{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T13:31:43Z","timestamp":1774877503041,"version":"3.50.1"},"reference-count":61,"publisher":"Wiley","license":[{"start":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T00:00:00Z","timestamp":1774828800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"},{"start":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T00:00:00Z","timestamp":1774828800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"funder":[{"DOI":"10.13039\/100019180","name":"HORIZON EUROPE European Research Council","doi-asserted-by":"publisher","award":["101141721"],"award-info":[{"award-number":["101141721"]}],"id":[{"id":"10.13039\/100019180","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100004344","name":"Adobe","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100004344","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100007065","name":"Nvidia","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100007065","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Computer Graphics Forum"],"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Our goal is to reconstruct scenes with stochastic, incoherent motion such as leaves moving in the wind, that can be particularly challenging because of small objects with similar appearance that move independently. Previous dynamic 3D Gaussian Splatting solutions either represent motion implicitly with neural networks achieving good quality but lower framerate, or explicitly with a function, often with higher training times and lower quality. To overcome these limitations, we propose an explicit method that introduces adaptive space\u2010time densification and smoother optimization. We introduce a new densification approach based on error moments that are used to guide primitive splitting, and we adaptively refine the number of keyframes used based on the variance of error. We observe that dynamic reconstruction from monocular video is hard for standard optimization pipelines. To counter this, we introduce a weighted Adam approach that improves results based on primitive visibility. Finally, to handle the hard case of independent motion of similar\u2010looking objects, we introduce an image\u2010driven as\u2010rigid\u2010as\u2010possible regularization. Our method has higher quality than previous explicit solutions, and has significantly higher framerate for rendering.<\/jats:p>","DOI":"10.1111\/cgf.70410","type":"journal-article","created":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T12:34:27Z","timestamp":1774874067000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Adaptive Spatio\u2010Temporal 3D Gaussian Splatting for Scenes with Oscillatory Motion"],"prefix":"10.1111","author":[{"ORCID":"https:\/\/orcid.org\/0009-0008-4236-3199","authenticated-orcid":false,"given":"Petros","family":"Tzathas","sequence":"first","affiliation":[{"name":"Inria, Universit\u00e9 C\u00f4te d'Azur  France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-4400-0862","authenticated-orcid":false,"given":"Jeffrey","family":"Hu","sequence":"additional","affiliation":[{"name":"Inria, Universit\u00e9 C\u00f4te d'Azur  France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9899-6365","authenticated-orcid":false,"given":"Andr\u00e9as","family":"Meuleman","sequence":"additional","affiliation":[{"name":"Inria, Universit\u00e9 C\u00f4te d'Azur  France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0124-0180","authenticated-orcid":false,"given":"Guillaume","family":"Cordonnier","sequence":"additional","affiliation":[{"name":"Inria, Universit\u00e9 C\u00f4te d'Azur  France"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9254-4819","authenticated-orcid":false,"given":"George","family":"Drettakis","sequence":"additional","affiliation":[{"name":"Inria, Universit\u00e9 C\u00f4te d'Azur  France"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2026,3,30]]},"reference":[{"key":"e_1_2_13_2_2","doi-asserted-by":"crossref","unstructured":"AttalB. HuangJ.