Quantitative Comparison of Sinc-Approximating Kernels for Medical Image Interpolation

Abstract. Interpolation is required in many medical image processing operations. From sampling theory, it follows that the ideal interpolation kernel is the sinc function, which is of infinite extent. In the attempt to obtain practical and computationally efficient image processing al-gorithms, many sinc-approximating interpolation kernels have been de-vised. In this paper we present the results of a quantitative comparison of 84 different sinc-approximating kernels, with spatial extents ranging from 2 to 10 grid points in each dimension. The evaluation involves the application of geometrical transformations to medical images from dif-ferent modalities (CT, MR, and PET), using the different kernels. The results show very clearly that, of all kernels with a spatial extent of 2 grid points, the linear interpolation kernel performs best. Of all kernels with an extent of 4 grid points, the cubic convolution kernel is the best (28 %- 75 % reduction of the errors as compared to linear interpolation). Even better results (44 %- 95 % reduction) are obtained with kernels of larger extent, notably the Welch, Cosine, Lanczos, and Kaiser windowed sinc kernels. In general, the truncated sinc kernel is one of the worst performing kernels.

Three-dimensional random Voronoi tessellations: From cubic crystal lattices to Poisson point processes

We perturb the SC, BCC, and FCC crystal structures with a spatial Gaussian noise whose adimensional strength is controlled by the parameter a, and analyze the topological and metrical properties of the resulting Voronoi Tessellations (VT). The topological properties of the VT of the SC and FCC crystals are unstable with respect to the introduction of noise, because the corresponding polyhedra are geometrically degenerate, whereas the tessellation of the BCC crystal is topologically stable even against noise of small but finite intensity. For weak noise, the mean area of the perturbed BCC and FCC crystals VT increases quadratically with a. In the case of perturbed SCC crystals, there is an optimal amount of noise that minimizes the mean area of the cells. Already for a moderate noise (a>0.5), the properties of the three perturbed VT are indistinguishable, and for intense noise (a>2), results converge to the Poisson-VT limit. Notably, 2-parameter gamma distributions are an excellent model for the empirical of of all considered properties. The VT of the perturbed BCC and FCC structures are local maxima for the isoperimetric quotient, which measures the degre of sphericity of the cells, among space filling VT. In the BCC case, this suggests a weaker form of the recentluy disproved Kelvin conjecture. Due to the fluctuations of the shape of the cells, anomalous scalings with exponents >3/2 is observed between the area and the volumes of the cells, and, except for the FCC case, also for a->0. In the Poisson-VT limit, the exponent is about 1.67. As the number of faces is positively correlated with the sphericity of the cells, the anomalous scaling is heavily reduced when we perform powerlaw fits separately on cells with a specific number of faces

Quantifying Beta‐Galactosylceramide Kinetics in Cerebrospinal Fluid of Healthy Subjects Using Deuterium Labeling

Therapeutics promoting myelin synthesis may enhance recovery in demyelinating diseases, such as multiple sclerosis. However, no suitable method exists to quantify myelination. The turnover of galactosylceramide (myelin component) is indicative of myelination in mice, but its turnover has not been determined in humans. Here, six healthy subjects consumed 120 mL 70% D2 O daily for 70 days to label galactosylceramide. We then used mass spectrometry and compartmental modeling to quantify the turnover rate of galactosylceramide in cerebrospinal fluid. Maximum deuterium enrichment of body water ranged from 1.5-3.9%, whereas that of galactosylceramide was much lower: 0.05-0.14%. This suggests a slow turnover rate, which was confirmed by the model-estimated galactosylceramide turnover rate of 0.00168 day-1 , which corresponds to a half-life of 413 days. Additional studies in patients with multiple sclerosis are needed to investigate whether galactosylceramide turnover could be used as an outcome measure in clinical trials with remyelination therapies.PharmacologyAnalytical BioScience

Ising model on 3D random lattices: A Monte Carlo study

We report single-cluster Monte Carlo simulations of the Ising model on three-dimensional Poissonian random lattices with up to 128,000 approx. 503 sites which are linked together according to the Voronoi/Delaunay prescription. For each lattice size quenched averages are performed over 96 realizations. By using reweighting techniques and finite-size scaling analyses we investigate the critical properties of the model in the close vicinity of the phase transition point. Our random lattice data provide strong evidence that, for the available system sizes, the resulting effective critical exponents are indistinguishable from recent high-precision estimates obtained in Monte Carlo studies of the Ising model and \phi^4 field theory on three-dimensional regular cubic lattices.Comment: 35 pages, LaTex, 8 tables, 8 postscript figure