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pith:YA77ZUE3

pith:2026:YA77ZUE3ZVKUG2VUZPQEQZGUNZ
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Topo-GS: Continuous Volumetric Embedding of High-Dimensional Data via Topological Gaussian Splatting

Jo\~ao Paulo Gois, Luis Gustavo Nonato

Topo-GS repurposes 3D Gaussian Splatting to cast high-dimensional projections as continuous volumetric reconstructions driven by local geometric constraints.

arxiv:2605.17011 v1 · 2026-05-16 · cs.GR · cs.CV · cs.LG

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\pithnumber{YA77ZUE3ZVKUG2VUZPQEQZGUNZ}

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4 Citations open
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Claims

C1strongest claim

we introduce Topo-GS, a framework that repurposes 3D Gaussian Splatting (3DGS) to cast multidimensional projection as a meshless volumetric reconstruction process... driven by local geometric constraints... solving orthogonal Procrustes targets... aligning the spatial covariance of each Gaussian to the local tangent space... topology-aware strategy that tailors the loss formulation to preserve either continuous 1D trajectories or cohesive 2D surfaces.

C2weakest assumption

That enforcing As-Rigid-As-Possible priors via orthogonal Procrustes alignment of Gaussian covariances to local tangent spaces, combined with topology-specific loss tailoring, will produce faithful continuous volumetric representations without introducing new artifacts or losing fidelity compared to discrete baselines.

C3one line summary

Topo-GS repurposes 3D Gaussian Splatting with local geometric constraints and topology-aware losses to produce continuous volumetric embeddings of high-dimensional data.

References

20 extracted · 20 resolved · 1 Pith anchors

[1] Visualizing structure and transitions in high-dimensional biological data, 2019 · doi:10.1038/s41587-019-0336-3
[2] Unveiling high-dimensional backstage: A survey for reliable visual analytics with dimensionality reduction 2025 · doi:10.1145/3706598.3713551
[3] 3d gaussian splatting for real-time radiance field rendering, 2023 · doi:10.1145/3592433
[4] A representation the- orem for locally compact quantum groups 2004
[5] O. Sorkine and M. Alexa, “As-rigid-as-possible surface modeling,” in Proceedings of the Fifth Eurographics Symposium on Geometry Processing, ser. SGP ’07. Goslar, DEU: Eurographics Association, 2007, 2007 · doi:10.2312/sgp/

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Receipt and verification
First computed 2026-05-20T00:03:35.837953Z
Builder pith-number-builder-2026-05-17-v1
Signature Pith Ed25519 (pith-v1-2026-05) · public key
Schema pith-number/v1.0

Canonical hash

c03ffcd09bcd55436ab4cbe04864d46e61feac879b36880c37cf8f0d39bd4dad

Aliases

arxiv: 2605.17011 · arxiv_version: 2605.17011v1 · doi: 10.48550/arxiv.2605.17011 · pith_short_12: YA77ZUE3ZVKU · pith_short_16: YA77ZUE3ZVKUG2VU · pith_short_8: YA77ZUE3
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Verify this Pith Number yourself
curl -sH 'Accept: application/ld+json' https://pith.science/pith/YA77ZUE3ZVKUG2VUZPQEQZGUNZ \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: c03ffcd09bcd55436ab4cbe04864d46e61feac879b36880c37cf8f0d39bd4dad
Canonical record JSON
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    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.GR",
    "submitted_at": "2026-05-16T14:21:08Z",
    "title_canon_sha256": "f739cafe70b50fdcc58d5b014cd7702e96a8f2a7beba544210e95dbbc72f201d"
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