Overview + Detail Visualization for Ensembles of Diffusion Tensors

Abstract

A Diffusion Tensor Imaging (DTI) group study consists of a collection of volumetric diffusion tensor datasets (i.e., an ensemble) acquired from a group of subjects. The multivariate nature of the diffusion tensor imposes challenges on the analysis and the visualization. These challenges are commonly tackled by reducing the diffusion tensors to scalar‐valued quantities that can be analyzed with common statistical tools. However, reducing tensors to scalars poses the risk of losing intrinsic information about the tensor. Visualization of tensor ensemble data without loss of information is still a largely unsolved problem. In this work, we propose an overview + detail visualization to facilitate the tensor ensemble exploration. We define an ensemble representative tensor and variations in terms of the three intrinsic tensor properties (i.e., scale, shape, and orientation) separately. The ensemble summary information is visually encoded into the newly designed aggregate tensor glyph which, in a spatial layout, functions as the overview. The aggregate tensor glyph guides the analyst to interesting areas that would need further detailed inspection. The detail views reveal the original information that is lost during aggregation. It helps the analyst to further understand the sources of variation and formulate hypotheses. To illustrate the applicability of our prototype, we compare with most relevant previous work through a user study and we present a case study on the analysis of a brain diffusion tensor dataset ensemble from healthy volunteers.

Uncertainty in the DTI Visualization Pipeline

“…Since the diffusion tensor is a second-order tensor, its covariance is represented by a fourth-order tensor, however, the visualization of the fourth-order tensor is rather difficult in this context. Basser et al [7] presented a novel technique for the spectral decomposition of the fourth-order covariance tensor (a) Uncertainity cones [50] (b) HiFiVE Glyphs [90] (c) Decomposed ensemble representation [110] (d) ODF glyphs [96] Fig . 4 Glyphs with uncertainty encoding and introduced the concept of tensorial normal distribution.…”

Towards Glyphs for Uncertain Symmetric Second‐Order Tensors

“…Assuming a Gaussian distribution to describe uncertainty in tensor data is common and widely accepted in the literature [BP03, BP07, AWHS16]. We remark that alternative models exist and are used in settings, where this assumption does not hold; for instance, [ZSL∗16, ZCH∗17] use a modified mean tensor.…”

“…): if two eigenvalues of the covariance tensor get close to each other, the corresponding eigenvectors (and therefore the 6 visualizations) may show discontinuities. In a similar approach for ensembles of tensor data, Zhang et al [ZCH∗17] provide a framework to combine several visualizations to gain a general overview of the whole ensemble, as well as a detailed information of distinct tensor properties. They divide uncertainty in three independent parts (scaling, shape and rotation) and encode each with one variance number.…”

Representative Consensus from Limited‐Size Ensembles

“…As a result, a significant body of work in the field of uncertainty visualization has been devoted to the topic of ensemble visualization. Various ensemble visualization techniques have been proposed to deal with quantifying and visualizing the uncertainty associated with commonly used datatypes, including scalar fields [PWH11], vector fields [PPH12], tensor fields [ZCH*17], temporal ensembles [FKRW17], network data [SNG*17] and their featuresets, such as isocontours or isosurfaces [WMK13,MWK14], shapes [DJW16], pathlines or streamlines [FBW16], vortex structures [OT12], and graph features, such as paths [RMR*17] and edges [GHL15]. Almost all these techniques use a probabilistic approach to quantify the amount of uncertainty present in the ensemble data.…”