The design of transfer functions for volume rendering is a non-trivial task. This is particularly true for multi-channel data sets, where multiple data values exist for each voxel, which require multi-dimensional transfer functions. In this article, we propose a new method for multi-dimensional transfer function design. Our new method provides a framework to combine multiple computational approaches and pushes the boundary of gradient-based multidimensional transfer functions to multiple channels, while keeping the dimensionality of transfer functions at a manageable level, that is, 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. Applying recently developed nonlinear dimensionality reduction algorithms reduce the high-dimensional data of the domain. In this article, we use Isomap and Locally Linear Embedding as well as a traditional algorithm, Principle Component Analysis. Our results show that these dimensionality reduction algorithms significantly improve the transfer function design process without compromising visualization accuracy. We demonstrate the effectiveness of our new dimensionality reduction algorithms with two volumetric confocal microscopy data sets.

中文翻译：

---

多通道体数据集多维传递函数的降维


体绘制传递函数的设计是一项艰巨的任务。对于多通道数据集尤其如此，其中每个体素存在多个数据值，这需要多维传递函数。在本文中，我们提出了一种多维传递函数设计的新方法。我们的新方法提供了一个结合多种计算方法的框架，并将基于梯度的多维传递函数的边界推向多个通道，同时将传递函数的维数保持在可管理的水平，即最多三个维度，这可以是以直观的方式直观地展示。我们的方法利用每个体素的通道强度、梯度、曲率和纹理属性。应用最近开发的非线性降维算法减少了域的高维数据。在本文中，我们使用 Isomap 和局部线性嵌入以及传统算法“主成分分析”。我们的结果表明，这些降维算法显着改进了传递函数设计过程，而不会影响可视化准确性。我们通过两个体积共焦显微镜数据集证明了新的降维算法的有效性。