{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,9]],"date-time":"2025-12-09T11:27:15Z","timestamp":1765279635737,"version":"3.41.0"},"reference-count":29,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2007,7,29]],"date-time":"2007-07-29T00:00:00Z","timestamp":1185667200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Graph."],"published-print":{"date-parts":[[2007,7,29]]},"abstract":"<jats:p>\n            Filtering is critical for representing detail, such as color textures or normal maps, across a variety of scales. While MIP-mapping texture maps is commonplace, accurate normal map filtering remains a challenging problem because of nonlinearities in shading---we cannot simply average nearby surface normals. In this paper, we show analytically that normal map filtering can be formalized as a spherical convolution of the\n            <jats:italic>normal distribution function<\/jats:italic>\n            (NDF) and the BRDF, for a large class of common BRDFs such as Lambertian, microfacet and factored measurements. This theoretical result explains many previous filtering techniques as special cases, and leads to a generalization to a broader class of measured and analytic BRDFs. Our practical algorithms leverage a significant body of work that has studied lighting-BRDF convolution. We show how spherical harmonics can be used to filter the NDF for Lambertian and low-frequency specular BRDFs, while spherical von Mises-Fisher distributions can be used for high-frequency materials.\n          <\/jats:p>","DOI":"10.1145\/1276377.1276412","type":"journal-article","created":{"date-parts":[[2007,9,14]],"date-time":"2007-09-14T13:44:55Z","timestamp":1189777495000},"page":"28","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":87,"title":["Frequency domain normal map filtering"],"prefix":"10.1145","volume":"26","author":[{"given":"Charles","family":"Han","sequence":"first","affiliation":[{"name":"Columbia University"}]},{"given":"Bo","family":"Sun","sequence":"additional","affiliation":[{"name":"Columbia University"}]},{"given":"Ravi","family":"Ramamoorthi","sequence":"additional","affiliation":[{"name":"Columbia University"}]},{"given":"Eitan","family":"Grinspun","sequence":"additional","affiliation":[{"name":"Columbia University"}]}],"member":"320","published-online":{"date-parts":[[2007,7,29]]},"reference":[{"key":"e_1_2_2_1_1","doi-asserted-by":"publisher","DOI":"10.5555\/1046920.1088718"},{"volume-title":"International Conference on Computer Vision, 383--390","author":"Basri R.","key":"e_1_2_2_2_1","unstructured":"Basri , R. , and Jacobs , D . 2001. Lambertian reflectance and linear subspaces . In International Conference on Computer Vision, 383--390 . Basri, R., and Jacobs, D. 2001. Lambertian reflectance and linear subspaces. In International Conference on Computer Vision, 383--390."},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1145\/166117.166141"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1145\/800248.507101"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1145\/1268517.1268546"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1145\/280814.280832"},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.2517-6161.1977.tb01600.x"},{"key":"e_1_2_2_8_1","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1953.0064"},{"key":"e_1_2_2_9_1","volume-title":"Graphics Interface Workshop on Local Illumination, 45--52","author":"Fournier A.","year":"1992","unstructured":"Fournier , A. 1992 . Normal distribution functions and multiple surfaces . In Graphics Interface Workshop on Local Illumination, 45--52 . Fournier, A. 1992. Normal distribution functions and multiple surfaces. In Graphics Interface Workshop on Local Illumination, 45--52."},{"key":"e_1_2_2_10_1","doi-asserted-by":"publisher","DOI":"10.1109\/ICCV.2005.162"},{"key":"e_1_2_2_11_1","unstructured":"Heckbert P. 1989. Fundamentals of texture mapping and image warping. Master's thesis UC Berkeley UCB\/CSD 89\/516.   Heckbert P. 1989. Fundamentals of texture mapping and image warping . Master's thesis UC Berkeley UCB\/CSD 89\/516."},{"key":"e_1_2_2_12_1","doi-asserted-by":"crossref","unstructured":"Hochbaum D. and Shmoys D. 1985. A best possible heuristic for the k-center problem. Mathematics of Operations Research.  Hochbaum D. and Shmoys D. 1985. A best possible heuristic for the k-center problem. 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Rep. 97-041 http:\/\/www.cs.unc.edu\/~olano\/papers\/ndm\/ndm.pdf, UNC."},{"key":"e_1_2_2_20_1","doi-asserted-by":"publisher","DOI":"10.1145\/383259.383271"},{"key":"e_1_2_2_21_1","doi-asserted-by":"publisher","DOI":"10.1145\/258694.258701"},{"key":"e_1_2_2_22_1","doi-asserted-by":"publisher","DOI":"10.1145\/566570.566612"},{"key":"e_1_2_2_23_1","doi-asserted-by":"publisher","DOI":"10.1145\/1073204.1073335"},{"key":"e_1_2_2_24_1","volume-title":"Proc Natl Conf on Artificial Intelligence: Workshop of AI for Web Search (AAAI","author":"Strehl A.","year":"2000","unstructured":"Strehl , A. , Ghosh , J. , and Mooney , R . 2000. Impact of similarity measures on web-page clustering . In Proc Natl Conf on Artificial Intelligence: Workshop of AI for Web Search (AAAI 2000 ), 58--64. Strehl, A., Ghosh, J., and Mooney, R. 2000. Impact of similarity measures on web-page clustering. 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