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Our key idea is a novel differentiable representation where each strand is encoded as a projected 2D curve in the texture space, which enables end-to-end optimization with differentiable rendering while respecting the structures of the hair geometry. Based on this representation, we develop a novel algorithm pipeline, where we first cluster hair strands into initial hair cards and project the strands into the texture space. We then conduct a two-stage optimization, where our first stage optimizes the orientation of each hair card separately, and after strand projection, our second stage conducts joint optimization over the entire hair card model for fine-tuning. Our method is evaluated on a range of hairstyles, including straight, wavy, curly, and coily hair. To capture the appearance of short or coily hair, our method comes with support for hair caps and cross-card.<\/jats:p>","DOI":"10.1145\/3763295","type":"journal-article","created":{"date-parts":[[2025,12,4]],"date-time":"2025-12-04T17:15:39Z","timestamp":1764868539000},"page":"1-13","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":2,"title":["Auto Hair Card Extraction for Smooth Hair with Differentiable Rendering"],"prefix":"10.1145","volume":"44","author":[{"ORCID":"https:\/\/orcid.org\/0009-0009-4714-1760","authenticated-orcid":false,"given":"Zhongtian","family":"Zheng","sequence":"first","affiliation":[{"name":"LIGHTSPEED, Shenzhen, China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-3458-0851","authenticated-orcid":false,"given":"Tao","family":"Huang","sequence":"additional","affiliation":[{"name":"LIGHTSPEED, Los Angeles, USA"}]},{"ORCID":"https:\/\/orcid.org\/0009-0002-8534-8964","authenticated-orcid":false,"given":"Haozhe","family":"Su","sequence":"additional","affiliation":[{"name":"LIGHTSPEED, Los Angeles, USA"}]},{"ORCID":"https:\/\/orcid.org\/0009-0004-0203-8501","authenticated-orcid":false,"given":"Xueqi","family":"Ma","sequence":"additional","affiliation":[{"name":"LIGHTSPEED, Shenzhen, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6049-7966","authenticated-orcid":false,"given":"Yuefan","family":"Shen","sequence":"additional","affiliation":[{"name":"LIGHTSPEED, Shenzhen, China"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-6585-3009","authenticated-orcid":false,"given":"Tongtong","family":"Wang","sequence":"additional","affiliation":[{"name":"LIGHTSPEED, Shenzhen, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7645-5931","authenticated-orcid":false,"given":"Yin","family":"Yang","sequence":"additional","affiliation":[{"name":"University of Utah, Salt Lake City, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0829-7075","authenticated-orcid":false,"given":"Xifeng","family":"Gao","sequence":"additional","affiliation":[{"name":"LIGHTSPEED, Seattle, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9348-526X","authenticated-orcid":false,"given":"Zherong","family":"Pan","sequence":"additional","affiliation":[{"name":"LIGHTSPEED, Seattle, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3326-7943","authenticated-orcid":false,"given":"Kui","family":"Wu","sequence":"additional","affiliation":[{"name":"LIGHTSPEED, Los Angeles, USA"}]}],"member":"320","published-online":{"date-parts":[[2025,12,4]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2004.00771.x"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1467-8659.2005.00876.x"},{"key":"e_1_2_1_3_1","volume-title":"Discrete Elastic Rods. 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