Abstractions of sequences, functions and operators

In volume data visualization, the classification is used to determine voxel visibility and is usually carried out by transfer functions that define a mapping between voxel value and color/opacity. The design of transfer functions is a key process in volume visualization applications. However, one transfer function that is suitable for a data set usually dose not suit others, so it is difficult and time-consuming for users to design new proper transfer function when the types of the studied data sets are changed. By introducing neural networks into the transfer function design, a general adaptive transfer function (GATF) is proposed in this paper. Experimental results showed that by using neural networks to guide the transfer function design, the robustness of volume rendering is promoted and the corresponding classification process is optimized.

A crucial step in volume rendering is the design of transfer functions that will highlight those aspects of the volume data that are of interest to the user. For many applications, boundaries carry most of the relevant information. Reliable detection of boundaries is often hampered by limitations of the imaging process, such as blurring and noise. We present a method to identify the materials that form the boundaries. These materials are then used in a new domain that facilitates interactive and semiautomatic design of appropriate transfer functions. We also show how the obtained boundary information can be used in region-growing-based segmentation.

Transfer function design in volume visualization has been a challenging problem due to the huge design space. In this work, we present a system which is capable of integrating the transfer function design results from a group of users. For a specified volume dataset, intermediate and final transfer function designs for many users with different backgrounds are collected. A 2D representation of the transfer function feature space, called transfer function map, is then constructed for each volume data set by MDS projection of the collected transfer function samples. With the proposed transfer function map, interactions, including flexible navigation in the transfer function feature space and transfer function design recommendation, have been developed.

Volume visualization and exploration through flexible transfer function design

The design of transfer functions for volume rendering is a difficult task. This is particularly true for multi-channel data sets, where multiple data values exist for each voxel. In this paper, we propose a new method for transfer function design. Our new method provides a framework to combine multiple approaches and pushes the boundary of gradient-based transfer functions to multiple channels, while still keeping the dimensionality of transfer functions to a manageable level, i.e., a maximum of three dimensions, which can be displayed visually in a straightforward way. Our approach utilizes channel intensity, gradient, curvature and texture properties of each voxel. The high-dimensional data of the domain is reduced by applying recently developed nonlinear dimensionality reduction algorithms. In this paper, we used Isomap as well as a traditional algorithm, Principle Component Analysis (PCA). Our results show that these dimensionality reduction algorithms significantly improve the transfer function design process without compromising visualization accuracy. In this publication we report on the impact of the dimensionality reduction algorithms on transfer function design for confocal microscopy data.

The power of any parallelizing compiler is limited by its program analyzers. Finding the right for program analysis is crucial. The various existing data dependence abstractions can be viewed simply as approximations of the others. Moreover, data dependences have common structures, which can be exhibited by abstraction of the structure of run-time computations (the leading idea of abstract interpretation [1]). We apply the classical framework of abstract interpretation, defined in [2], to data dependence analysis. We show that data dependence abstractions (simple data dependence, dependence levels, direction vectors, distance vectors, iteration data dependence graph, expanded data dependence graph, statement data dependence graph) and data-flow dependence abstractions (defined in [3]) are abstract interpretations of the program semantics. The standard collecting semantics is defined from the small step operational trace semantics of a subset of a sequential imperative language. By successive Galois connection based abstractions, data dependences are designed as abstract semantics, that approximate the standard collecting semantics. Then the hierarchy of data dependences is constructed as a part of the lattice of abstract interpretations. The correspondence between concrete and abstract properties is established by a pair of functions that is a Galois connection. The Galois connection formalizes the loss of information of the process. Moreover, the composition of Galois connections is a Galois connection and this property allows for a compositional design of successive approximations. This formalization of the data dependence analysis corresponds to a shift from syntax, of which most of the existing data dependence analyses are based on, to semantics. This could allow the application of the achievements of the program analysis community to dependence analysis.

The transfer function design is important for medical image visualization. Through the analysis of current transfer function design method, we propose a clustering algorithm with the help of gradation-gradient colored histogram to realize the classification for volume data, which is convenient to highlight the tissues of interest. Additionally, the number of these combined clusterings and the clustering centers can be determined rapidly through the color distribution of the gradation-gradient colored histogram. Of course, the method makes the clustering algorithm more effective and more reasonable. Currently, the transformation of three-dimensional data field from data attributes to optical attributes using the transfer function is carried out in the RGB color space. In this paper, combining the advantages of HSL color mode, we map the identifying information to HSL color space firstly. Through the method, it’s easy and intuitive for us to adjust the visual quality. Based on the method of transfer function design for volume rendering given in this paper, we conduct an experiment with the program of OpenGL/GLSL to realize the medical image visualization using ray-casting volume rendering algorithm. The experimental results show that this method is effective and corrective.

The transfer function is responsible for the three-dimensional image classification and its design is a key process in volume visualization applications. However, it is difficult and time-consuming for the users to design new proper transfer function when the types of the studied images change. By introducing a general regression neural network (GRNN) into the transfer function design, together with a proper image evaluation strategy, a new volume rendering framework is proposed in this paper. Experimental results showed that by using GRNN to guide the transfer function design, the robustness of volume rendering is promoted and the corresponding classification process is optimized.

