{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:20:19Z","timestamp":1787322019052,"version":"build-2736575974"},"reference-count":55,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Imaging Sci."],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>Recovering three-dimensional (3D) structures such as object poses from limited two-dimensional (2D) information is an important research problem in computer vision, graphics, and robotics. The estimation of object pose from single images or multiple casual images could be ill-conditioned math problems. There is a popular family of algorithms of geometric sparse representation for 3D pose recovery (GSR-3D) that pretrains an overcomplete dictionary of 3D basis poses $B$, and then matches the detected 2D object pose $Y$ by jointly estimating the transformation $R$, projection $\\Pi,$ and combination coefficients $c$, assuming $Y \\approx \\Pi \\sum_i c_i R B_i$. In this paper, we make the first step of analyzing to which extent could we solve this ill-conditioned problem, and of understanding how the recovery error is affected by fundamental factors, e.g., dictionary size, observation noise, and running time. As these factors are implicit in objective functions, we analyze with the help of various sparse regularizers and a multistage optimizer, and prove that the recovery error $\\mathcal L(l)$ decays w.r.t. the number of stages $l$ with a high probability, $Prob\\left(\\mathcal L(l) &lt; \\rho^{l-1} \\mathcal L(0) + \\delta \\right) \\geq 1- \\epsilon$, where the constants $0&lt; \\rho &lt;1, 0&lt;\\delta, 0&lt;\\epsilon \\ll 1$ are related to the aforementioned factors. To the best of our knowledge, this is the first theoretical analysis in this line of research. Experiments are conducted to support our improvement upon previous regularization within the same framework. This will further characterize the trade-off between speed and accuracy towards real-time geometric inference in applications.<\/jats:p>","DOI":"10.1137\/19m1299955","type":"journal-article","created":{"date-parts":[[2021,2,22]],"date-time":"2021-02-22T12:14:46Z","timestamp":1613996086000},"page":"246-270","source":"Crossref","is-referenced-by-count":1,"title":["Towards Statistically Provable Geometric 3D Human Pose Recovery"],"prefix":"10.1137","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4454-1744","authenticated-orcid":true,"given":"Jianqiao","family":"Wangni","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dahua","family":"Lin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ji","family":"Liu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kostas","family":"Daniilidis","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jianbo","family":"Shi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2021,2,22]]},"reference":[{"key":"atypb2","first-page":"3686","author":"Andriluka M.","year":"2014","journal-title":"Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, IEEE"},{"key":"atypb3","first-page":"561","author":"Bogo F.","year":"2016","journal-title":"Springer"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1561\/2200000016"},{"key":"atypb5","doi-asserted-by":"crossref","unstructured":"P. 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