-B. RichardtC. ZollhoeferM. KopfJ. O'TooleM. KimC.: HyperReel: High-fidelity 6-DoF video with ray-conditioned sampling. InCVPR(2023). 2","DOI":"10.1109\/CVPR52729.2023.01594"},{"key":"e_1_2_13_3_2","doi-asserted-by":"publisher","DOI":"10.1145\/566654.566592"},{"key":"e_1_2_13_3_3","doi-asserted-by":"crossref","unstructured":"doi:10.1145\/566654.566592. 7","DOI":"10.1145\/566654.566592"},{"key":"e_1_2_13_4_2","doi-asserted-by":"crossref","unstructured":"BarronJ. T. MildenhallB. VerbinD. SrinivasanP. P. HedmanP.: Mip-nerf 360: Unbounded anti-aliased neural radiance fields.CVPR(2022). 2 7","DOI":"10.1109\/CVPR52688.2022.00539"},{"key":"e_1_2_13_5_2","doi-asserted-by":"crossref","unstructured":"BarronJ. T. MildenhallB. VerbinD. SrinivasanP. P. HedmanP.: Zip-nerf: Anti-aliased grid-based neural radiance fields.ICCV(2023). 2","DOI":"10.1109\/ICCV51070.2023.01804"},{"key":"e_1_2_13_6_2","unstructured":"Bul\u00f2S. R. PorziL. KontschiederP.:Revising densification in gaussian splatting 2024. arXiv:2404.06109. 2 4 5"},{"key":"e_1_2_13_7_2","unstructured":"ChoW. O. ChoI. KimS. BaeJ. UhY. KimS. J.: 4d scaffold gaussian splatting with dynamic-aware anchor growing for efficient and high-fidelity dynamic scene reconstruction. InArxiv(2025). 2 8 9 14"},{"key":"e_1_2_13_8_2","doi-asserted-by":"crossref","unstructured":"ChenY. ChenZ. ZhangC. WangF. YangX. WangY. CaiZ. YangL. LiuH. LinG.: Gaussianeditor: Swift and controllable 3d editing with gaussian splatting. InCVPR(2024). 2","DOI":"10.1109\/CVPR52733.2024.02029"},{"key":"e_1_2_13_9_2","unstructured":"DengX. DiaoC. LiM. YuR. XuD.:Improving densification in 3d gaussian splatting for high-fidelity rendering 2025. arXiv:2508.12313. 2"},{"key":"e_1_2_13_10_2","unstructured":"DengX. DiaoC. LiM. YuR. XuD.:Improving densification in 3d gaussian splatting for high-fidelity rendering 2025. URL:https:\/\/arxiv.org\/abs\/2508.12313 arXiv: 2508.12313. 2 6 9"},{"key":"e_1_2_13_11_2","doi-asserted-by":"crossref","unstructured":"DuanY. WeiF. DaiQ. HeY. ChenW. ChenB.: 4d-rotor gaussian splatting: Towards efficient novel-view synthesis for dynamic scenes. InProc. SIGGRAPH(2024). 1 2","DOI":"10.1145\/3641519.3657463"},{"key":"e_1_2_13_12_2","doi-asserted-by":"publisher","DOI":"10.1145\/3680528.3687592"},{"key":"e_1_2_13_12_3","doi-asserted-by":"crossref","unstructured":"doi:10.1145\/3680528.3687592. 2 6 9","DOI":"10.1145\/3680528.3687592"},{"key":"e_1_2_13_13_2","doi-asserted-by":"crossref","unstructured":"FrankeL. R\u00fcckertD. FinkL. InnmannM. StammingerM.: Vet: Visual error tomography for point cloud completion and high-quality neural rendering. InACM SIGGRAPH Asia Conference Proceedings(2023). 4","DOI":"10.1145\/3610548.3618212"},{"key":"e_1_2_13_14_2","doi-asserted-by":"crossref","unstructured":"GaoC. SarafA. KopfJ. HuangJ.-B.: Dynamic view synthesis from dynamic monocular video. InICCV(2021). 3","DOI":"10.1109\/ICCV48922.2021.00566"},{"key":"e_1_2_13_15_2","unstructured":"HuangY.-H. SunY.