Ikeuchi Laboratory The University of Tokyo Japan Polarizationbased

Ikeuchi Laboratory The University of Tokyo Japan Polarization-based Shape Estimation of Transparent Objects for Digitizing Cultural Assets Daisuke Miyazaki Katsushi Ikeuchi The University of Tokyo International Symposium on the CREST Digital Archiving Project

Introduction(1/3) Polarization raytracing(7) Shape estimation(6) Experiment(5) Conclusion(2) Objective l Estimate 3 D shape of transparent object l Analyze the polarization phenomena Polarization analysis Real transparent object Virtual transparent object International Symposium on the CREST Digital Archiving Project

Introduction(2/3) Polarization raytracing(7) Shape estimation(6) Experiment(5) Conclusion(2) Application fields Modeling cultural assets 3 D catalog in web site Manufacturing robot Object recognition to recycle International Symposium on the CREST Digital Archiving Project

Introduction(3/3) Polarization raytracing(7) Shape estimation(6) Experiment(5) Conclusion(2) Methods developed in this project Previous project Miyazaki et al. 2004 Miyazaki et al. 2002 Today’s talk International Symposium on the CREST Digital Archiving Project

Introduction(3) Polarization raytracing(1/7) Shape estimation(6) Experiment(5) Conclusion(2) Polarization l l l Light = wave oscillates Oscillates in certain direction polarization DOP = degree of polarization Incident Light Unpolarized (DOP 0) Polarizer Perfectly polarized (DOP 1) Reflected Air Object Transmitted Partially polarized (DOP 0~1) International Symposium on the CREST Digital Archiving Project

Introduction(3) Polarization raytracing(2/7) Shape estimation(6) Experiment(5) Conclusion(2) Reflection and transmission Light Unpolarized Normal Depends upon Partially polarized Air Object Partially polarized International Symposium on the CREST Digital Archiving Project

Introduction(3) Polarization raytracing(3/7) Shape estimation(6) Experiment(5) Conclusion(2) Tracing the light rays Calculate reflection and transmission International Symposium on the CREST Digital Archiving Project

Introduction(3) Polarization raytracing(4/7) Shape estimation(6) Experiment(5) Conclusion(2) Polarization raytracing Ray tracing Calculate intensity Conventional raytracing Ray tracing Calculate polarization Polarization raytracing International Symposium on the CREST Digital Archiving Project

Introduction(3) Polarization raytracing(5/7) Shape estimation(6) Experiment(5) Conclusion(2) Mueller calculus Conventional raytracing Intensity: Scalar Reflectivity&transmissivity: Scalar Polarization raytracing Polarization state: 4 D vector Reflection&transmisstion matrix: 4 x 4 matrix International Symposium on the CREST Digital Archiving Project

Introduction(3) Polarization raytracing(6/7) Shape estimation(6) Experiment(5) Conclusion(2) Example of Mueller calculus Conventional raytracing Reflected intensity Scalar reflectivity Scalar incident intensity Scalar Polarization raytracing Reflection vector reflection matrix incidence vector International Symposium on the CREST Digital Archiving Project

Introduction(3) Polarization raytracing(7/7) Shape estimation(6) Experiment(5) Conclusion(2) Example of matrices Reflection Transmission Rotation Phase shift International Symposium on the CREST Digital Archiving Project

Introduction(3) Polarization raytracing(7) Shape estimation(1/6) Shape estimation Initial shape Experiment(5) Conclusion(2) Iterative computation with updating the shape 2 min Input DOP (degree of polarization) Caculated DOP with polarization raytracing Final shape International Symposium on the CREST Digital Archiving Project

Introduction(3) Polarization raytracing(7) Shape estimation(2/6) Experiment(5) Conclusion(2) Error function min dxdy Input Calculated Relationship between normal & height Calculate height and normal International Symposium on the CREST Digital Archiving Project

