Fast extraction of adaptive multiresolution meshes with guaranteed properties from volumetric data

We present a new algorithm for extracting adaptive multiresolution triangle meshes from volume datasets. The algorithm guarantees that the topological genus of the generated mesh is the same as the genus of the surface embedded in the volume dataset at all levels of detail. In addition to this "hard constraint" on the genus of the mesh, the user can choose to specify some number of soft geometric constraints, such as triangle aspect ratio, minimum or maximum total number of vertices, minimum and/or maximum triangle edge lengths, maximum magnitude of various error metrics per triangle or vertex, including maximum curvature (area) error, maximum distance to the surface, and others. The mesh extraction process is fully automatic and does not require manual adjusting of parameters to produce the desired results as long as the user does not specify incompatible constraints. The algorithm robustly handles special topological cases, such as trimmed surfaces (intersections of the surface with the volume boundary), and manifolds with multiple disconnected components (several closed surfaces embedded in the same volume dataset). The meshes may self-intersect at coarse resolutions. However, the self-intersections are corrected automatically as the resolution of the meshes increase. We show several examples of meshes extracted from complex volume datasets

Fast extraction of adaptive multiresolution meshes with guaranteed properties from volumetric data

We present a new algorithm for extracting adaptive multiresolution triangle meshes from volume datasets. The algorithm guarantees that the topological genus of the generated mesh is the same as the genus of the surface embedded in the volume dataset at all levels of detail. In addition to this "hard constraint" on the genus of the mesh, the user can choose to specify some number of soft geometric constraints, such as triangle aspect ratio, minimum or maximum total number of vertices, minimum and/or maximum triangle edge lengths, maximum magnitude of various error metrics per triangle or vertex, including maximum curvature (area) error, maximum distance to the surface, and others. The mesh extraction process is fully automatic and does not require manual adjusting of parameters to produce the desired results as long as the user does not specify incompatible constraints. The algorithm robustly handles special topological cases, such as trimmed surfaces (intersections of the surface with the volume boundary), and manifolds with multiple disconnected components (several closed surfaces embedded in the same volume dataset). The meshes may self-intersect at coarse resolutions. However, the self-intersections are corrected automatically as the resolution of the meshes increase. We show several examples of meshes extracted from complex volume datasets

Segmentation of primary breast tumor nuclei in histological images

Breast cancer (BCa) is a heterogeneous and diverse disease. They are sub-classified into four major subtypes – luminal A, luminal B, Her2-overexpressing and basal-like. It has been seen that the phenotypic variability between BCa occurs within, but not across these major subtypes. These subtypes not only have distinct behaviors but also differ in responses to therapy which highlights the importance of identifying each subtype of BCa for appropriate therapeutic decisions. In order to determine pathologic staging, pathologists routinely evaluate various features like Regional lymph node metastasis status and histologic grade. Such histological analysis though useful and cost-effective, largely depends on the experience of the pathologist performing the analysis. To achieve a better reproducibility and reduced dependence on the pathologist, there is a need to develop a system to objectively predict tumor subtype which was previously possible only through expensive molecular testing and immunohistochemistry (IHC). In order to establish an Image analysis paradigm to generate predictions of tumor sub-type objectively, a reliable method to segment nuclei to analyze their properties individually has been discussed. The performance of this method is evaluated and is seen to perform better - qualitatively and quantitatively compared to a preliminary segmentation

Spatial Trends in Groundwater Arsenic Concentrations

Arsenic presents complex spatial occurrence trends that can be difficult to identify and understand. This project sought to understand geographic trends in arsenic occurrence using a visualization technique. The approach taken was to link geospatially referenced arsenic concentration information from a water quality database with elevation data contained in Digital Terrain Elevation Data (DTED) files. DTED files are available for all land masses across the world for public download. This allows for the development of three-dimensional plots of arsenic concentration and topography. The plots developed in this manner show that high arsenic is associated with the transition from plains to piedmont on the western side of the Delaware River Valley in New Jersey. In Oklahoma high arsenic is found along the North Canadian River Valley. In New Mexico high concentrations are generally high in the Rio Grande Valley but with an area of low concentration in the southern portion of this valley. In California, arsenic concentrations are high in the middle of the Central Valley but moderate somewhat toward the edges. These results are consistent with mobilization of arsenic by reductive processes in the organic-rich sediments of river valleys, but further statistical analysis is required to confirm the significance of this association. The visualization software used here is broadly applicable and a user guide for this software is available on request