-T. YangZ. LyuX. CaoY.-P. QiX.: Sc-gs: Sparse-controlled gaussian splatting for editable dynamic scenes.arXiv preprint arXiv:2312.14937(2023). 1 8 9"},{"key":"e_1_2_13_16_2","doi-asserted-by":"publisher","DOI":"10.1145\/3641519.3657428"},{"key":"e_1_2_13_17_2","doi-asserted-by":"publisher","DOI":"10.1145\/1073204.1073323"},{"key":"e_1_2_13_17_3","doi-asserted-by":"crossref","unstructured":"doi:10.1145\/1073204.1073323. 7","DOI":"10.1145\/1073204.1073323"},{"key":"e_1_2_13_18_2","doi-asserted-by":"publisher","DOI":"10.1145\/3585499"},{"key":"e_1_2_13_19_2","unstructured":"KingmaD. BaJ.: Adam: A method for stochastic optimization.International Conference on Learning Representations(122014). 7"},{"key":"e_1_2_13_20_2","doi-asserted-by":"publisher","DOI":"10.1145\/3592433"},{"key":"e_1_2_13_21_2","unstructured":"KheradmandS. RebainD. SharmaG. SunW. TsengJ. IsackH. KarA. TagliasacchiA. YiK. M.:3d gaussian splatting as markov chain monte carlo 2024. 2"},{"key":"e_1_2_13_22_2","doi-asserted-by":"crossref","unstructured":"KatsumataK. VoD. M. NakayamaH.: A compact dynamic 3d gaussian representation for real-time dynamic view synthesis. InECCV(2024). 3","DOI":"10.1007\/978-3-031-73016-0_23"},{"key":"e_1_2_13_23_2","doi-asserted-by":"crossref","unstructured":"LiZ. ChenZ. LiZ. XuY.: Spacetime gaussian feature splatting for real-time dynamic view synthesis. InProceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition (CVPR)(June2024) pp.8508\u20138520. 2","DOI":"10.1109\/CVPR52733.2024.00813"},{"key":"e_1_2_13_24_2","unstructured":"LiuY.-L. GaoC. MeulemanA. TsengH.-Y. SarafA. KimC. ChuangY.-Y. KopfJ. HuangJ.-B.: Robust dynamic radiance fields. InCVPR(2023). 3"},{"key":"e_1_2_13_25_2","unstructured":"LiuY.-C. H\u00f6lleinL. NiessnerM. DaiA.: Quick-splat: Fast 3d surface reconstruction via learned gaussian initialization. InICCV(2025). 2"},{"key":"e_1_2_13_26_2","doi-asserted-by":"crossref","unstructured":"LiuJ. HuW. YangZ. ChenJ. WangG. ChenX. CaiY. GaoH.-a. ZhaoH.: Rip-nerf: Anti-aliasing radiance fields with ripmap-encoded platonic solids. InACM SIGGRAPH Conference Proceedings(2024). 2","DOI":"10.1145\/3641519.3657402"},{"key":"e_1_2_13_27_2","doi-asserted-by":"crossref","unstructured":"LiangY. KhanN. LiZ. Nguyen-PhuocT. LanmanD. TompkinJ. XiaoL.: Gaufre: Gaussian deformation fields for realtime dynamic novel view synthesis. InProc. IEEE\/CVF Winter Conference on Applications of Computer Vision (WACV)(2025). 2","DOI":"10.1109\/WACV61041.2025.00262"},{"key":"e_1_2_13_28_2","doi-asserted-by":"crossref","unstructured":"LuitenJ. KopanasG. LeibeB. RamananD.: Dynamic 3d gaussians: Tracking by persistent dynamic view synthesis. In3DV(2024). 1 7","DOI":"10.1109\/3DV62453.2024.00044"},{"key":"e_1_2_13_29_2","doi-asserted-by":"publisher","DOI":"10.1017\/ATSIP.2013.5"},{"key":"e_1_2_13_30_2","doi-asserted-by":"crossref","unstructured":"LombardiS. SimonT. SaragihJ. SchwartzG. LehrmannA. SheikhY.: Neural volumes: Learning dynamic renderable volumes from images.ACM Transactions on Graphics(2019). 2","DOI":"10.1145\/3306346.3323020"},{"key":"e_1_2_13_31_2","doi-asserted-by":"publisher","DOI":"10.1145\/3450626.3459863"},{"key":"e_1_2_13_32_2","doi-asserted-by":"crossref","unstructured":"LiT. SlavchevaM. ZollhoeferM. GreenS. LassnerC. KimC. SchmidtT. LovegroveS. GoeseleM. NewcombeR. LvZ.: Neural 3d video synthesis from multi-view video. In2022 IEEE\/CVF Conference on Computer Vision and Pattern Recognition (CVPR)(2022) pp.5511\u20135521. doi:10.1109\/CVPR52688.2022.00544. 