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MSz: An Efficient Parallel Algorithm for Correcting Morse-Smale Segmentations in Error-Bounded Lossy Compressors

Yuxiao Li, Xin Liang, Bei Wang, Yongfeng Qiu, Lin Yan, Hanqi Guo

TL;DR

This work tackles the problem of preserving Morse-Smale segmentations in error-bounded lossy compression by introducing an edit-based paradigm that generates per-vertex edits at compression time and applies them during decompression to recover exact MS segmentations within the prescribed bound. It develops a parallel workflow comprising C-loops (fixing false critical points) and R-loops (fixing mislabelled regular points) that converges in finite iterations. The method is applicable to existing compressors (demonstrated with SZ3 and ZFP) and is accelerated on shared memory and GPUs, achieving substantial speedups on NVIDIA A100 hardware. Key contributions include a theoretically grounded, convergence-guaranteed editing framework, a parallel implementation to mitigate runtime overhead, and comprehensive evaluation across fluid dynamics, ocean, and cosmology datasets showing improved MS fidelity with competitive compression ratios. This approach enables topology-preserving data analysis in large-scale simulations, offering practical gains for end-users needing reliable topological features without sacrificing overall data fidelity.

Abstract

This research explores a novel paradigm for preserving topological segmentations in existing error-bounded lossy compressors. Today's lossy compressors rarely consider preserving topologies such as Morse-Smale complexes, and the discrepancies in topology between original and decompressed datasets could potentially result in erroneous interpretations or even incorrect scientific conclusions. In this paper, we focus on preserving Morse-Smale segmentations in 2D/3D piecewise linear scalar fields, targeting the precise reconstruction of minimum/maximum labels induced by the integral line of each vertex. The key is to derive a series of edits during compression time; the edits are applied to the decompressed data, leading to an accurate reconstruction of segmentations while keeping the error within the prescribed error bound. To this end, we developed a workflow to fix extrema and integral lines alternatively until convergence within finite iterations; we accelerate each workflow component with shared-memory/GPU parallelism to make the performance practical for coupling with compressors. We demonstrate use cases with fluid dynamics, ocean, and cosmology application datasets with a significant acceleration with an NVIDIA A100 GPU.

MSz: An Efficient Parallel Algorithm for Correcting Morse-Smale Segmentations in Error-Bounded Lossy Compressors

TL;DR

This work tackles the problem of preserving Morse-Smale segmentations in error-bounded lossy compression by introducing an edit-based paradigm that generates per-vertex edits at compression time and applies them during decompression to recover exact MS segmentations within the prescribed bound. It develops a parallel workflow comprising C-loops (fixing false critical points) and R-loops (fixing mislabelled regular points) that converges in finite iterations. The method is applicable to existing compressors (demonstrated with SZ3 and ZFP) and is accelerated on shared memory and GPUs, achieving substantial speedups on NVIDIA A100 hardware. Key contributions include a theoretically grounded, convergence-guaranteed editing framework, a parallel implementation to mitigate runtime overhead, and comprehensive evaluation across fluid dynamics, ocean, and cosmology datasets showing improved MS fidelity with competitive compression ratios. This approach enables topology-preserving data analysis in large-scale simulations, offering practical gains for end-users needing reliable topological features without sacrificing overall data fidelity.

Abstract

This research explores a novel paradigm for preserving topological segmentations in existing error-bounded lossy compressors. Today's lossy compressors rarely consider preserving topologies such as Morse-Smale complexes, and the discrepancies in topology between original and decompressed datasets could potentially result in erroneous interpretations or even incorrect scientific conclusions. In this paper, we focus on preserving Morse-Smale segmentations in 2D/3D piecewise linear scalar fields, targeting the precise reconstruction of minimum/maximum labels induced by the integral line of each vertex. The key is to derive a series of edits during compression time; the edits are applied to the decompressed data, leading to an accurate reconstruction of segmentations while keeping the error within the prescribed error bound. To this end, we developed a workflow to fix extrema and integral lines alternatively until convergence within finite iterations; we accelerate each workflow component with shared-memory/GPU parallelism to make the performance practical for coupling with compressors. We demonstrate use cases with fluid dynamics, ocean, and cosmology application datasets with a significant acceleration with an NVIDIA A100 GPU.
Paper Structure (30 sections, 1 theorem, 9 equations, 12 figures, 2 tables)

This paper contains 30 sections, 1 theorem, 9 equations, 12 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Error-Bounded Lossy Compression
  4. Topology Preservation in Lossy Compression
  5. Morse-Smale Complexes and Segmentations
  6. Background: Morse-Smale Segmentation in Piecewise Linear Scalar Fields
  7. Problem Statement
  8. Methodology
  9. Critical Point Loops (C-Loops)
  10. False Positive Maximum
  11. False Positive Minimum
  12. False Negative Maximum/Minimum
  13. Regular Point Loops (R-Loops)
  14. Convergence of Alternating C- and R-loops
  15. Parallel Computation and Compression of Edits
  16. ...and 15 more sections

Key Result

Lemma 1

One can find a finite number $k$ of iterations such that $g_i^{(k)} < g_j^{(k)}$, if initially $g_i^{(0)} > g_j^{(0)}$ and $f_i < f_j$.

Figures (12)

  • Figure 1: Impacts of lossy compression (SZ3 and ZFP) on MS segmentations of the Adenine Thymine (AT) dataset: (a) percentages of vertices with wrong segmentation labels w.r.t different error bound; (b) and (c): critical points and separatrices in the original data and SZ3's decompressed data with a relative error bound of $10^{-3}$.
  • Figure 2: Constituents of MS segmentations.
  • Figure 3: Compression (top) and decompression (bottom) workflows. Our algorithm derives vertexwise edits with two distinct loops: (1) C-loops that iteratively fix all false critical points and (2) R-loops that fix all false labeled regular points. C- and R-loops execute alternatively until there is no false critical/regular point. The edits, which are losslessly stored, are used to correct MS segmentations in the decompression stage.
  • Figure 4: Fixing an FPmax at vertex $i$. The height of the blue cylinder above each vertex represents its lower bound ($f - \xi$), and the height of the pink cylinder represents its current value.
  • Figure 5: Fixing an FNmax (and subsequently, a troublemaker, FPmin, FNmax, and another troublemaker) across multiple C- and R-loops. The purple and green arrows in (b) and (d) show the ascending neighbor of vertex $i$ in the original and decompressed data, respectively.
  • ...and 7 more figures

Theorems & Definitions (4)

  • Lemma 1
  • Definition 1: FPmax
  • Definition 2: FPmin
  • Definition 3: FNmax/FNmin