Mesh-to-raster based non-rigid registration of multi-modal images

Region of interest (ROI) alignment in medical images plays a crucial role in diagnostics, procedure planning, treatment, and follow-up. Frequently, a model is represented as triangulated mesh while the patient data is provided from CAT scanners as pixel or voxel data. Previously, we presented a 2D method for curve-to-pixel registration. This paper contributes (i) a general mesh-to-raster (M2R) framework to register ROIs in multi-modal images; (ii) a 3D surface-to-voxel application, and (iii) a comprehensive quantitative evaluation in 2D using ground truth provided by the simultaneous truth and performance level estimation (STAPLE) method. The registration is formulated as a minimization problem where the objective consists of a data term, which involves the signed distance function of the ROI from the reference image, and a higher order elastic regularizer for the deformation. The evaluation is based on quantitative light-induced fluoroscopy (QLF) and digital photography (DP) of decalcified teeth. STAPLE is computed on 150 image pairs from 32 subjects, each showing one corresponding tooth in both modalities. The ROI in each image is manually marked by three experts (900 curves in total). In the QLF-DP setting, our approach significantly outperforms the mutual information-based registration algorithm implemented with the Insight Segmentation and Registration Toolkit (ITK) and Elastix

Study On Covolume-Upwind Finite Volume Approximations For Linear Parabolic Partial Differential Equations

In this thesis we solve two-dimensional linear parabolic partial differential equations with pure Dirichelet boundary conditions, using the bilinear covolume-upwind finite volume method on rectangular grids to discretize the spatial variables and the Crank-Nicholson method for the time variable. These PDEs provide a model for problems from various fields of engineering and applied sciences, such as unsteady viscous flow problems, the simulation of oil extraction from underground reservoirs, transport of air and ground water pollutants and modeling of semiconductor devices. Finite volume method has the important advantage of allowing the conversion of integrations over the control volume to integrations over its boundary based on Green\u27s Theorem. Then, one can use quadrature rules to approximate the resulting integrals. In order to avoid non-physical oscillations that can arise from the numerical solution of convection-dominated problems when using the central finite volume scheme, we generate non-standard control volumes using local Peclet\u27s numbers and the upwind principle. We numerically compare the covolume-upwind finite volume method with the central and the upwind finite volume schemes, demonstrating stability and better convergence of the method through various examples