception are two complementary sensing
modalities. Cameras and inertial measurement units (IMU) are the corresponding
sensors for these two modalities. The low cost and light weight of camera-IMU
sensor combinations make them ubiquitous in robotic navigation. Visual-inertial
Navigation is a state estimation problem, that estimates the ego-motion and
local environment of the sensor platform. This paper presents visual-inertial
navigation in the classical state estimation framework, first illustrating the
estimation problem in terms of state variables and system models, including
related quantities representations (Parameterizations), IMU dynamic and camera
measurement models, and corresponding general probabilistic graphical models
(Factor Graph). Secondly, we investigate the existing model-based estimation
methodologies, these involve filter-based and optimization-based frameworks and
related on-manifold operations. We also discuss the calibration of some
relevant parameters, also initialization of state of interest in
optimization-based frameworks. Then the evaluation and improvement of VIN in
terms of accuracy, efficiency, and robustness are discussed. Finally, we
briefly mention the recent development of learning-based methods that may
become alternatives to traditional model-based methods.Comment: 35 pages, 10 figure
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