A parallel and memory efficient algorithm for constructing the contour tree

Abstract

The contour tree is a topological structure associated with a scalar function that tracks the connectivity of the evolving level sets of the function. It supports intuitive and interactive visual exploration and analysis of the scalar function. This paper describes a fast, parallel, and memory efficient algorithm for constructing the contour tree of a scalar function on shared memory systems. Comparisons with existing implementations show significant improvement in both the running time and the memory expended. The proposed algorithm is particularly suited for large datasets that do not fit in memory. For example, the contour tree for a scalar function defined on a 8.6 billion vertex domain (2048 × 2048 × 2048 volume data) can be efficiently constructed using less than 10GB of memory.

Computing Contour Trees for 2D Piecewise Polynomial Functions

“…Similarly the global split tree is computed by stitching the local split trees. The stitching procedure is similar to the one proposed by Acharya and Natarajan [AN15]. We describe it here for completeness, see also Algorithm S titch J oin T rees .…”

“…This case analysis is cumbersome even for the case of quadratic interpolants. Pascucci and Cole‐McLaughlin [PCM04] and Acharya and Natarajan [AN15] describe parallel algorithms to compute the contour tree for piecewise trilinear interpolants over a 3D grid. Minima and maxima are restricted to vertices of the grid and there are only four possible join/split tree configurations.…”

“…Carr and Snoeyink [CS09] propose an abstract framework for handling interpolants of arbitrary order and design a finite state automaton for computing the contour tree. This framework was employed either explicitly or implicitly for computing the contour tree in parallel for both trilinear interpolants [PCM04, AN15] and for piecewise linear interpolants [MDN12, LPG*14]. These algorithms used combinatorial routines to compute the tree corresponding to an individual cell.…”

Parallel peak pruning for scalable SMP contour tree computation

“…Similarly, Acharya & Natarajan [1] also compute the contour tree by splitting the data into blocks and combining the resulting local trees. Within each block, their algorithm identifies critical points, and constructs monotone paths from saddles to extrema to build topology graphs, following Chiang et al [9].…”

“…While there is a well-established algorithm [7] for computing merge trees and contour trees, the picture is patchier for distributed and data-parallel algorithms. While some approaches exist, they either target a distributed model [1], or have serial sections [16], do not come with strong formal guarantees on performance, and do not report methods for augmenting the contour tree with regular vertices, which is required for secondary computations such as geometric measures [8]. We therefore report a pure dataparallel algorithm with strong formal guarantees and practical runtime, that computes either the merge tree or the contour tree, augmented by any arbitrary number of regular vertices.…”