{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:31:41Z","timestamp":1760232701479,"version":"build-2065373602"},"reference-count":43,"publisher":"MDPI AG","issue":"22","license":[{"start":{"date-parts":[[2022,11,16]],"date-time":"2022-11-16T00:00:00Z","timestamp":1668556800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Beijing Institute of Graphic Communication\u2019s Scientific Research Projects","award":["BIGC Ec202003","BIGC Ec202102","BIGC Ec202302","PID2019-107816GB-I00\/SRA\/10.13039\/501100011033"],"award-info":[{"award-number":["BIGC Ec202003","BIGC Ec202102","BIGC Ec202302","PID2019-107816GB-I00\/SRA\/10.13039\/501100011033"]}]},{"name":"Beijing Institute of Graphic Communication\u2019s Scientific Research and Innovation Team Project","award":["BIGC Ec202003","BIGC Ec202102","BIGC Ec202302","PID2019-107816GB-I00\/SRA\/10.13039\/501100011033"],"award-info":[{"award-number":["BIGC Ec202003","BIGC Ec202102","BIGC Ec202302","PID2019-107816GB-I00\/SRA\/10.13039\/501100011033"]}]},{"name":"Ministry of Science and Innovation of the National Government of Spain","award":["BIGC Ec202003","BIGC Ec202102","BIGC Ec202302","PID2019-107816GB-I00\/SRA\/10.13039\/501100011033"],"award-info":[{"award-number":["BIGC Ec202003","BIGC Ec202102","BIGC Ec202302","PID2019-107816GB-I00\/SRA\/10.13039\/501100011033"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Based on previous visual assessments of 440 color pairs of 3D-printed samples, we tested the performance of eight color-difference formulas (CIELAB, CIEDE2000, CAM02-LCD, CAM02-SCD, CAM02-UCS, CAM16-LCD, CAM16-SCD, and CAM16-UCS) using the standardized residual sum of squares (STRESS) index. For the whole set of 440 color pairs, the introduction of kL (lightness parametric factor), b (exponent in total color difference), and kL + b produced an average STRESS decrease of 2.6%, 26.9%, and 29.6%, respectively. In most cases, the CIELAB formula was significantly worse statistically than the remaining seven formulas, for which no statistically significant differences were found. Therefore, based on visual results using 3D-object colors with the specific shape, size, gloss, and magnitude of color differences considered here, we concluded that the CIEDE2000, CAM02-, and CAM16-based formulas were equivalent and thus cannot recommend only one of them. Disregarding CIELAB, the average STRESS decreases in the kL + b-optimized formulas from changes in each one of the four analyzed parametric factors were not statistically significant and had the following values: 6.2 units changing from color pairs with less to more than 5.0 CIELAB units; 2.9 units changing the shape of the samples (lowest STRESS values for cylinders); 0.7 units changing from nearly-matte to high-gloss samples; and 0.5 units changing from 4 cm to 2 cm samples.<\/jats:p>","DOI":"10.3390\/s22228869","type":"journal-article","created":{"date-parts":[[2022,11,17]],"date-time":"2022-11-17T06:24:42Z","timestamp":1668666282000},"page":"8869","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Optimizing Color-Difference Formulas for 3D-Printed Objects"],"prefix":"10.3390","volume":"22","author":[{"given":"Min","family":"Huang","sequence":"first","affiliation":[{"name":"Printing and Packaging Engineering, Beijing Institute of Graphic Communication, Beijing 102600, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xinyuan","family":"Gao","sequence":"additional","affiliation":[{"name":"Printing and Packaging Engineering, Beijing Institute of Graphic Communication, Beijing 102600, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jie","family":"Pan","sequence":"additional","affiliation":[{"name":"Printing and Packaging Engineering, Beijing Institute of Graphic Communication, Beijing 102600, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiu","family":"Li","sequence":"additional","affiliation":[{"name":"Printing and Packaging Engineering, Beijing Institute of Graphic Communication, Beijing 102600, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Caroline","family":"Hemingray","sequence":"additional","affiliation":[{"name":"School of Design, University of Leeds, Leeds LS2 9JT, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7197-7159","authenticated-orcid":false,"given":"Kaida","family":"Xiao","sequence":"additional","affiliation":[{"name":"School of Design, University of Leeds, Leeds LS2 9JT, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7226-4190","authenticated-orcid":false,"given":"Manuel","family":"Melgosa","sequence":"additional","affiliation":[{"name":"Optics Department, Faculty of Sciences, University of Granada, 18071 Granada, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,11,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"109943","DOI":"10.1016\/j.matdes.2021.109943","article-title":"Accurate and computational: A review of color reproduction in full-color 3D printing","volume":"209","author":"Yuan","year":"2021","journal-title":"Mater. Des."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Barreto, M.A., Perez-Gonzalez, J., Herr, H.M., and Huegel, J.C. (2022). ARACAM: A RGB-D multi-view photogrammetry system for lower limb 3D reconstruction applications. Sensors, 22.","DOI":"10.3390\/s22072443"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1002\/col.20300","article-title":"Request for existing experimental datasets on color differences","volume":"32","author":"Melgosa","year":"2007","journal-title":"Color Res. Appl."