{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,15]],"date-time":"2026-04-15T17:55:58Z","timestamp":1776275758452,"version":"3.50.1"},"reference-count":36,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2019,7,16]],"date-time":"2019-07-16T00:00:00Z","timestamp":1563235200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001700","name":"Ministry of Education, Culture, Sports, Science and Technology","doi-asserted-by":"publisher","award":["15H05925"],"award-info":[{"award-number":["15H05925"]}],"id":[{"id":"10.13039\/501100001700","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001700","name":"Ministry of Education, Culture, Sports, Science and Technology","doi-asserted-by":"publisher","award":["15H02727"],"award-info":[{"award-number":["15H02727"]}],"id":[{"id":"10.13039\/501100001700","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001700","name":"Ministry of Education, Culture, Sports, Science and Technology","doi-asserted-by":"publisher","award":["24700176"],"award-info":[{"award-number":["24700176"]}],"id":[{"id":"10.13039\/501100001700","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Imaging"],"abstract":"<jats:p>One of the main problems faced by the photometric stereo method is that several measurements are required, as this method needs illumination from light sources from different directions. A solution to this problem is the color photometric stereo method, which conducts one-shot measurements by simultaneously illuminating lights of different wavelengths. However, the classic color photometric stereo method only allows measurements of white objects, while a surface-normal estimation of a multicolored object using this method is theoretically impossible. Therefore, it is necessary to add some constraints to estimate the surface normal of a multicolored object using the framework of the color photometric stereo method. In this study, a median filter is employed as the constraint condition of albedo, and the surface normal of the occluding boundary is employed as the constraint condition of the surface normal. By employing a median filter as the constraint condition, the smooth distribution of the albedo and normal is calculated while the sharp features at the boundary of different albedos and normals are preserved. The surface normal at the occluding boundary is propagated into the inner part of the object region, and forms the abstract shape of the object. Such a surface normal gives a great clue to be used as an initial guess to the surface normal. To demonstrate the effectiveness of this study, a measurement device that can realize the multispectral photometric stereo method with seven colors is employed instead of the classic color photometric stereo method with three colors.<\/jats:p>","DOI":"10.3390\/jimaging5070064","type":"journal-article","created":{"date-parts":[[2019,7,17]],"date-time":"2019-07-17T02:44:03Z","timestamp":1563331443000},"page":"64","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["Color Photometric Stereo Using Multi-Band Camera Constrained by Median Filter and Occluding Boundary"],"prefix":"10.3390","volume":"5","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7312-0543","authenticated-orcid":false,"given":"Daisuke","family":"Miyazaki","sequence":"first","affiliation":[{"name":"Graduate School of Information Sciences, Hiroshima City University, Hiroshima 731-3194, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuka","family":"Onishi","sequence":"additional","affiliation":[{"name":"Graduate School of Information Sciences, Hiroshima City University, Hiroshima 731-3194, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shinsaku","family":"Hiura","sequence":"additional","affiliation":[{"name":"Graduate School of Engineering, University of Hyogo, Hyogo 671-2280, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,7,16]]},"reference":[{"key":"ref_1","unstructured":"Silver, W.M. (1980). Determining Shape and Reflectance Using Multiple Images. [Master\u2019s Thesis, Massachusetts Institute of Technology]."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1117\/12.7972479","article-title":"Photometric method for determining surface orientation from multiple images","volume":"19","author":"Woodham","year":"1980","journal-title":"Opt. Eng."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Drew, M., and Kontsevich, L. (1994, January 21\u201323). Closed-form attitude determination under spectrally varying illumination. