{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T07:22:33Z","timestamp":1783063353203,"version":"3.54.6"},"reference-count":48,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T00:00:00Z","timestamp":1783036800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/legalcode"}],"funder":[{"name":"JST FOREST Program","award":["JPMJFR206R"],"award-info":[{"award-number":["JPMJFR206R"]}]},{"DOI":"10.13039\/501100002241","name":"Japan Science and Technology Agency","doi-asserted-by":"crossref","award":["JPMJPF222"],"award-info":[{"award-number":["JPMJPF222"]}],"id":[{"id":"10.13039\/501100002241","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001691","name":"Japan Society for the Promotion of Science","doi-asserted-by":"crossref","award":["24K22830"],"award-info":[{"award-number":["24K22830"]}],"id":[{"id":"10.13039\/501100001691","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[2026,7,3]]},"abstract":"<jats:p>Many non-photorealistic rendering (NPR) styles, such as feature lines and hatching, are defined by image-space structure inherited from hand-drawn media. While recent path-space formulations like the stylized rendering equation (SRE) enable stylization to interact naturally with light transport, they provide no mechanism for enforcing image-space consistency.<\/jats:p>\n                  <jats:p>\n                    We present a conceptual framework for\n                    <jats:italic toggle=\"yes\">lifting<\/jats:italic>\n                    image-space stylizations into path-space in a principled, SRE-compatible manner. Our key observation is that image-space consistency can be achieved by establishing geometrically-driven mappings from image-space to path-space. We demonstrate this through two complementary stylizations: feature lines and tone.\n                  <\/jats:p>\n                  <jats:p>\n                    For feature line rendering, we introduce a\n                    <jats:italic toggle=\"yes\">conditional<\/jats:italic>\n                    lifting based on partial path-space variation, where a geometric path parametrization is combined with parallel transport to preserve image-space structure under distribution effects. This enables a curvature-aware, stochastic, geometry-driven formulation of line detection that generalizes prior ray-based methods. For tone-based styles, such as hatching and halftone, we propose a\n                    <jats:italic toggle=\"yes\">canonical<\/jats:italic>\n                    lifting anchored to a material-independent mapping, motivated by stationary-phase arguments from wave optics. Its locally invertible approximation enables evaluation of image-space tone fields at arbitrary path vertices while preserving image-space structure under complex light transport.\n                  <\/jats:p>\n                  <jats:p>Both methods are implemented as ordinary style functions under the SRE and work with existing estimation and sampling strategies; demonstrating how image-space structure can be preserved within path-space rendering, enabling a broader class of expressive, physically-grounded NPR styles.<\/jats:p>","DOI":"10.1145\/3811359","type":"journal-article","created":{"date-parts":[[2026,7,3]],"date-time":"2026-07-03T07:05:51Z","timestamp":1783062351000},"page":"1-15","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Lifting Lines and Tone: Image-Space Stylization in Path-Space"],"prefix":"10.1145","volume":"45","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-5457-8158","authenticated-orcid":false,"given":"Rex","family":"West","sequence":"first","affiliation":[{"name":"Aoyama Gakuin University, Tokyo, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8838-0455","authenticated-orcid":false,"given":"Sayan","family":"Mukherjee","sequence":"additional","affiliation":[{"name":"The University of Tokyo, Tokyo, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8252-0522","authenticated-orcid":false,"given":"Yonghao","family":"Yue","sequence":"additional","affiliation":[{"name":"Aoyama Gakuin University, Tokyo, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[2026,7,3]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/344779.344814"},{"key":"e_1_2_2_2_1","volume-title":"The Scattering of Electromagnetic Waves from Rough Surfaces","author":"Beckmann Petr","unstructured":"Petr Beckmann and Andr\u00e9 Spizzichino. 1963. 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