2. Hašan [2] Dong [3] 3D Papas [4] Brunton [5] 3D [6] UV 3. UV LUT: Lookup Table LUT LUT 計測系 出力系 半透明材質の計測 UV インクの計測 要求材質の設計 ルックアップテーブル逆引き 印刷 2 印刷時の半透明
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1 UV 1,a) 1,b) 1,c) 1,d) 1,e) UV UV UV UV UV 1. 3D 3D 3D [1] 3D UV 1 UV UV UV: Ultraviolet 1 a) takatani.tsuyoshi.to2@is.naist.jp b) fujita.koki.fg9@is.naist.jp c) ktanaka@is.naist.jp d) funatomi@is.naist.jp e) mukaigawa@is.naist.jp 食品サンプル本物 1 UV UV-LED UV UV UV UV 1
2 2. Hašan [2] Dong [3] 3D Papas [4] Brunton [5] 3D [6] UV 3. UV LUT: Lookup Table LUT LUT 計測系 出力系 半透明材質の計測 UV インクの計測 要求材質の設計 ルックアップテーブル逆引き 印刷 2 印刷時の半透明感合成 ルックアップテーブル構築 LUT UV LUT LUT [7] 3(a) 1 3(b) PSF: Point Spread Function PSF PSF PSF MTF: Modulation Transfer Function 3(c) PSF PSF MTF 3.2 2
3 3 レーザ光 強度 フーリエ変換 逆フーリエ変換 強度 位置 空間周波数 (a) (b) (c) MTF (a) (b)(a) PSF (c)(b) MTF PSF [9] MTF LUT 5 r 1, t 1 r 2, t 2 r, t r = r 1 + t 2 1r 2 (1 + r 1 r 2 + r 2 1r ) = r 1 + t2 1r 2 1 r 1 r 2 (1) t = t 1 t 2 (1 + r 1 r 2 + r 2 1r ) 消しゴム アクリル板 = t 1t 2 1 r 1 r 2 (2) PSF R 1 (x), T 1 (x) PSF R 2 (x), T 2 (x) PSF R(x) =R 1 (x) + ((T 1 R 2 ) T 1 )(x) + ((((T 1 R 2 ) R 1 ) R 2 ) T 1 )(x) + (3) 4 MTF MTF [8] MTF MTF MTF 4 RGB MTF MTF MTF MTF MTF MTF LUT UV PSF (3) MTF F[R](f x ) = F[R 1 ](f x ) + F[T 1 ](f x )F[R 2 ](f x )F[T 1 ](f x ) + = F[R 1 ](f x ) + F[T 1](f x ) 2 F[R 2 ](f x ) 1 F[R 1 ](f x )F[R 2 ](f x ) (4) f x F[ ] x PSF MTF (1) MTF F[T ](f x ) = F[T 1]F[T 2 ] 1 F[R 1 ]F[R 2 ] (5) (4) (5) UV MTF MTF MTF MTF LUT MTF 3
4 r 1 t 1 t 1 t 1 r 1 r 1 r 2 r 2 t 2 t 2 t 2 RGB カメラ 5 プロジェクタ 2 [9] 6 MTF 3.3 r t 対象物体 MTF UV MTF MTF LUT MTF LUT MTF Mf A, M f B RMSE: Root-Mean-Square Error E AB 1 { 2 E AB = (Mf A F (f x) Mf x)} B(f (6) f x F F MTF RMSE MTF MTF [8] MTF [8] MTF 6 Vivitek QUMI Q8 RGB FLIR Grasshopper [mm 1 ] 9 X-rite ColorChecker Passport 4.2 UV MTF UV MTF UV UV 1 (4) MTF R S R S = F[R 1 ] + F[T 1] 2 1 F[R 1 ] (7) MTF 1 UV 2 (4) 2 MTF (7) 1 MTF MTF R D R D = F[R 1 ] + F[T 1] 2 S 1 F[R 1 ]S (8) UV MTF F[R 1 ] = R 2 S R D R 2 S + R S + R S R D 1 (9) F[T 1 ] = (R S F[R 1 ])(1 F[R 1 ]) (10) UV Roland LEF-300 UV MTF 7 UV C M Y K K CMY 100% MTF UV MTF MTF MTF RMSE 3 MTF MTF 8 RMSE (1) RMSE RMSE 4 MTF UV 4