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Seattle, WA, USA.","DOI":"10.1109\/CVPR.1994.323939"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1047","DOI":"10.1364\/JOSAA.11.001047","article-title":"Reconstruction of shape from shading in color images","volume":"11","author":"Kontsevich","year":"1994","journal-title":"J. Opt. Soc. Am. A"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"3050","DOI":"10.1364\/JOSAA.11.003050","article-title":"Gradient and curvature from photometric stereo including local confidence estimation","volume":"11","author":"Woodham","year":"1994","journal-title":"J. Opt. Soc. Am."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Anderson, R., Stenger, B., and Cipolla, R. (2011, January 6\u201313). Color photometric stereo for multicolored surfaces. Proceedings of the International Conference on Computer Vision, Barcelona, Spain.","DOI":"10.1109\/ICCV.2011.6126495"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2104","DOI":"10.1109\/TPAMI.2011.37","article-title":"Video normals from colored lights","volume":"33","author":"Brostow","year":"2011","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Chakrabarti, A., and Sunkavalli, K. (2016, January 25\u201328). Single-image RGB photometric stereo with spatially-varying albedo. Proceedings of the International Conference on 3D Vision, Stanford, CA, USA.","DOI":"10.1109\/3DV.2016.34"},{"key":"ref_9","unstructured":"Drew, M.S. (1995, January 21\u201323). Reduction of rank-reduced orientation-from-color problem with many unknown lights to two-image known-illuminant photometric stereo. Proceedings of the International Symposium on Computer Vision, Coral Gables, FL, USA."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"286","DOI":"10.1006\/cviu.1996.0059","article-title":"Direct solution of orientation-from-color problem using a modification of Pentland\u2019s light source direction estimator","volume":"64","author":"Drew","year":"1996","journal-title":"Comput. Vis. Image Understand."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1371","DOI":"10.1364\/JOSAA.17.001371","article-title":"Color from shape from color: A simple formalism with known light sources","volume":"17","author":"Drew","year":"2000","journal-title":"J. Opt. Soc. Am. A"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Fyffe, G., Yu, X., and Debevec, P. (2011, January 8\u201310). Single-shot photometric stereo by spectral multiplexing. Proceedings of the IEEE International Conference on Computational Photography, Pittsburgh, PA, USA.","DOI":"10.1109\/ICCPHOT.2011.5753116"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Hernandez, C., Vogiatzis, G., Brostow, G.J., Stenger, B., and Cipolla, R. (2007, January 14\u201321). Non-rigid photometric stereo with colored lights. Proceedings of the IEEE International Conference on Computer Vision, Rio de Janeiro, Brazil.","DOI":"10.1109\/ICCV.2007.4408939"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Hern\u00e1ndez, C., Vogiatzis, G., and Cipolla, R. (2008, January 12\u201318). Shadows in three-source photometric stereo. Proceedings of the ECCV 2008, Marseille, France.","DOI":"10.1007\/978-3-540-88682-2_23"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Jiao, H., Luo, Y., Wang, N., Qi, L., Dong, J., and Lei, H. (2016, January 13\u201316). Underwater multi-spectral photometric stereo reconstruction from a single RGBD image. Proceedings of the Asia-Pacific Signal and Information Processing Association Annual Summit and Conference, Jeju, South Korea.","DOI":"10.1109\/APSIPA.2016.7820773"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Kim, H., Wilburn, B., and Ben-Ezra, M. (2010, January 5\u201311). Photometric stereo for dynamic surface orientations. Proceedings of the European Conference on Computer Vision, LNCS 6311, Crete, Greece.","DOI":"10.1007\/978-3-642-15549-9_5"},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Landstrom, A., Thurley, M.J., and Jonsson, H. (2013, January 26\u201328). Sub-millimeter crack detection in casted steel using color photometric stereo. Proceedings of the International Conference on Digital Image Computing: Techniques and Applications, Hobart, TAS, Australia.","DOI":"10.1109\/DICTA.2013.6691532"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2745","DOI":"10.1364\/JOSAA.11.002745","article-title":"Properties of color images of surfaces under multiple illuminants","volume":"11","author":"Petrov","year":"1994","journal-title":"J. Opt. Soc. Am. A"},{"key":"ref_19","unstructured":"Rahman, S., Lam, A., Sato, I., and Robles-Kelly, A. (2014, January 1\u20135). Color photometric stereo using a rainbow light for non-Lambertian multicolored surfaces. Proceedings of the Asian Conference on Computer Vision, Singapore."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Roubtsova, N., and Guillemaut, J.Y. (2014, January 8\u201311). Colour Helmholtz stereopsis for reconstruction of complex dynamic scenes. Proceedings of the International Conference on 3D Vision, Tokyo, Japan.","DOI":"10.1109\/3DV.2014.59"},{"key":"ref_21","unstructured":"Cipolla, R., Battiato, S., and Farinella, G.M. (2010). Practical 3d reconstruction based on photometric stereo. Computer Vision: Detection, Recognition and Reconstruction, Springer."