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

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

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

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

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

Role of Cryptococcus neoformans Rho1 GTPases in the PKC1 signaling pathway in response to thermal stress

To initiate and establish infection in mammals, the opportunistic fungal pathogen Cryptococcus neoformans must survive and thrive upon subjection to host temperature. Primary maintenance of cell integrity is controlled through the protein kinase C1 (PKC1) signaling pathway, which is regulated by a Rho1 GTPase in Saccharomyces cerevisiae. We identified three C. neoformans Rho GTPases, Rho1, Rho10, and Rho11, and have begun to elucidate their role in growth and activation of the PKC1 pathway in response to thermal stress. Western blot analysis revealed that heat shock of wild-type cells resulted in phosphorylation of Mpk1 mitogen-activated protein kinase (MAPK). Constitutive activation of Rho1 caused phosphorylation of Mpk1 independent of temperature, indicating its role in pathway regulation. A strain with a deletion of RHO10 also displayed this constitutive Mpk1 phosphorylation phenotype, while one with a deletion of RHO11 yielded phosphorylation similar to that of wild type. Surprisingly, like a rho10Δ strain, a strain with a deletion of both RHO10 and RHO11 displayed temperature sensitivity but mimicked wild-type phosphorylation, which suggests that Rho10 and Rho11 have coordinately regulated functions. Heat shock-induced Mpk1 phosphorylation also required the PKC1 pathway kinases Bck1 and Mkk2. However, Pkc1, thought to be the major regulatory kinase of the cell integrity pathway, was dispensable for this response. Together, our results argue that Rho proteins likely interact via downstream components of the PKC1 pathway or by alternative pathways to activate the cell integrity pathway in C. neoformans

Cryptococcus neoformans phosphoinositide-dependent kinase 1 (PDK1) ortholog is required for stress tolerance and survival in murine phagocytes

Cryptococcus neoformans PKH2-01 and PKH2-02 are orthologous to mammalian PDK1 kinase genes. Although orthologs of these kinases have been extensively studied in S. cerevisiae, little is known about their function in pathogenic fungi. In this study, we show that PKH2-02 but not PKH2-01 is required for C. neoformans to tolerate cell wall, oxidative, nitrosative, and antifungal drug stress. Deletion of PKH2-02 leads to decreased basal levels of Pkc1 activity and, consequently, reduced activation of the cell wall integrity mitogen-activated protein kinase (MAPK) pathway in response to cell wall, oxidative, and nitrosative stress. PKH2-02 function also is required for tolerance of fluconazole and amphotericin B, two important drugs for the treatment of cryptococcosis. Furthermore, OSU-03012, an inhibitor of human PDK1, is synergistic and fungicidal in combination with fluconazole. Using a Galleria mellonella model of low-temperature cryptococcosis, we found that PKH2-02 is also required for virulence in a temperature-independent manner. Consistent with the hypersensitivity of the pkh2-02Δ mutant to oxidative and nitrosative stress, this mutant shows decreased survival in murine phagocytes compared to that of wild-type (WT) cells. In addition, we show that deletion of PKH2-02 affects the interaction between C. neoformans and phagocytes by decreasing its ability to suppress production of tumor necrosis factor alpha (TNF-α) and reactive oxygen species. Taken together, our studies demonstrate that Pkh2-02-mediated signaling in C. neoformans is crucial for stress tolerance, host-pathogen interactions, and both temperature-dependent and -independent virulence