591 research outputs found
Detection of Outer Rotations on 3D-Vector Fields with Iterative Geometric Correlation
Correlation is a common technique for the detection of shifts. Its
generalization to the multidimensional geometric correlation in Clifford
algebras has proven a useful tool for color image processing, because it
additionally contains information about rotational misalignment. In this paper
we prove that applying the geometric correlation iteratively can detect the
outer rotational misalignment for arbitrary three-dimensional vector fields.
Thus, it develops a foundation applicable for image registration and pattern
matching. Based on the theoretical work we have developed a new algorithm and
tested it on some principle examples
A General Geometric Fourier Transform Convolution Theorem
The large variety of Fourier transforms in geometric algebras inspired the
straight forward definition of ``A General Geometric Fourier Transform`` in
Bujack et al., Proc. of ICCA9, covering most versions in the literature. We
showed which constraints are additionally necessary to obtain certain features
like linearity, a scaling, or a shift theorem. In this paper we extend the
former results by a convolution theorem
Detection of Total Rotations on 2D-Vector Fields with Geometric Correlation
Correlation is a common technique for the detection of shifts. Its
generalization to the multidimensional geometric correlation in Clifford
algebras additionally contains information with respect to rotational
misalignment. It has been proven a useful tool for the registration of vector
fields that differ by an outer rotation. In this paper we proof that applying
the geometric correlation iteratively has the potential to detect the total
rotational misalignment for linear two-dimensional vector fields. We further
analyze its effect on general analytic vector fields and show how the rotation
can be calculated from their power series expansions
Autonomous Golf Cart Firmware
The Autonomous Golf Cart Project is a project sponsored by the Cal Poly Robotics Club. The multidisciplinary team is adding sensors and electronics to a regular golf cart with the goal to drive the golf cart around campus without and human input. This task requires a plethora of hardware and firmware to control that hardware. The firmware provides an interface for higher level software to then control the hardware and therefore drive the golf cart. This report is focused on the hardware modifications and the firmware used in order to drive the golf cart from a computer
Towards Automatic Feature-based Visualization
Visualizations are well suited to communicate large amounts of complex data. With increasing resolution in the spatial and temporal domain simple imaging techniques meet their limits, as it is quite difficult to display multiple variables in 3D or analyze long video sequences. Feature detection techniques reduce the data-set to the essential structures and allow for a highly abstracted representation of the data. However, current feature detection algorithms commonly rely on a detailed description of each individual feature. In this paper, we present a feature-based visualization technique that is solely based on the data. Using concepts from computational mechanics and information theory, a measure, local statistical complexity, is defined that extracts distinctive structures in the data-set. Local statistical complexity assigns each position in the (multivariate) data-set a scalar value indicating regions with extraordinary behavior. Local structures with high local statistical complexity form the features of the data-set. Volume-rendering and iso-surfacing are used to visualize the automatically extracted features of the data-set. To illustrate the ability of the technique, we use examples from diffusion, and flow simulations in two and three dimensions
Convolution products for hypercomplex Fourier transforms
Hypercomplex Fourier transforms are increasingly used in signal processing
for the analysis of higher-dimensional signals such as color images. A main
stumbling block for further applications, in particular concerning filter
design in the Fourier domain, is the lack of a proper convolution theorem. The
present paper develops and studies two conceptually new ways to define
convolution products for such transforms. As a by-product, convolution theorems
are obtained that will enable the development and fast implementation of new
filters for quaternionic signals and systems, as well as for their higher
dimensional counterparts.Comment: 18 pages, two columns, accepted in J. Math. Imaging Visio
Tracking Lines in Higher Order Tensor Fields
While tensors occur in many areas of science and engineering, little has been done to visualize tensors with order higher than two. Tensors of higher orders can be used for example to describe complex diffusion patterns in magnetic resonance imaging (MRI). Recently, we presented a method for tracking lines in higher order tensor fields that is a generalization of methods known from first order tensor fields (vector fields) and symmetric second order tensor fields. Here, this method is applied to magnetic resonance imaging where tensor fields are used to describe diffusion patterns for example of hydrogen in the human brain. These patterns align to the internal structure and can be used to analyze interconnections between different areas of the brain, the so called tractography problem. The advantage of using higher order tensor lines is the ability to detect crossings locally, which is not possible in second order tensor fields. In this paper, the theoretical details will be extended and tangible results will be given on MRI data sets
Eyelet particle tracing - steady visualization of unsteady flow
It is a challenging task to visualize the behavior of time-dependent 3D vector fields. Most of the time an overview of unsteady fields is provided via animations, but, unfortunately, animations provide only transient impressions of momentary flow. In this paper we present two approaches to visualize time varying fields with fixed geometry. Path lines and streak lines represent such a steady visualization of unsteady vector fields, but because of occlusion and visual clutter it is useless to draw them all over the spatial domain. A selection is needed. We show how bundles of streak lines and path lines, running at different times through one point in space, like through an eyelet, yield an insightful visualization of flow structure ('eyelet lines'). To provide a more intuitive and appealing visualization we also explain how to construct a surface from these lines. As second approach, we use a simple measurement of local changes of a field over time to determine regions with strong changes. We visualize these regions with isosurfaces to give an overview of the activity in the dataset. Finally we use the regions as a guide for placing eyelets
HOT–Lines: Tracking Lines in Higher Order Tensor Fields
Tensors occur in many areas of science and engineering. Especially, they are used to describe charge, mass and energy transport (i.e. electrical conductivity tensor, diffusion tensor, thermal conduction
tensor resp.) If the locale transport pattern is complicated, usual second order tensor representation is not sufficient. So far, there are no appropriate visualization methods for this case. We point out similarities of symmetric higher order tensors and spherical harmonics. A spherical harmonic representation is used to improve tensor glyphs. This paper unites the definition of streamlines and tensor lines and generalizes tensor lines to those applications where second order tensors representations fail. The algorithm is tested on the tractography problem in diffusion tensor magnetic resonance imaging (DT-MRI) and improved
for this special application
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