},{"key":"ref_4","unstructured":"(2019). Colorimetry\u2014Part 4: CIE 1976 L*a*b* Colour Space (Standard No. ISO\/CIE 11664-4)."},{"key":"ref_5","unstructured":"(2014). Colorimetry\u2014Part 6: CIEDE2000 Colour-Difference Formula (Standard No. ISO\/CIE DIS 11664-6)."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"320","DOI":"10.1002\/col.20227","article-title":"Uniform colour spaces based on CIECAM02 colour appearance model","volume":"31","author":"Luo","year":"2006","journal-title":"Color Res. Appl."},{"key":"ref_7","unstructured":"(2004). A Colour Appearance Model for Colour Management Systems: CIECAM (Standard No. CIE 159)."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"703","DOI":"10.1002\/col.22131","article-title":"Comprehensive color solutions: CAM16, CAT16, and CAM16-UCS","volume":"42","author":"Li","year":"2017","journal-title":"Color Res. Appl."},{"key":"ref_9","unstructured":"(2022). The CIE 2016 Colour Appearance Model for Colour Management Systems: CIECAM16 (Standard No. CIE 248:2022)."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1002\/col.5080110107","article-title":"Chromaticity-discrimination ellipses for surface colours","volume":"11","author":"Luo","year":"1986","journal-title":"Color Res. Appl."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1111\/j.1520-6378.1994.tb00054.x","article-title":"Color-discrimination thresholds translated from the CIE (x,y,Y) space to the CIE 1976 (L*,a*,b*)","volume":"19","author":"Melgosa","year":"1994","journal-title":"Color Res. Appl."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1167\/10.9.10","article-title":"Color appearance of real objects varying in material, hue, and shape","volume":"10","author":"Giesel","year":"2010","journal-title":"J. Vision"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1167\/10.9.5","article-title":"Perceived glossiness and lightness under real-world illumination","volume":"10","author":"Olkkonen","year":"2010","journal-title":"J. Vision"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1145\/2832905","article-title":"Pushing the limits of 3D color printing: Error diffusion with translucent materials","volume":"35","author":"Brunton","year":"2015","journal-title":"ACM Trans. Graph."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"A306","DOI":"10.1364\/JOSAA.33.00A306","article-title":"Low levels of specularity support operational color constancy, particularly when surface and illumination geometry can be inferred","volume":"33","author":"Lee","year":"2016","journal-title":"J. Opt. Soc. Am. A"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1017\/S0952523808080267","article-title":"Surface gloss and color perception of 3D objects","volume":"25","author":"Xiao","year":"2008","journal-title":"Visual. Neurosci."},{"key":"ref_17","unstructured":"CIE (2022, November 09). TC 8-17. Methods for Evaluating Colour Difference between 3D Colour Objects. Available online: http:\/\/cie.co.at\/technicalcommittees\/methods-evaluating-colour-difference-between-3d-colour-objects."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Tsai, T.-H., and Cheng, C.-S. (2022). Automatic optical inspection system for wire color sequence detection. Sensors, 22.","DOI":"10.3390\/s22155885"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Wang, Y., Zhao, Q., Chen, J., Wang, W., Yu, S., and Yang, X. (2022). Color design decisions for ceramic products based on quantification of perceptual characteristics. Sensors, 22.","DOI":"10.3390\/s22145415"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"827","DOI":"10.1071\/SR04169","article-title":"Colour variation in standard soil-colour charts","volume":"43","author":"Huertas","year":"2005","journal-title":"Aust. J. Soil Res."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Liu, G., Tian, S., Mo, Y., Chen, R., and Zhao, Q. (2022). On the acquisition of high-quality digital images and extraction of effective color information for soil water content testing. Sensors, 22.","DOI":"10.3390\/s22093130"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"24237","DOI":"10.1364\/OE.432729","article-title":"Color-difference evaluation for 3D printed objects","volume":"29","author":"Jiang","year":"2021","journal-title":"Opt. Express"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"He, R., Xiao, K., Pointer, M., Melgosa, M., and Bressler, Y. (2022). Optimizing parametric factors in CIELAB and CIEDE2000 color-difference formulas for 3D printed spherical objects. Materials, 15.","DOI":"10.3390\/ma15124055"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"916","DOI":"10.1364\/JOSAA.452656","article-title":"Influences of shape, size and gloss on the perceived color difference of 3D printed objects","volume":"39","author":"Huang","year":"2022","journal-title":"J. Opt. Soc. Am. A"},{"key":"ref_25","unstructured":"(2016). Recommended Method for Evaluating the Performance of Colour-Difference Formulae (Standard No. CIE 217)."