Data sets resulting from physical simulations typically contain a multitude of physical variables. It is, therefore, desirable that visualization methods take into account the entire multi-field volume data rather than concentrating on one variable. We present a visualization approach based on surface extraction from multi-field particle volume data. The surfaces segment the data with respect to the underlying multi-variate function. Decisions on segmentation properties are based on the analysis of the multi-dimensional feature space. The feature space exploration is performed by an automated multi-dimensional hierarchical clustering method, whose resulting density clusters are shown in the form of density level sets in a 3D star coordinate layout. In the star coordinate layout, the user can select clusters of interest. A selected cluster in feature space corresponds to a segmenting surface in object space. Based on the segmentation property induced by the cluster membership, we extract a surface from the volume data. Our driving applications are Smoothed Particle Hydrodynamics (SPH) simulations, where each particle carries multiple properties. The data sets are given in the form of unstructured point-based volume data. We directly extract our surfaces from such data without prior resampling or grid generation. The surface extraction computes individual points on the surface, which is supported by an efficient neighborhood computation. The extracted surface points are rendered using point-based rendering operations. Our approach combines methods in scientific visualization for object-space operations with methods in information visualization for feature-space operations.

Visualization of high-dimensional data requires a mapping to a visual space. Whenever the goal is to preserve similarity relations a frequent strategy is to use 2D projections, which afford intuitive interactive exploration, e.g., by users locating and selecting groups and gradually drilling down to individual objects. In this paper, we propose a framework for projecting high-dimensional data to 3D visual spaces, based on a generalization of the LeastSquare Projection (LSP). We compare projections to 2D and 3D visual spaces both quantitatively and through a user study considering certain exploration tasks. The quantitative analysis confirms that 3D projections outperform 2D projections in terms of precision. The user study indicates that certain tasks can be more reliably and confidently answered with 3D projections. Nonetheless, as 3D projections are displayed on 2D screens, interaction is more difficult. Therefore, we incorporate suitable interaction functionalities into a framework that supports 3D transformations, predefined optimal 2D views, coordinated 2D and 3D views, and hierarchical 3D cluster definition and exploration. For visually encoding data clusters in a 3D setup, we employ color coding of projected data points as well as four types of surface renderings. A second user study evaluates the suitability of these visual encodings. Several examples illustrate the framework's applicability for both visual exploration of multidimensional abstract (non-spatial) data as well as the feature space of multi-variate spatial data.

Fetal hematopoietic cells that express the common acute lymphoblastic leukemia antigen (CALLA) were purified from both fetal liver and fetal bone marrow by immune rosetting with sheep erythrocytes coated with rabbit anti-mouse immunoglobulin and by fluorescence-activated cell sorting. Dual fluorescence techniques disclosed that these cells were heterogenous with respect to the expression of a series of differentiation and activation antigens defined by monoclonal antibodies. Thus, whereas all CALLA+ cells were Ia+ and expressed two activation antigens, J2 and T10, only 30-50% expressed B1 antigen. Furthermore, using methanol-fixed cells, it could be shown that approximately 20% contained intracytoplasmic mu chains (cyto-mu) and that approximately 15% were positive for the terminal transferase enzyme (TdT) marker. The CALLA+ fetal cells thus closely resemble the childhood acute lymphoblastic leukemia cell with respect to surface marker phenotype. A population of CALLA- cells devoid of mature erythroid and myeloid surface markers was found to contain higher numbers of TdT+ cells but lower numbers of cyto-mu, B1, and Ia+ cells than the CALLA+ subset. In vitro analysis of normal, purified CALLA+ cells demonstrated that incubation at 37 degrees C with J5 monoclonal antibody specific for CALLA resulted in the specific modulation of surface antigen. Similar results have previously been obtained with CALLA+ tumor cells. Although phenotypic analysis of CALLA+ cells suggests that these cells are relatively immature lymphoid cells, CALLA+ cells do not appear to contain either myeloid precursor cells (CFU-G/M) or the earliest lymphoid stem cells.

We tested the efficacy of passive serotherapy in the treatment of acute lymphoblastic leukemia in four patients who had relapsed while receiving standard chemotherapeutic agents. Each patient received multiple intravenous infusions of J-5 monoclonal antibody specific for common acute lymphoblastic leukemia antigen (CALLA). In the three patients with circulating leukemic cells, there was a rapid decrease in circulating blasts that began immediately after antibody infusion, but not all leukemic cells were cleared, and remaining cells appeared to be resistant to further serotherapy. Although J-5 antibody was also demonstrable on bone marrow lymphoblasts immediately after antibody infusion in one patient, there was no change in bone marrow cellularity or differential during serotherapy. Analysis of the cell surface phenotype of leukemic cells during serotherapy and in vitro studies with patient cells suggests that resistance to serotherapy was mediated in part by antigenic modulation of CALLA in response to J-5 antibody.

Abstract-Smooth surface extraction using partial differential equations (PDEs) is a well-known and widely used technique for visualizing volume data. Existing approaches operate on gridded data and mainly on regular structured grids. When considering unstructured point-based volume data where sample points do not form regular patterns nor are they connected in any form, one would typically resample the data over a grid prior to applying the known PDE-based methods. We propose an approach that directly extracts smooth surfaces from unstructured point-based volume data without prior resampling or mesh generation. When operating on unstructured data one needs to quickly derive neighborhood information. The respective information is retrieved by partitioning the 3D domain into cells using a kd-tree and operating on its cells. We exploit neighborhood information to estimate gradients and mean curvature at every sample point using a four-dimensional least-squares fitting approach. Gradients and mean curvature are required for applying the chosen PDE-based method that combines hyperbolic advection to an isovalue of a given scalar field and mean curvature flow. Since we are using an explicit time-integration scheme, time steps and neighbor locations are bounded to ensure convergence of the process. To avoid small global time steps, one can use asynchronous local integration. We extract a smooth surface by successively fitting a smooth auxiliary function to the data set. This auxiliary function is initialized as a signed distance function. For each sample and for every time step we compute the respective gradient, the mean curvature, and a stable time step. With these informations the auxiliary function is manipulated using an explicit Euler time integration. The process successively continues with the next sample point in time. If the norm of the auxiliary function gradient in a sample exceeds a given threshold at some time, the auxiliary function is reinitialized to a signed distance function. After convergence of the evolvution, the resulting smooth surface is obtained by extracting the zero isosurface from the auxiliary function using direct isosurface extraction from unstructured point-based volume data and rendering the extracted surface using point-based rendering methods.