{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,15]],"date-time":"2026-05-15T22:44:43Z","timestamp":1778885083968,"version":"3.51.4"},"reference-count":39,"publisher":"Association for Computing Machinery (ACM)","issue":"6","license":[{"start":{"date-parts":[[2015,11,2]],"date-time":"2015-11-02T00:00:00Z","timestamp":1446422400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1451828"],"award-info":[{"award-number":["1451828"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[2015,11,4]]},"abstract":"<jats:p>\n            The bidirectional reflectance distribution function (BRDF) is critical for rendering, and accurate material representation requires data-driven reflectance models. However, isotropic BRDFs are 3D functions, and measuring the reflectance of a flat sample can require a million incident and outgoing direction pairs, making the use of measured BRDFs impractical. In this paper, we address the problem of reconstructing a measured BRDF from a limited number of samples. We present a novel mapping of the BRDF space, allowing for extraction of descriptive principal components from measured databases, such as the MERL BRDF database. We optimize for the best sampling directions, and explicitly provide the optimal set of incident and outgoing directions in the Rusinkiewicz parameterization for\n            <jats:italic>n<\/jats:italic>\n            = {1, 2, 5, 10, 20} samples. Based on the principal components, we describe a method for accurately reconstructing BRDF data from these limited sets of samples. We validate our results on the MERL BRDF database, including favorable comparisons to previous sets of industry-standard sampling directions, as well as with BRDF measurements of new flat material samples acquired with a gantry system. As an extension, we also demonstrate how this method can be used to find optimal sampling directions when imaging a sphere of a homogeneous material; in this case, only two images are often adequate for high accuracy.\n          <\/jats:p>","DOI":"10.1145\/2816795.2818085","type":"journal-article","created":{"date-parts":[[2015,10,27]],"date-time":"2015-10-27T12:36:39Z","timestamp":1445949399000},"page":"1-11","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":105,"title":["On optimal, minimal BRDF sampling for reflectance acquisition"],"prefix":"10.1145","volume":"34","author":[{"given":"Jannik Boll","family":"Nielsen","sequence":"first","affiliation":[{"name":"Technical University of Denmark"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Henrik Wann","family":"Jensen","sequence":"additional","affiliation":[{"name":"University of California, San Diego"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ravi","family":"Ramamoorthi","sequence":"additional","affiliation":[{"name":"University of California, San Diego"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2015,11,2]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.1145\/2461912.2461978"},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.5555\/1018408.1018636"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/563858.563893"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1145\/2601097.2601193"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/2343483.2343493"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/357290.357293"},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1364\/JOSAA.21.000001"},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/280814.280864"},{"key":"e_1_2_2_9_1","volume-title":"A gonioreflectometer for measuring the bidirectional reflectance of material for use in illumination computation. Master's thesis","author":"Foo S. C.","unstructured":"Foo , S. C. 1997. A gonioreflectometer for measuring the bidirectional reflectance of material for use in illumination computation. Master's thesis , Cornell University . Foo, S. C. 1997. A gonioreflectometer for measuring the bidirectional reflectance of material for use in illumination computation. Master's thesis, Cornell University."},{"key":"e_1_2_2_10_1","doi-asserted-by":"publisher","DOI":"10.1145\/1243980.1243984"},{"key":"e_1_2_2_11_1","doi-asserted-by":"publisher","DOI":"10.1109\/ICCV.2007.4408935"},{"key":"e_1_2_2_12_1","volume-title":"Computer Vision and Pattern Recognition","volume":"1","author":"Hertzmann A.","unstructured":"Hertzmann , A. , and Seitz , S. M . 2003. Shape and materials by example: A photometric stereo approach . In Computer Vision and Pattern Recognition , vol. 1 , IEEE, 533. Hertzmann, A., and Seitz, S. M. 2003. Shape and materials by example: A photometric stereo approach. In Computer Vision and Pattern Recognition, vol. 1, IEEE, 533."},{"key":"e_1_2_2_13_1","doi-asserted-by":"publisher","DOI":"10.1145\/1778765.1778834"},{"key":"e_1_2_2_14_1","first-page":"11","article-title":"Development of a method of classifying paints according to gloss","volume":"97","author":"Hunter R. S.","year":"1939","unstructured":"Hunter , R. S. , and Judd , D. B. 1939 . Development of a method of classifying paints according to gloss . ASTM Bulletin , 97 , 11 -- 18 . Hunter, R. S., and Judd, D. B. 1939. Development of a method of classifying paints according to gloss. ASTM Bulletin, 97, 11--18.","journal-title":"ASTM Bulletin"},{"key":"e_1_2_2_15_1","volume-title":"The measurement of appearance","author":"Hunter R. S.","unstructured":"Hunter , R. S. 1987. The measurement of appearance . John Wiley & Sons . Hunter, R. S. 1987. The measurement of appearance. John Wiley & Sons."},{"key":"e_1_2_2_16_1","doi-asserted-by":"publisher","DOI":"10.1137\/120870748"},{"key":"e_1_2_2_17_1","doi-asserted-by":"publisher","DOI":"10.1145\/258734.258801"},{"key":"e_1_2_2_18_1","doi-asserted-by":"publisher","DOI":"10.1111\/1467-8659.00695"},{"key":"e_1_2_2_19_1","doi-asserted-by":"publisher","DOI":"10.1145\/2077341.2077350"},{"key":"e_1_2_2_20_1","doi-asserted-by":"publisher","DOI":"10.5555\/2383815.2383829"},{"key":"e_1_2_2_21_1","doi-asserted-by":"publisher","DOI":"10.1145\/882262.882343"},{"key":"e_1_2_2_22_1","volume-title":"Eurographics Rendering Workshop, 241--247","author":"Matusik W.","year":"2003","unstructured":"Matusik , W. , Pfister , H. , Brand , M. , and McMillan , L. 2003 . Efficient isotropic BRDF measurement . In Eurographics Rendering Workshop, 241--247 . Matusik, W., Pfister, H., Brand, M., and McMillan, L. 2003. Efficient isotropic BRDF measurement. In Eurographics Rendering Workshop, 241--247."},{"key":"e_1_2_2_23_1","doi-asserted-by":"publisher","DOI":"10.5555\/2383654.2383671"},{"key":"e_1_2_2_24_1","doi-asserted-by":"publisher","DOI":"10.5555\/2383894.2383945"},{"key":"e_1_2_2_25_1","doi-asserted-by":"crossref","unstructured":"Nicodemus F. E. Richmond J. C. Hsia J. J. Ginsberg I. W. and Limperis T. 1977. Geometric Considerations and Nomenclature for Reflectance (NBS Monograph 160). National Bureau of Standards (US).  Nicodemus F. E. Richmond J. C. Hsia J. J. Ginsberg I. W. and Limperis T. 1977. Geometric Considerations and Nomenclature for Reflectance (NBS Monograph 160). 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Reflectometer for measuring the bidirectional reflectance of rough surfaces. Applied optics 37 16 3450--3454.  White D. Saunders P. Bonsey S. J. van de Ven J. and Edgar H. 1998. Reflectometer for measuring the bidirectional reflectance of rough surfaces. 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