Bayesian Point Set Registration

Point set registration involves identifying a smooth invertible transformation between corresponding points in two point sets, one of which may be smaller than the other and possibly corrupted by observation noise. This problem is traditionally decomposed into two separate optimization problems: (i) assignment or correspondence, and (ii) identification of the optimal transformation between the ordered point sets. In this work, we propose an approach solving both problems simultaneously. In particular, a coherent Bayesian formulation of the problem results in a marginal posterior distribution on the transformation, which is explored within a Markov chain Monte Carlo scheme. Motivated by Atomic Probe Tomography (APT), in the context of structure inference for high entropy alloys (HEA), we focus on the registration of noisy sparse observations of rigid transformations of a known reference configuration.Lastly, we test our method on synthetic data sets.Comment: 15 pages, 20 figure

Magnetic stimulation for non-homogeneous biological structures

BACKGROUND: Magnetic stimulation has gained relatively wide application in studying nervous system structures. This technology has the advantage of reduced excitation of sensory nerve endings, and hence results in quasi-painless action. It has become clinically accepted modality for brain stimulation. However, theoretical and practical solutions for assessment of induced current distribution need more detailed and accurate consideration. Some possible analyses are proposed for distribution of the current induced from excitation current contours of different shape and disposition. Relatively non-difficult solutions are shown, applicable for two- and three-dimensional analysis. METHODS: The boundary conditions for field analysis by the internal Dirichlet problem are introduced, based on the vector potential field excited by external current coils. The feedback from the induced eddy currents is neglected. Finite element modeling is applied for obtaining the electromagnetic fields distribution in a non-homogeneous domain. RESULTS: The distributions were obtained in a non-homogeneous structure comprised of homogeneous layers. A tendency was found of the induced currents to follow paths in lower resistivity layers, deviating from the expected theoretical course for a homogeneous domain. Current density concentrations occur at the boundary between layers, suggesting the possibility for focusing on, or predicting of, a zone of stimulation. CONCLUSION: The theoretical basis and simplified approach for generation of 3D FEM networks for magnetic stimulation analysis are presented, applicable in non-homogeneous and non-linear media. The inconveniences of introducing external excitation currents are avoided. Thus, the possibilities are improved for analysis of distributions induced by time-varying currents from contours of various geometry and position with respect to the medium

Effect of Contour Shape of Nervous System Electromagnetic Stimulation Coils on the Induced Electrical Field Distribution

BACKGROUND: Electromagnetic stimulation of the nervous system has the advantage of reduced discomfort in activating nerves. For brain structures stimulation, it has become a clinically accepted modality. Coil designs usually consider factors such as optimization of induced power, focussing, field shape etc. In this study we are attempting to find the effect of the coil contour shape on the electrical field distribution for magnetic stimulation. METHOD AND RESULTS: We use the maximum of the induced electric field stimulation in the region of interest as the optimization criterion. This choice required the application of the calculus of variation, with the contour perimeter taken as a pre-set condition. Four types of coils are studied and compared: circular, square, triangular and an 'optimally' shaped contour. The latter yields higher values of the induced electrical field in depths up to about 30 mm, but for depths around 100 mm, the circular shape has a slight advantage. The validity of the model results was checked by experimental measurements in a tank with saline solution, where differences of about 12% were found. In view the accuracy limitations of the computational and measurement methods used, such differences are considered acceptable. CONCLUSION: We applied an optimization approach, using the calculus of variation, which allows to obtain a coil contour shape corresponding to a selected criterion. In this case, the optimal contour showed higher intensities for a longer line along the depth-axis. The method allows modifying the induced field structure and focussing the field to a selected zone or line