On the characterization of non-negative volume-matching surface splines

AbstractIn this paper we study the surface spline which minimizes the Dirichlet Integral over a two-dimensional bounded domain, among all non-negative functions satisfying a finite number of volume-matching constraints. Existence and uniqueness of this surface spline are proved. A characterization by a variational inequality is given, revealing local and boundary behaviour of the surface spline. This characterization is of importance in the construction of numerical algorithms for the production of non-negative smooth surfaces from aggregated data

Volume-volume matching

Oftentimes in visualization, the goal of using volume datasets is not just to visualize them but also to analyze and compare them. In order to compare the two volumes, we cannot take all the voxels into consideration. The size of a typical volume data set is quite large (maybe a billion or more voxels), thus it is not feasible to compare all these voxels to all in the other volume set. This project uses optimization methods to find the best orientation for aligning a second volume data set with a first. Using these methods, we will be able to determine how well one medical data volume matches against a "normally-developed" volume of the same type

Ground and Space Radar Volume Matching and Comparison Software

This software enables easy comparison of ground- and space-based radar observations. The software was initially designed to compare ground radar reflectivity from operational, ground based Sand C-band meteorological radars with comparable measurements from the Tropical Rainfall Measuring Mission (TRMM) satellite s Precipitation Radar (PR) instrument. The software is also applicable to other ground-based and space-based radars. The ground and space radar volume matching and comparison software was developed in response to requirements defined by the Ground Validation System (GVS) of Goddard s Global Precipitation Mission (GPM) project. This software innovation is specifically concerned with simplifying the comparison of ground- and spacebased radar measurements for the purpose of GPM algorithm and data product validation. This software is unique in that it provides an operational environment to routinely create comparison products, and uses a direct geometric approach to derive common volumes of space- and ground-based radar data. In this approach, spatially coincident volumes are defined by the intersection of individual space-based Precipitation Radar rays with the each of the conical elevation sweeps of the ground radar. Thus, the resampled volume elements of the space and ground radar reflectivity can be directly compared to one another

A User-Friendly Protocol for Mandibular Segmentation of CBCT Images for Superimposition and Internal Structure Analysis

Background: Since cone-beam computed tomography (CBCT) technology has been widely adopted in orthodontics, multiple attempts have been made to devise techniques for mandibular segmentation and 3D superimposition. Unfortunately, as the software utilized in these methods are not specifically designed for orthodontics, complex procedures are often necessary to analyze each case. Thus, this study aimed to establish an orthodontist-friendly protocol for segmenting the mandible from CBCT images that maintains access to the internal anatomic structures. Methods: The “sculpting tool” in the Dolphin 3D Imaging software was used for segmentation. The segmented mandible images were saved as STL files for volume matching in the 3D Slicer to validate the repeatability of the current protocol and were exported as DICOM files for internal structure analysis and voxel-based superimposition. Results: The mandibles of all tested CBCT datasets were successfully segmented. The volume matching analysis showed high consistency between two independent segmentations for each mandible. The intraclass correlation coefficient (ICC) analysis on 20 additional CBCT mandibular segmentations further demonstrated the high consistency of the current protocol. Moreover, all of the anatomical structures for superimposition identified by the American Board of Orthodontics were found in the voxel-based superimposition, demonstrating the ability to conduct precise internal structure analyses with the segmented images. Conclusion: An efficient and precise protocol to segment the mandible while retaining access to the internal structures was developed on the basis of CBCT images. © 2021 by the authors. Licensee MDPI, Basel, Switzerland

Assessment of Left Ventricular Function in Cardiac MSCT Imaging by a 4D Hierarchical Surface-Volume Matching Process

Multislice computed tomography (MSCT) scanners offer new perspectives for cardiac kinetics evaluation with 4D dynamic sequences of high contrast and spatiotemporal resolutions. A new method is proposed for cardiac motion extraction in multislice CT. Based on a 4D hierarchical surface-volume matching process, it provides the detection of the heart left cavities along the acquired sequence and the estimation of their 3D surface velocity fields. A Markov random field model is defined to find, according to topological descriptors, the best correspondences between a 3D mesh describing the left endocardium at one time and the 3D acquired volume at the following time. The global optimization of the correspondences is realized with a multiresolution process. Results obtained on simulated and real data show the capabilities to extract clinically relevant global and local motion parameters and highlight new perspectives in cardiac computed tomography imaging

Numerical techniques for fast generation of large discrete-element models

In recent years, civil engineers have started to use discrete-element modelling to simulate large-scale soil volumes thanks to technological improvements in both hardware and software. However, existing procedures to prepare ‘representative elementary volumes’ are unsatisfactory in terms of computational cost and sample homogeneity. In this work, a simple but efficient procedure to initialise large-scale discrete-element models is presented. Periodic cells are first generated with a sufficient number of particles (enough to consider the cell a representative elementary volume) matching the desired particle size distribution and equilibrated at the desired stress state, porosity and coordination number. When the cell is in equilibrium, it is replicated in space to fill the problem domain. And when the model is filled, only a small number of mechanical cycles is needed to equilibrate a large domain. The result is an equilibrated homogeneous sample at the desired initial state in a large volume