Introduction(3) Polarization raytracing(7) Shape estimation(3/6) Experiment(5) Conclusion(2) Calculate normal from shape Set initial height H properly Calculate gradient p&q by differentiating height H International Symposium on the CREST Digital Archiving Project

Introduction(3) Polarization raytracing(7) Shape estimation(4/6) Experiment(5) Conclusion(2) Update normal Input DOP Calculated DOP Light ray Change normal Object Error Ray changes International Symposium on the CREST Digital Archiving Project

Introduction(3) Polarization raytracing(7) Shape estimation(5/6) Experiment(5) Conclusion(2) Calculate height from normal Updated normal Relaxation method Calculated height International Symposium on the CREST Digital Archiving Project

Introduction(3) Polarization raytracing(7) Shape estimation(6/6) Experiment(5) Conclusion(2) Algorithm overview Initial height Normal from height Minimize 2 Input Calc. Update normal Output height Stop when 2 Input Height from normal Calc. is small enough International Symposium on the CREST Digital Archiving Project

Introduction(3) Polarization raytracing(7) Shape estimation(6) Experiment(1/5) Conclusion(2) Experimental setup Monochrome camera Camera adapter Computer IR/UV cut-off filter Linear polarizer Geodesic dome Plastic sphere 40 W lamp Polarizer controller Transparent object inside International Symposium on the CREST Digital Archiving Project

Introduction(3) Polarization raytracing(7) Shape estimation(6) Experiment(2/5) Conclusion(2) Simulational result 25 loop Initial 20 loop Frontal shape(estimated) Frontal shape(truth) Rear shape(known) Refractive index 1. 5 & Illumination (known) International Symposium on the CREST Digital Archiving Project

Introduction(3) Polarization raytracing(7) Shape estimation(6) Experiment(3/5) Conclusion(2) Experimental result Acrylic hemisphere Refractive index 1. 5 Diameter 30 mm Initial (previous method) Error(height): 2. 8 mm Error(normal): 14 Initial (previous method) 3000 1500 0 25 Error/loop 50 50 loop Error(height): 0. 61 mm Error(normal): 7. 0 10 loop International Symposium on the CREST Digital Archiving Project

Introduction(3) Polarization raytracing(7) Shape estimation(6) Experiment(4/5) Conclusion(2) Experimental result Initial Acrylic object Diameter(base)24 mm Refractive index 1. 5 5 loop 50 loop Error(height) 0. 24 mm International Symposium on the CREST Digital Archiving Project

Introduction(3) Polarization raytracing(7) Shape estimation(6) Experiment(5/5) Conclusion(2) Experimental result Glass(refractive index 1. 5) 10 loop Initial(previous method) International Symposium on the CREST Digital Archiving Project

Introduction(3) Polarization raytracing(7) Shape estimation(6) Experiment(5) Conclusion(1/2) Summary Polarization raytracing Iteration Initial shape Calculated polarization data 2 min Input polarization data Object Shape International Symposium on the CREST Digital Archiving Project

Introduction(3) Polarization raytracing(7) Shape estimation(6) Experiment(5) Conclusion(2/2) Future work for another project Realtime measurement Commercial product ? Estimating refractive index Modeling cultural assets International Symposium on the CREST Digital Archiving Project

Ikeuchi Laboratory The University of Tokyo Japan Thank you Supported by Japan Science and Technology Agency Special thanks to Interfaculty Initiative in Information Studies, The University of Tokyo International Symposium on the CREST Digital Archiving Project

Ikeuchi Laboratory The University of Tokyo Japan Daisuke Miyazaki 2005 Creative Commons Attribution 4. 0 International License. http: //www. cvl. iis. u-tokyo. ac. jp/ Daisuke Miyazaki, Katsushi Ikeuchi, "Polarization-based Shape Estimation of Transparent Objects for Digitizing Cultural Assets, " in Proceedings of International Symposium on the CREST Digital Archiving Project, pp. 34 -41, Tokyo, Japan, 2005. 03 International Symposium on the CREST Digital Archiving Project