Low-Dose Computed Tomography Filtering Using Geodesic Distances

Due to the concerns related to patient exposure to X-ray, the dosage used in computed tomography must be reduced (Low-dose Computed Tomography - LDCT). One of the effects of LDCT is the degradation in the quality of the final reconstructed image. In this work, we propose a method of filtering LDCT sinograms that are subject to signal-dependent Poisson noise. To filter this type of noise, we use a Bayesian approach, changing the Non-local Means (NLM) algorithm to use geodesic stochastic distances for Gamma distribution, the conjugate prior to Poisson, as a similarity metric between each projection point. Among the geodesic distances evaluated, we found a closed solution for the Shannon entropy for Gamma distributions. We compare our method with the following methods based on NLM: PoissonNLM, Stochastic Poisson NLM, Stochastic Gamma NLM and the original NLM after Anscombe transform. We also compare with BM3D after Anscombe transform. Comparisons are made on the final images reconstructed by the Filtered-Back Projection (FBP) and Projection onto Convex Sets (POCS) methods using the metrics PSNR and SSIM.

Interplay of curvature and rigidity in shape-based models of confluent tissue

Rigidity transitions in simple models of confluent cells have been a powerful organizing principle in understanding the dynamics and mechanics of dense biological tissue. In this work we explore the interplay between geometry and rigidity in two-dimensional vertex models confined to the surface of a sphere. By considering shapes of cells defined by perimeters whose magnitude depends on geodesic distances and areas determined by spherical polygons, the critical shape index in such models is affected by the size of the cell relative to the radius of the sphere on which it is embedded. This implies that cells can collectively rigidify by growing the size of the sphere, i.e. by tuning the curvature of their domain. Finite-temperature studies indicate that cell motility is affected well away from the zero-temperature transition point.