{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T10:14:33Z","timestamp":1780481673590,"version":"3.54.1"},"reference-count":53,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2026,5,30]],"date-time":"2026-05-30T00:00:00Z","timestamp":1780099200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Dynamic three-dimensional (3-D) reconstruction of small objects moving at high speed is fundamentally limited by the number of viewpoints that a fixed camera array can provide at any single time instant. When the camera count is insufficient, single-frame multi-view stereo produces incomplete or inaccurate geometry. This paper proposes a multi-frame temporal integration approach that overcomes this limitation by exploiting the rigid-body assumption: because a falling object maintains its shape across consecutive frames, images captured at different time instants can be combined into a single, viewpoint-enriched reconstruction. A three-layer circular array of 32 synchronized RGB cameras captures 1440 \u00d7 1080 images at 160 fps, and a free-fall-oriented algorithm automatically detects active frames, selects informative temporal windows, and feeds the accumulated multi-frame images into a structure-from-motion and multi-view stereo (SfM-MVS) pipeline, effectively multiplying the number of viewpoints without additional hardware. The algorithm simultaneously recovers the 6-DOF pose trajectory of each object from the SfM-estimated camera parameters. Progressive accumulation experiments on freely falling soybeans (approximately 9\u201310 mm diameter) show that a single 32-camera frame already achieves an F-score exceeding 0.97 at a 0.5 mm threshold against an industrial structured-light scanner reference, and that accumulating additional temporal frames reaches a stable convergence plateau with both objects reaching a plateau F-score of 0.984. Beyond approximately one to two accumulated frames, additional frames yield diminishing returns, confirming that a small number of temporal frames is sufficient for convergent sub-millimeter accuracy. Across 30 independent free-fall trials with three objects, the system achieves an overall mean error of 0.146\u00b10.033 mm and an overall F-score of 0.980\u00b10.006\u2014a mean relative error of approximately 1.6% on 8\u201310 mm targets\u2014and fine surface features such as structural cracks are resolved at a fidelity sufficient for visual defect identification. These results establish rigid-body multi-frame temporal integration as an effective strategy for high-throughput, non-contact 3-D inspection of small objects in motion.<\/jats:p>","DOI":"10.3390\/s26113457","type":"journal-article","created":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T17:11:01Z","timestamp":1780333861000},"page":"3457","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Multi-Frame Temporal Integration for 3-D Shape Measurement of Freely Falling Small Objects Using a High-Speed Camera Array"],"prefix":"10.3390","volume":"26","author":[{"given":"Hao","family":"Duan","sequence":"first","affiliation":[{"name":"Graduate School of Innovation and Practice for Smart Society, Hiroshima University, Higashi-Hiroshima Campus, Higashihiroshima 739-0046, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shaopeng","family":"Hu","sequence":"additional","affiliation":[{"name":"Digital Manufacturing Education and Research Center, Hiroshima University, Higashi-Hiroshima Campus, Higashihiroshima 739-0046, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2881-6998","authenticated-orcid":false,"given":"Feiyue","family":"Wang","sequence":"additional","affiliation":[{"name":"Graduate School of Advanced Science and Engineering, Hiroshima University, Higashi-Hiroshima Campus, Higashihiroshima 739-0046, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4773-1575","authenticated-orcid":false,"given":"Kohei","family":"Shimasaki","sequence":"additional","affiliation":[{"name":"Graduate School of Advanced Science and Engineering, Hiroshima University, Higashi-Hiroshima Campus, Higashihiroshima 739-0046, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7728-2363","authenticated-orcid":false,"given":"Idaku","family":"Ishii","sequence":"additional","affiliation":[{"name":"Graduate School of Advanced Science and Engineering, Hiroshima University, Higashi-Hiroshima Campus, Higashihiroshima 739-0046, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,5,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Seitz, S.M., Curless, B., Diebel, J., Scharstein, D., and Szeliski, R. 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