Computer Graphics Laboratory, Hiroshima City University All images are compressed. The images in this file is not the original ones. Polarization stereo using graph cut (Miyazaki, Ikeuchi) 1

Computer Graphics Laboratory, Hiroshima City University Photometric stereo using graph cut and M-estimation for a virtual tumulus in the presence of highlights and shadows Daisuke MiyazakiThe University of TokyoPreviously Hiroshima City UniversityCurrently Katsushi IkeuchiThe University of Tokyo Polarization stereo using graph cut (Miyazaki, Ikeuchi) 2

CG Lab, Hiroshima City University Virtual Tumulus Polarization stereo using graph cut (Miyazaki, Ikeuchi) 3 [Laser range sensor][Photometric stereo] Virtual Tumulus Project Fine details Overall geometry

CG Lab, Hiroshima City University Proposed method Photometric stereo Graph cut Robust to outliers: shadow, specular reflection Point light source in far distance with small size: directional light Typically around 5 to 8 number of light sources The direction (and the power) of light sources are known Polarization stereo using graph cut (Miyazaki, Ikeuchi) 4

CG Lab, Hiroshima City University Candidates of surface normal Polarization stereo using graph cut (Miyazaki, Ikeuchi) 5 [Example] Choose 3 intensities from 5 inputs Photometric Stereo using 3 intensities

CG Lab, Hiroshima City University Candidates selection Polarization stereo using graph cut (Miyazaki, Ikeuchi) Neighboring surface normal: smooth Image Diffuse-only pixel Contaminated pixel with specular/shadow Candidates Graph cut Smooth surface normal Choose

CG Lab, Hiroshima City University Cost function Polarization stereo using graph cut (Miyazaki, Ikeuchi) 7 Data costSmoothness cost Sum of all pixels Constant weight

CG Lab, Hiroshima City University Data cost of pixel p Polarization stereo using graph cut (Miyazaki, Ikeuchi) 8 M-estimation (Lorentz function) Robust to outlier (shadow, specular reflection, noise) Image brightness Albedo (Diffuse reflectance) including light source color and brightness Surface normal Light source direction Shading (Lambert's law) (Cosine function)

CG Lab, Hiroshima City University Smoothness cost of neighboring pixels p & q Polarization stereo using graph cut (Miyazaki, Ikeuchi) 9 Albedo Surface normal

CG Lab, Hiroshima City University Graph structure Polarization stereo using graph cut (Miyazaki, Ikeuchi) sink source pq p sink source 10

CG Lab, Hiroshima City University Algorithm overview Polarization stereo using graph cut (Miyazaki, Ikeuchi) K C 3 candidates (surface normal & albedo) 2.Initial value 3.Graph cut (Estimate surface normal) [albedo fixed] 4.Graph cut (Estimate albedo) [surface normal fixed] 5.Iterate 3-4

CG Lab, Hiroshima City University Example of input images Polarization stereo using graph cut (Miyazaki, Ikeuchi) 12 Specular object

CG Lab, Hiroshima City University Result Polarization stereo using graph cut (Miyazaki, Ikeuchi) 13 Median-PS: Miyazaki et al. IJCV 2010 GC-PS: Proposed method

CG Lab, Hiroshima City University Evaluation Polarization stereo using graph cut (Miyazaki, Ikeuchi) 14 Input Conventional PS Shadowcut PS Wu's PS Median PS Proposed method  (149%) Surface normal (error)  (300%)  (80%)  (99%)  (100%)

CG Lab, Hiroshima City University The University Museum, The University of Tokyo Polarization stereo using graph cut (Miyazaki, Ikeuchi) 15 Chlamys australis (Australian scallop)

CG Lab, Hiroshima City University Museum Result Polarization stereo using graph cut (Miyazaki, Ikeuchi) 16

CG Lab, Hiroshima City University Segonko Tumulus Relief colored by red, green, yellow paints Not open to the public ~A.D.500 Relief colored by red, green, yellow paints Not open to the public ~A.D.500 Polarization stereo using graph cut (Miyazaki, Ikeuchi) 17 Kumamoto

CG Lab, Hiroshima City UniversityPolarization stereo using graph cut (Miyazaki, Ikeuchi) Aug 1st:preparation 2007 Aug 2nd:scanning (typhoon) 2007 Aug 3rd:data processing 2007 Aug 4th:scanning (hot) 2007 Aug 5th:data processing 2007 Aug 6th:scanning (sudden shower) 2007 Aug 7th:finishing 2007 Aug 1st:preparation 2007 Aug 2nd:scanning (typhoon) 2007 Aug 3rd:data processing 2007 Aug 4th:scanning (hot) 2007 Aug 5th:data processing 2007 Aug 6th:scanning (sudden shower) 2007 Aug 7th:finishing Scanning Mission

CG Lab, Hiroshima City University 8-Light Measurement System Polarization stereo using graph cut (Miyazaki, Ikeuchi) 19 Photometric Wing

CG Lab, Hiroshima City University Scanning Polarization stereo using graph cut (Miyazaki, Ikeuchi) 20

CG Lab, Hiroshima City University Images Polarization stereo using graph cut (Miyazaki, Ikeuchi) 21 Input image Rendered image

CG Lab, Hiroshima City University Segonko result Polarization stereo using graph cut (Miyazaki, Ikeuchi) 22

CG Lab, Hiroshima City UniversityPolarization stereo using graph cut (Miyazaki, Ikeuchi) 23 Fukuoka Sakurakyo Tumulus Keyhole-shaped tumulus 41m End of 6th century Carved triangle Painted with red, green, yellow Closed Mission: 2010 Jan

CG Lab, Hiroshima City UniversityPolarization stereo using graph cut (Miyazaki, Ikeuchi) 24

CG Lab, Hiroshima City UniversityPolarization stereo using graph cut (Miyazaki, Ikeuchi) 25

CG Lab, Hiroshima City University Conclusion Polarization stereo using graph cut (Miyazaki, Ikeuchi) 26 Graph Cut Photometric Stereo 3D Digital Archiving Virtual MuseumSegonko TumulusSakurakyo Tumulus

CG Lab, Hiroshima City University Future Work Polarization stereo using graph cut (Miyazaki, Ikeuchi) 27 Shadow & specular Faded texture Discontinuity Hiroshima A-bombed materials

Computer Graphics Laboratory, Hiroshima City University (c) Daisuke Miyazaki 2010 All rights reserved. Daisuke Miyazaki, Katsushi Ikeuchi, "Photometric stereo using graph cut and M-estimation for a virtual tumulus in the presence of highlights and shadows," Proceedings of Workshop on Application of Computer Vision to Archaeology, San Francisco, CA USA, June 2010 Polarization stereo using graph cut (Miyazaki, Ikeuchi) 28