Volume visualization has been widely used to simulate and observe complex data in the fields of science, engineering, biomedicine, etc. One central topic of volume visualization is the transfer function (TF) of volume rendering. By setting TF, users design the mapping of voxels to optical properties of 3D datasets. However, the design of TF is usually a blind process. How to classify all volume data accurately and design a suitable TF fleetly is the key to improve the efficiency of volume rendering. In this paper, we propose a new TF design approach based on extreme gradient boosting (XGBoost) algorithm for fast visualization. First, the features are extracted from 3D volume data. Then we use the XGBoost model to classify the volume data and design TF. Finally, we assign the optical properties to the voxels to express and reveal the relevant features of dataset. This approach can help users to render the volume data efficiently. It has been tested and achieved satisfactory result.

The application of n-dimensional transfer functions for feature segmentation has become increasingly popular in volume rendering. Recent work has focused on the utilization of higher order dimensional transfer functions incorporating spatial dimensions (x, y, and z) along with traditional feature space dimensions (value and value gradient). However, as the dimensionality increases, it becomes exceedingly dicult to abstract the transfer function into an intuitive and interactive workspace. In this work we focus on populating the traditional two-dimensional histogram with a set of derived metrics from the spatial (x, y and z) and feature space (value, value gradient, etc.) domain to create a set of abstract feature space transfer function domains. Current two-dimensional transfer function widgets typically consist of a two-dimensional histogram where each entry in the histogram represents the number of voxels that maps to that entry. In the case of an abstract transfer function design, the amount of spatial variance at that histogram coordinate is mapped instead, thereby relating additional information about the data abstraction in the projected space. Finally, a non-parametric kernel density estimation approach for feature space clustering is applied in the abstracted space, and the resultant transfer functions are discussed with respect to the space abstraction.

The use of multi-dimensional transfer functions for direct volume rendering has been shown to be an effective means of extracting materials and their boundaries for both scalar and multivariate data. The most common multi-dimensional transfer function consists of a two-dimensional (2D) histogram with axes representing a subset of the feature space (e.g., value vs. value gradient magnitude), with each entry in the 2D histogram being the number of voxels at a given feature space pair. Users then assign color and opacity to the voxel distributions within the given feature space through the use of interactive widgets (e.g., box, circular, triangular selection). Unfortunately, such tools lead users through a trial-and-error approach as they assess which data values within the feature space map to a given area of interest within the volumetric space. In this work, we propose the addition of non-parametric clustering within the transfer function feature space in order to extract patterns and guide transfer function generation. We apply a non-parametric kernel density estimation to group voxels of similar features within the 2D histogram. These groups are then binned and colored based on their estimated density, and the user may interactively grow and shrink the binned regions to explore feature boundaries and extract regions of interest. We also extend this scheme to temporal volumetric data in which time steps of 2D histograms are composited into a histogram volume. A three-dimensional (3D) density estimation is then applied, and users can explore regions within the feature space across time without adjusting the transfer function at each time step. Our work enables users to effectively explore the structures found within a feature space of the volume and provide a context in which the user can understand how these structures relate to their volumetric data. We provide tools for enhanced exploration and manipulation of the transfer function, and we show that the initial transfer function generation serves as a reasonable base for volumetric rendering, reducing the trial-and-error overhead typically found in transfer function design.

Transfer function design is an integrated component in volume visualization and data exploration. The common trial-and-error approach for transfer function searching is a very difficult and time consuming process. A goal oriented and parameterized transfer function model is therefore crucial in guiding the transfer function searching process for better and more meaningful visualization results. The paper presents an image based transfer function model that integrates 3D image processing tools into the volume visualization pipeline to facilitate the search for an image based transfer function in volume data visualization and exploration. The model defines a transfer function as a sequence of 3D image processing procedures, and allows the users to adjust a set of qualitative and descriptive parameters to achieve their subjective visualization goals. 3D image enhancement and boundary detection tools, and their integration methods with volume visualization algorithms are described. The application of this approach for 3D microscopy data exploration and analysis is also discussed.

Transfer function design is an integrated component in volume visualization and data exploration. The common trial-and-error approach for transfer function searching is a very difficult and time consuming process. A goal oriented and parameterized transfer function model is therefore crucial in guiding the transfer function searching process for better and more meaningful visualization results. The paper presents an image based transfer function model that integrates 3D image processing tools into the volume visualization pipeline to facilitate the search for an image based transfer function in volume data visualization and exploration. The model defines a transfer function as a sequence of 3D image processing procedures, and allows the users to adjust a set of qualitative and descriptive parameters to achieve their subjective visualization goals. 3D image enhancement and boundary detection tools, and their integration methods with volume visualization algorithms are described. The application of this approach for 3D microscopy data exploration and analysis is also discussed.

Analytic, simulated, scanned datasets were used to evaluate two representative data-centric methods for designing transfer functions (TFs), which are a key factor determining the quality of volume rendered images. They map the physical fields of a given volume dataset to the optical properties, such as color and opacity. Designing proper TFs is difficult because they depend on both the context of the target volume dataset and the purpose of the visual exploration. A system called “Ivory” was developed to assist in the design of TFs. With it, a better TF can be composed so as to inherit different features from two original TFs.

A central component of expressive volume rendering is the identification of tissue or material types and their respective boundaries. To perform appropriate data classification, transfer functions can be defined in highdimensional histograms, removing restrictions of purely 1D scalar value classification. The presented work aims at alleviating the problems of interactive multi-dimensional transfer function design by coupling high-dimensional, probabilistic, data-centric segmentation with interaction in the natural 3D space of the volume. We fit variable Gaussian Mixture Models to user specified subsets of the data set, yielding a probabilistic data model of the identified material type and its sources. The resulting classification allows for efficient transfer function design and multi-material volume rendering as demonstrated in several benchmark data sets.