MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

High-Throughput Glomeruli Analysis of micro-CT Kidney Images Using Tree Priors and Scalable Sparse Computation

Kidney-related diseases have incrementally become one major cause of death. Glomeruli are the physiological units in the kidney responsible for the blood filtration. Therefore, their statistics including number and volume, directly describe the efficiency and health state of the kidney. Stereology is the current quantification method relying on histological sectioning, sampling and further 2D analysis, being laborious and sample destructive. New micro-Computed Tomography (μCT) imaging protocols resolute structures down to capillary level. However large-scale glomeruli analysis remains challenging due to object identifiability, allotted memory resources and computational time. We present a methodology for high-throughput glomeruli analysis that incorporates physiological apriori information relating the kidney vasculature with estimates of glomeruli counts. We propose an effective sampling strategy that exploits scalable sparse segmentation of kidney regions for refined estimates of both glomeruli count and volume. We evaluated the proposed approach on a database of μCT datasets yielding a comparable segmentation accuracy as an exhaustive supervised learning method. Furthermore we show the ability of the proposed sampling strategy to result in improved estimates of glomeruli counts and volume without requiring a exhaustive segmentation of the μCT image. This approach can potentially be applied to analogous organizations, such as for example the quantification of alveoli in lungs