5 情報処理学会研究報告 シアン マゼンタ イエロー 図 7 計測した UV インクの反射 透過 MTF 乳白アクリル板 イエロー マゼンタ シアン 消しゴム 図 8 CMY 単色を印刷した場合の合成 MTF と実際の印刷物の計測 MTF の比較 表1 CMY 単色を印刷した場合の合成 MTF と印刷物の計測 MTF て その反射 MTF を再現する 表面テクスチャによる影 を比較した際の RMSE 響を低減するため 材質が比較的均一な小領域の反射 MTF 材質 UV インク 消しゴム 乳白アクリル板 平均 を計測し それを要求反射 MTF とした LUT は 半透明 シアン 材質として消しゴム 乳白アクリルの 3 種類を マゼンタ イエロー 用い CMY の 3 種類の UV インクについて 最大 5 層ま 平均 での全組合せについて反射 MTF を合成することで構築し たところ 1089 種類の要因組合せとなった 5.2 逆引きによる半透明感再現の検討 最後に 逆引きによる半透明感再現について検討する ここでは 図 9 に示すサーモン 牛肉 キウイを対象とし 2018 Information Processing Society of Japan 構築した LUT 内を探索した結果 最も距離が近くなる 組合せは サーモンの場合 に マゼンタ マゼ ンタの順で 2 層印刷したもので RMSE は 牛肉の場 5
6 サーモン PSF PSF MTF PTF: Phase Transfer Function JST ACT-I JSPS JP17K19979 JP17J05602 牛肉キウイ 9 MTF 3 RMSE RMSE MTF LUT MTF MTF LUT UV 100% 6. UV MTF UV MTF LUT MTF MTF RMSE LUT [1] Ion, A., Frohnhofen, J., Wall, L., Kovacs, R., Alistar, M., Lindsay, J., Lopes, P., Chen, H.-T. and Baudisch, P.: Metamaterial mechanisms, Proceedings of the 29th Annual Symposium on User Interface Software and Technology, ACM, pp (2016). [2] Hašan, M., Fuchs, M., Matusik, W., Pfister, H. and Rusinkiewicz, S.: Physical Reproduction of Materials with Specified Subsurface Scattering, ACM Transactions on Graphics (Proc. SIGGRAPH), Vol. 29, No. 3 (2010). [3] Dong, Y., Wang, J., Pellacini, F., Tong, X. and Guo, B.: Fabricating Spatially-varying Subsurface Scattering, ACM Trans. Graph., Vol. 29, No. 4, pp. 62:1 62:10 (online), DOI: / (2010). [4] Papas, M., Regg, C., Jarosz, W., Bickel, B., Jackson, P., Matusik, W., Marschner, S. and Gross, M.: Fabricating Translucent Materials Using Continuous Pigment Mixtures, ACM Trans. Graph., Vol. 32, No. 4, pp. 146:1 146:12 (online), DOI: / (2013). [5] Brunton, A., Arikan, C. A. and Urban, P.: Pushing the Limits of 3D Color Printing: Error Diffusion with Translucent Materials, ACM Trans. Graph., Vol. 35, No. 1, pp. 4:1 4:13 (online), DOI: / (2015). [6] 2017 pp (2017). [7] : (2016). [8] Cuccia, D. J., Bevilacqua, F., Durkin, A. J. and Tromberg, B. J.: Modulated imaging: quantitative analysis and tomography of turbid media in the spatialfrequency domain, Opt. Lett., Vol. 30, No. 11, pp (online), DOI: /OL (2005). [9] Kubelka, P.: New Contributions to the Optics of Intensely Light-Scattering Materials. Part II: Nonhomogeneous Layers, J. Opt. Soc. Am., Vol. 44, No. 4, pp (online), DOI: /JOSA (1954). 6
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