14","DOI":"10.1109\/CVPR52688.2022.00544"},{"key":"e_1_2_13_33_2","doi-asserted-by":"crossref","unstructured":"LiZ. WangQ. ColeF. TuckerR. SnavelyN.: Dynibar: Neural dynamic image-based rendering. InCVPR(2023). 3","DOI":"10.1109\/CVPR52729.2023.00416"},{"key":"e_1_2_13_34_2","doi-asserted-by":"crossref","unstructured":"LeiJ. WengY. HarleyA. GuibasL. DaniilidisK.:Mosca: Dynamic gaussian fusion from casual videos via 4d motion scaffolds 2024. arXiv:2405.17421. 2 3 7","DOI":"10.1109\/CVPR52734.2025.00578"},{"key":"e_1_2_13_35_2","unstructured":"LeeJ. WonC. JungH. BaeI. JeonH.-G.: Fully explicit dynamic gaussian splatting. InProceedings of the Neural Information Processing Systems(2024). 3 4"},{"key":"e_1_2_13_36_2","doi-asserted-by":"crossref","unstructured":"MallickS. S. GoelR. KerblB. SteinbergerM. CarrascoF. V. De La TorreF.: Taming 3dgs: High-quality radiance fields with limited resources. InSIGGRAPH Asia 2024 Conference Papers(2024). 2 7","DOI":"10.1145\/3680528.3687694"},{"key":"e_1_2_13_37_2","unstructured":"MinkaT. P.:Old and new matrix algebra useful for statistics. URL:https:\/\/api.semanticscholar.org\/CorpusID:15971655. 5 12"},{"key":"e_1_2_13_38_2","doi-asserted-by":"publisher","DOI":"10.1137\/0601049"},{"key":"e_1_2_13_39_2","doi-asserted-by":"publisher","DOI":"10.1145\/3730913"},{"key":"e_1_2_13_40_2","doi-asserted-by":"crossref","unstructured":"ParkJ. BuiM.-Q. V. BelloJ. L. G. MoonJ. OhJ. KimM.: Splinegs: Robust motion-adaptive spline for real-time dynamic 3d gaussians from monocular video. InProceedings of the Computer Vision and Pattern Recognition Conference (CVPR)(2025). 2 3","DOI":"10.1109\/CVPR52734.2025.02502"},{"issue":"4","key":"e_1_2_13_41_2","article-title":"Modalnerf: Neural modal analysis and synthesis for free-viewpoint navigation in dynamically vibrating scenes","volume":"42","author":"Petitjean A.","year":"2023","journal-title":"Computer Graphics Forum (Proceedings of the Eurographics Symposium on Rendering)"},{"key":"e_1_2_13_42_2","doi-asserted-by":"crossref","unstructured":"ParkK. SinhaU. BarronJ. T. BouazizS. GoldmanD. B. SeitzS. M. Martin-BruallaR.: Nerfies: Deformable neural radiance fields.ICCV(2021). 7","DOI":"10.1109\/ICCV48922.2021.00581"},{"key":"e_1_2_13_43_2","doi-asserted-by":"publisher","DOI":"10.1145\/3528223.3530121"},{"key":"e_1_2_13_44_2","first-page":"109","volume-title":"Proceedings of the Fifth Eurographics Symposium on Geometry Processing","author":"Sorkine O.","year":"2007"},{"key":"e_1_2_13_45_2","doi-asserted-by":"crossref","unstructured":"Sch\u00f6nbergerJ. L. FrahmJ.-M.: Structure-from-motion revisited. InConference on Computer Vision and Pattern Recognition (CVPR)(2016). 4","DOI":"10.1109\/CVPR.2016.445"},{"key":"e_1_2_13_46_2","doi-asserted-by":"crossref","unstructured":"ShihM.-L. HuangJ.-B. KimC. ShahR. KopfJ. GaoC.: Modeling ambient scene dynamics for free-view synthesis. InACM SIGGRAPH Conference Papers(2024). 1 2 3 8 9","DOI":"10.1145\/3641519.3657488"},{"key":"e_1_2_13_47_2","doi-asserted-by":"crossref","unstructured":"StearnsC. HarleyA. W. UyM. DubostF. TombariF. WetzsteinG. GuibasL.: Dynamic gaussian marbles for novel view synthesis of casual monocular videos. InSIGGRAPH Asia Conference Papers(2024). 3","DOI":"10.1145\/3680528.3687681"},{"key":"e_1_2_13_48_2","doi-asserted-by":"crossref","unstructured":"TomasiC. ManduchiR.: Bilateral filtering for gray and color images.Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271)(1998) 839\u2013846. URL:https:\/\/api.semanticscholar.org\/CorpusID:14308539. 