Learn More
TensorFlow [1] is an interface for expressing machine learning algorithms, and an implementation for executing such algorithms. A computation expressed using TensorFlow can be executed with little or no change on a wide variety of heterogeneous systems, ranging from mobile devices such as phones and tablets up to large-scale distributed systems of hundreds(More)
Visualization of 3D tensor fields continues to be a major challenge in terms of providing intuitive and uncluttered images that allow the users to better understand their data. The primary focus of this paper is on finding a formulation that lends itself to a stable numerical algorithm for extracting stable and persistent topological features from 2nd order(More)
This paper addresses several issues related to topological analysis of 3D second order symmetric tensor fields. First, we show that the degenerate features in such data sets form stable topological lines rather than points, as previously thought. Second, the paper presents two different methods for extracting these features by identifying the individual(More)
Tensor topology is useful in providing a simplified and yet detailed representation of a tensor field. Recently the field of 3D tensor topology is advanced by the discovery that degenerate tensors usually form lines in their most basic configurations. These lines form the backbone for further topological analysis. A number of ways for extracting and tracing(More)
Analysis of degenerate tensors is a fundamental step in finding the topological structures and separatrices in tensor fields. Previous work in this area have been limited to analyzing symmetric second order tensor fields. In this paper, we extend the topological analysis to 2D general (asymmetric) second order tensor fields. We show that it is not(More)
Topological analysis of 3D tensor fields starts with the identification of degeneracies in the tensor field. In this paper, we present a new, intuitive and numerically stable method for finding degenerate tensors in symmetric second order 3D tensors. This method is formulated based on a description of a tensor having an isotropic spherical component and a(More)
Visualizing second-order 3D tensor fields continue to be a challenging task. Although there are several algorithms that have been presented, no single algorithm by itself is sufficient for the analysis because of the complex nature of tensor fields. In this paper, we present two new methods, based on volume deformation, to show the effects of the tensor(More)
We present three methods of visualizing tensor fields that offer new ways of looking at tensor volumes. All three methods are based on the interaction of simulated light and the tensor field. Conceptually, rays are shot from a certain direction into the tensor volume. These rays are influenced by the surrounding tensor field and bent as they traverse(More)
We introduce the underlying theory behind degenerate points in 2D tensor fields to study the local flow characteristics in the vicinity of linear and non-linear singularities. The structural stability of these features and their corresponding separatrices are also analyzed. From here, we highlight the main techniques for visualizing and simplifying the(More)