Feature Extraction & Visualization of ALMA Data Cubes through Topological Data Analysis

Investigators

• Paul Rosen – University of South Florida
• Bei Wang – University of Utah
• Chris Johnson – University of Utah
• Betsy Mills – San Jose State University
• Jeff Kern – National Radio Astronomy Observatory

Collaborators

• Anil Seth – University of Utah
• Adam Ginsburg – National Radio Astronomy Observatory
• Julia Kamenetzky – Westminster College, Salt Lake City

About

ALMA-TDA is a persistent homology based engine for noise removal in ALMA data cubes. ALMA-TDA uses a data structure known as the contour tree to summarize and simplify the data. The figure to the right shows an example of the process. ALMA-TDA takes a scalar function from a data cube, computes a topological skeleton in the form of a contour tree, and simplifies that skeleton and the scalar field. The feature removal only impacts regions that connect pairs of critical points. In this way, ALMA-TDA provides the minimum perturbation of the field required to remove unwanted features. 
(a) An image of a 2D scalar function before simplification. (b) 3D height map of the contours corresponding to the scalar function shown in (a). (c) The contour tree structures that capture the features (i.e., relationships among local minima, local maxima, and saddle points). (d)-(f): The image, 3D height map, and the contour tree after simplifying the features.

Get the Software!

Binaries of our software, including a usage manual, can be downloaded from: https://github.com/SCIInstitute/ALMA-TDA/releases
Source code may be accessed at: https://github.com/SCIInstitute/ALMA-TDA

Demonstration of Simplification

The following example (data provided by Anil Seth) demonstrates our ability to simplify volumes. Each pair represents a layer before (left) and after (right) simplification using the Contour Tree.
       
       
       
       
       
       

Publications

• Paul Rosen, Bei Wang, Anil Seth, Betsy Mills, Adam Ginsburg, Julia Kamenetzky, Jeff Kern, Chris R. Johnson, Using Contour Trees in the Analysis and Visualization of Radio Astronomy Data Cubes, under submission to IEEE InfoVis, 2017.
  Preprint available at: https://cspaul.com/projects/alma-tda/ALMA-TDA-InfoVis17.pdf
• Paul Rosen, Junyi Tu, and Les Piegl, A Hybrid Solution to Calculating Augmented Join Trees of 2D Scalar Fields in Parallel}, accepted to CAD Conference and Exhibition, extend abstract, 2017.
  Preprint available at: https://cspaul.com/projects/alma-tda/ALMA-TDA-CAD17.pdf
• Paul Rosen, Junyi Tu, and Les Piegl, A Hybrid Solution to Parallel Calculation of Augmented Join Trees of Scalar Fields in Any Dimension, under submission to the Journal of Computer Aided Design and Applications, 2017.
  Preprint available at: https://cspaul.com/projects/alma-tda/ALMA-TDA-CADandA.pdf
• Bei Wang, Analysis and Visualization of ALMA Data Cubes, Workshop for Women in Computational Topology (WinCompTop), Poster, 2016
  Poster available at: https://cspaul.com/projects/alma-tda/16-08-Wang-WinCompTop.pdf

Presentations

• Paul Rosen, Opportunities to Advance Visualization Capabilities for ALMA Data Cubes through Topological Data Analysis, Socorro NM, Jan 2016
• Paul Rosen, Feature Extraction & Data Cube Visualization Through Topological Data Analysis, Future Science Development Workshop, Charlottesville VA, Aug 2016
• Bei Wang, Advancing the Visualization Capabilities of ALMA Data Cubes through Topological Data Analysis, High Energy and Astrophysics (HEAP) Seminar Series, University of Utah, Salt Lake City UT, Sept 2016
• Paul Rosen, Feature Extraction & Data Cube Visualization Through Topological Data Analysis, CASA Users Group, Socorro NM (presented remotely), Sept 2016
• Paul Rosen, Exploring Applications of Persistent Homology in Signal and Image Processing, USF Computer Vision Group, Oct 2016

Panel

• Panel on ALMA TDA, Salt Lake City UT, Jan 2017
  • Participants: Paul Rosen, Bei Wang, Ayla Khan, Betsy Mills, Chris Johnson, Adam Ginsburg, Julia Kamenetzky

Mission

Science Case

Radio astronomy is currently undergoing a revolution driven by new observing capabilities. The current generation of radio and millimeter telescopes, particularly the Atacama Large Millimeter Array (ALMA), offers enormous advances in capabilities, including significantly increased sensitivity, spatial and spectral resolution, and spectral bandwidth. While these advances represent an unprecedented opportunity to advance scientific understanding, they also pose a significant challenge. Although the higher sensitivity and resolution they provide in some cases yield new detections of sources with well-ordered structure that is easy to interpret with current tools (e.g., HL Tau [9]), these advances equally often lead to the detection of structure with increased spatial and spectral complexity (e.g., new molecules in the chemically-rich massive star forming region Sgr B2, outflows in the nuclear region of the nearby galaxy NGC 253, and rich kinematic structure in the giant molecular cloud “The Brick” [1, 2, 12]). The new complexity present in current spectral line datasets challenges not only the existing tools for fundamental analysis of these datasets, but also users’ ability to explore and visualize their data.
Whether scientists can navigate and correctly interpret this new complexity will determine their success in addressing a number of important scientific questions. Among the topics driven by the detection of more complex structures are ISM turbulence [4, 13], the star formation process [7], filaments [11], molecular cloud structure and kinematics [12], and the kinematics of nearby galaxies [5, 6, 8] and high redshift galaxies [10, 14].
An even greater challenge arises from our ability to detect an increased number of spectral lines in more and more sources. There simply are no tools capable of simultaneously visualizing, comparing, and analyzing the dozens to hundreds of data cubes for all of the detected spectral lines in a given source. Such standard methods of both visualizing and exploring data as moment maps, channel maps, playing cube like a video, or 3D models, cannot scale up to the case of large numbers of lines, even in non-complex, well-ordered cases, such as rotating disks, or expanding stellar shells. Users become overwhelmed by, for example, comparing these typical diagnostics for two lines, side by side or one at a time. In the richest sources with thousands of lines, such comparisons will simply be impossible—it becomes necessary to resort to methods that entirely throw away either the spectral information such as Principle Component Analysis (PCA) of moment maps or the spatial information that requires model fitting of complex spectra. As a result, both exploration and analysis of the data becomes not only time consuming, but potentially incomplete.

References