7","DOI":"10.1109\/ICCV.1998.710815"},{"key":"e_1_2_13_49_2","doi-asserted-by":"crossref","unstructured":"TretschkE. TewariA. GolyanikV. Zollh\u00f6ferM. LassnerC. TheobaltC.: Non-rigid neural radiance fields: Reconstruction and novel view synthesis of a dynamic scene from monocular video. InICCV(2021). 3","DOI":"10.1109\/ICCV48922.2021.01272"},{"key":"e_1_2_13_50_2","unstructured":"WuG. YiT. FangJ. XieL. ZhangX. WeiW. LiuW. TianQ. WangX.: 4d gaussian splatting for real-time dynamic scene rendering. InCVPR(2024). 1 2 8 9 10"},{"key":"e_1_2_13_51_2","unstructured":"WangQ. YeV. GaoH. ZengW. AustinJ. LiZ. KanazawaA.: Shape of motion: 4d reconstruction from a single video. InInternational Conference on Computer Vision (ICCV)(2025). 2"},{"key":"e_1_2_13_52_2","doi-asserted-by":"crossref","unstructured":"WangY. YangP. XuZ. SunJ. ZhangZ. ChenY. BaoH. PengS. ZhouX.: Freetimegs: Free gaussian primitives at anytime anywhere for dynamic scene reconstruction. InCVPR(2025). 2","DOI":"10.1109\/CVPR52734.2025.02026"},{"key":"e_1_2_13_53_2","doi-asserted-by":"publisher","DOI":"10.1145\/3687919"},{"key":"e_1_2_13_54_2","doi-asserted-by":"crossref","unstructured":"XieT. ZongZ. QiuY. LiX. FengY. YangY. JiangC.:Physgaussian: Physics-integrated 3d gaussians for generative dynamics 2023. arXiv:2311.12198. 2","DOI":"10.1109\/CVPR52733.2024.00420"},{"key":"e_1_2_13_55_2","doi-asserted-by":"crossref","unstructured":"YangZ. GaoX. ZhouW. JiaoS. ZhangY. JinX.: Deformable 3d gaussians for high-fidelity monocular dynamic scene reconstruction. InCVPR(2024). 1 2 3","DOI":"10.1109\/CVPR52733.2024.01922"},{"key":"e_1_2_13_56_2","unstructured":"YuanY.-J. SunY.-T. LaiY.-K. MaY. JiaR. GaoL.: Nerf-editing: geometry editing of neural radiance fields. InCVPR(2022) pp.18353\u201318364. 2"},{"key":"e_1_2_13_57_2","unstructured":"YaoW. XieS. LiL. ZhangW. LaiZ. DaiS. ZhangK. WangZ.:Sd-gs: Structured deformable 3d gaussians for efficient dynamic scene reconstruction 2025. URL:https:\/\/arxiv.org\/abs\/2507.07465 arXiv:2507.07465. 2"},{"key":"e_1_2_13_58_2","unstructured":"YangZ. YangH. PanZ. ZhangL.: Real-time photorealistic dynamic scene representation and rendering with 4d gaussian splatting. InInternational Conference on Learning Representations (ICLR)(2024). 1 2 8 9"},{"key":"e_1_2_13_59_2","doi-asserted-by":"crossref","unstructured":"ZhangZ. HuW. LaoY. HeT. ZhaoH.: Pixel-gs: Density control with pixel-aware gradient for 3d gaussian splatting. InECCV(2024). 2","DOI":"10.1007\/978-3-031-72655-2_19"}],"container-title":["Computer Graphics Forum"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1111\/cgf.70410","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1111\/cgf.70410","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1111\/cgf.70410","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,30]],"date-time":"2026-03-30T12:34:32Z","timestamp":1774874072000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1111\/cgf.70410"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,3,30]]},"references-count":61,"alternative-id":["10.1111\/cgf.70410"],"URL":"https:\/\/doi.org\/10.1111\/cgf.70410","archive":["Portico"],"relation":{},"ISSN":["0167-7055","1467-8659"],"issn-type":[{"value":"0167-7055","type":"print"},{"value":"1467-8659","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,3,30]]},"assertion":[{"value":"2026-03-30","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"e70410"}}