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1007\/s11263-011-0482-7","article-title":"Self-calibrated, multi-spectral photometric stereo for 3D face capture","volume":"97","author":"Vogiatzis","year":"2012","journal-title":"Int. J. Comput. Vis."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Gotardo, P.F.U., Simon, T., Sheikh, Y., and Mathews, I. (2015, January 7\u201313). Photogeometric scene flow for high-detail dynamic 3D reconstruction. Proceedings of the IEEE International Conference on Computer Vision, Santiago, Chile.","DOI":"10.1109\/ICCV.2015.103"},{"key":"ref_24","unstructured":"Wolff, L.B., Shafer, S.A., and Healey, G. (1992). Geometrical considerations and nomenclature of reflectance. Radiometry, Jones and Bartlett Publishers, Inc."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Qu\u00e9au, Y., Mecca, R., and Durou, J.-D. (2016, January 27\u201330). Unbiased photometric stereo for colored surfaces: A variational approach. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Las Vegas, NV, USA.","DOI":"10.1109\/CVPR.2016.472"},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Oswald, M.R., T\u00f6ppe, E., and Cremers, D. (2012, January 16\u201321). Fast and globally optimal single view reconstruction of curved objects. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Providence, RI, USA.","DOI":"10.1109\/CVPR.2012.6247718"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"576","DOI":"10.1007\/s10851-017-0773-x","article-title":"Normal integration: A survey","volume":"60","author":"Durou","year":"2018","journal-title":"J. Math. Imaging Vis."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"174","DOI":"10.1016\/0734-189X(86)90114-3","article-title":"The variational approach to shape from shading","volume":"33","author":"Horn","year":"1986","journal-title":"Comput. Vis. Graph. Image Process."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"141","DOI":"10.1016\/0004-3702(81)90023-0","article-title":"Numerical shape from shading and occluding boundaries","volume":"17","author":"Ikeuchi","year":"1981","journal-title":"Artif. Intell."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1109\/34.3909","article-title":"A method for enforcing integrability in shape from shading algorithms","volume":"10","author":"Frankot","year":"1988","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1007\/s41095-016-0075-z","article-title":"Fast and accurate surface normal integration on non-rectangular domains","volume":"3","author":"Boroujerdi","year":"2017","journal-title":"Comput. Vis. Media"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"2728","DOI":"10.1364\/JOSAA.18.002728","article-title":"Sensor sharpening for computational color constancey","volume":"18","author":"Barnard","year":"2001","journal-title":"J. Opt. Soc. Am. A"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1553","DOI":"10.1364\/JOSAA.11.001553","article-title":"Spectral sharpening: Sensor transformations for improved color constancey","volume":"11","author":"Finlayson","year":"1994","journal-title":"J. Opt. Soc. Am. A"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Kawakami, R., and Ikeuchi, K. (2009, January 20\u201325). Color estimation from a single surface color. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, Miami, FL, USA.","DOI":"10.1109\/CVPR.2009.5206645"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1050","DOI":"10.1016\/j.imavis.2006.04.025","article-title":"Object surface recovery using a multi-light photometric stereo technique for non-Lambertian surfaces subject to shadows and specularities","volume":"25","author":"Sun","year":"2007","journal-title":"Image Vis. Comput."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1016\/j.imavis.2016.11.006","article-title":"Photometric stereo with only two image: A theoretical study and numerical solution","volume":"57","author":"Mecca","year":"2017","journal-title":"Image Vis. Comput."}],"container-title":["Journal of Imaging"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2313-433X\/5\/7\/64\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:06:15Z","timestamp":1760187975000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2313-433X\/5\/7\/64"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,7,16]]},"references-count":36,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2019,7]]}},"alternative-id":["jimaging5070064"],"URL":"https:\/\/doi.org\/10.3390\/jimaging5070064","relation":{},"ISSN":["2313-433X"],"issn-type":[{"value":"2313-433X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,7,16]]}}}