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"597","DOI":"10.1364\/OE.23.000597","article-title":"Power functions improving the performance of color-difference formulas","volume":"23","author":"Huang","year":"2015","journal-title":"Opt. Express"},{"key":"ref_27","unstructured":"(2019). Validity of Formulae for Predicting Small Colour Differences (Standard No. CIE 230:2019)."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"298","DOI":"10.1002\/(SICI)1520-6378(199710)22:5<298::AID-COL3>3.0.CO;2-S","article-title":"Some aspects of the visual scaling of large colour differences","volume":"22","author":"Pointer","year":"1997","journal-title":"Color Res. Appl."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"33302","DOI":"10.1364\/OE.462628","article-title":"Parametric effects in color-difference evaluation","volume":"30","author":"Xu","year":"2022","journal-title":"Opt. Express"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1360","DOI":"10.1364\/JOSAA.461542","article-title":"Metrics of color-difference formula improvement","volume":"39","author":"Carter","year":"2022","journal-title":"J. Opt. Soc. Am. A"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"949","DOI":"10.1364\/JOSAA.28.000949","article-title":"Notes on the application of the standardized residual sum of squares index for the assessment of intra- and inter-observer variability in color-difference experiments","volume":"28","author":"Melgosa","year":"2011","journal-title":"J. Opt. Soc. Am. A"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"2067","DOI":"10.1364\/JOSAA.23.002067","article-title":"Influence of random dot textures on perception of suprathreshold color differences","volume":"23","author":"Huertas","year":"2006","journal-title":"J. Opt. Soc. Am. A"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"316","DOI":"10.1002\/col.20693","article-title":"Evaluation of colour-difference formulae for different colour-difference magnitudes","volume":"37","author":"Wang","year":"2012","journal-title":"Color Res. Appl."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"326","DOI":"10.1002\/col.20689","article-title":"Testing uniform colour spaces and colour-difference formulae using printed samples","volume":"37","author":"Huang","year":"2012","journal-title":"Color Res. Appl."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"394","DOI":"10.1002\/col.1055","article-title":"Colour-difference evaluation using CRT colours. Part I: Data gathering and testing colour difference formulae","volume":"26","author":"Cui","year":"2001","journal-title":"Color Res. Appl."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"3359","DOI":"10.3788\/AOS20103011.3359","article-title":"Study on the influence of gloss on printed samples medium-small color difference with the psychophysical method of comparison","volume":"30","author":"Huang","year":"2010","journal-title":"Acta Opt. Sin."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"108","DOI":"10.1002\/col.5080060212","article-title":"A comparison of the CIE 1976 color spaces","volume":"6","author":"Pointer","year":"1981","journal-title":"Color Res. Appl."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"8069","DOI":"10.1364\/AO.33.008069","article-title":"Uniformity of some recent color metrics tested with an accurate color-difference tolerance dataset","volume":"33","author":"Melgosa","year":"1994","journal-title":"Appl. Opt."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"356","DOI":"10.1002\/(SICI)1520-6378(199910)24:5<356::AID-COL7>3.0.CO;2-N","article-title":"Investigation of parametric effects using large colour differences","volume":"24","author":"Guan","year":"1999","journal-title":"Color Res. Appl."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1851","DOI":"10.3788\/AOS20103006.1851","article-title":"Study on small color difference evaluation using printed samples with different gloss","volume":"30","author":"Huang","year":"2010","journal-title":"Acta Opt. Sin."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"3458","DOI":"10.1364\/OE.22.003458","article-title":"Measuring color differences in automotive samples with lightness flop: A test of the AUDI2000 color-difference formula","volume":"22","author":"Melgosa","year":"2014","journal-title":"Opt. Express"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1841","DOI":"10.1364\/JOSAA.28.001841","article-title":"Performance measures of color-difference equations: Correlation coefficient versus standardized residual sum of squares","volume":"28","author":"Kirchner","year":"2011","journal-title":"J. Opt. Soc. Am. A"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1111\/j.1478-4408.1972.tb03062.x","article-title":"The measurement and assessment of colour differences for industrial use. II. The accuracy of colour-difference equations","volume":"88","author":"Coates","year":"1972","journal-title":"J. Soc. Dyers Colour."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/22\/8869\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:19:29Z","timestamp":1760145569000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/22\/8869"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,11,16]]},"references-count":43,"journal-issue":{"issue":"22","published-online":{"date-parts":[[2022,11]]}},"alternative-id":["s22228869"],"URL":"https:\/\/doi.org\/10.3390\/s22228869","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2022,11,16]]}}}