Recovering Surfaces from the Gauss Map

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1 ISS CODE RUXUEW Journal o Sotware Vol7 Sulement ovember htt//wwwjosorgcn 006 b o Journal o Sotware All rights reserved Tel/Fa Recovering Suraces rom the Gauss Ma HU Mao-Lin XIE Shi-Peng The Laborator o Intelligent Comuting and Signal Processing Anhui Universit Heei 009 China School o Mathematics and Scientiic Comuting Anhui Universit Heei 009 China Corresonding author Phn hml@ahueducn Hu ML Xie SP Recovering suraces rom the Gauss ma Journal o Sotware 0067Sul0 htt//wwwjosorgcn/ /7/shtm Abstract This aer studies D surace integration rom novel angle The authors consider the construction to the multile surace atches not one surace rom the Gauss ma The algorithm takes as its inut a D ield o surace normal estimates delivered or instance b a shae-rom-shading or shae-rom-teture rocedure The authors disintegrate the Gauss ma into two unctions b the sherical coordinates and then borrow the ideas rom routine image rocessing theor to ilter the two unctions and to segment the sace surace into several subsurace at last the authors use the integrabilit to recover the subsurace individuall The method onl eloits the general techniues in image rocessing but can sul better results than the revious researches which are onl based on one unction model eseciall in the reservence the edges between dierent suraces The method is evaluated on snthetic and real data delivered b a shae-rom-shading algorithm The aroach rovides an actuall wa to use the normal mas o the surace Ke words Gauss ma; surace recovering; Green ormula; shae-rom-shading ; ; Green ; ;Green ; Suorted b the Foundation o Intelligence Project o Higher Education o Anhui China ; the Innovative Research Team o Project in Anhui Universit o China Received ; Acceted

2 Journal o Sotware Vol7 Sulement ovember 006 MRI CT ; ; Delauna [7] [] BrechbÜller [89] [0] Horn Brooks [7] KimmelBruckstein Siddii [] Frankot Chellaa Leclerc Bobick [45] Tsai Shah [6] Bichsel Pentland [7] [8] [9] Green 4

3 T cosφ cosθ sinφ cosθ sinθ T 0 φ < π π / θ < π / sin cosφ θ T Fig Fitting the let igure b one unction blurs the details Fig The segment o and and the disosition o them has three regions and two regions their disosition has si regions 6 H H Lalace Young H

4 4 Journal o Sotware Vol7 Sulement ovember 006 [0] 4 ; ; ;4 T T PDE PDE [] i i i Ω Ω Ω β α d d d d d d Ω i α Tikhonov Euler-Lagrange 0 0 α β α β 4 β α 4 t t α β α β Green

5 5 u u l c L d L c uv v - v u v v u v 0 d 0 u 0 v c Green Worthington Hancock [8] Fig The eeriment on the snthetic data The to row shows the Gauss mas o the intersection o two sheres and the recover surace the ais shows the erormance analsis under random noise the number in the ais eress the densit o noise % % [8]

6 6 Journal o Sotware Vol7 Sulement ovember COIL COIL 90 5%~9% Table Statistics o the recover algorithm % Bichsel Pentland [7] Zhang [9] 8 4~ % 6% Table Statistics or the Bichsel and Pentland method Bichsel Pentland %

7 7 Fig4 To row Original image and obtained normals o surace and the segment rom the Gauss ma; Middle row Two views o the reconstructed surace 4 ; Fig5 To row Original image and obtained normals o surace and the segment rom the Gauss ma; Middle row Two views o the reconstructed surace 5 ;

8 8 Journal o Sotware Vol7 Sulement ovember 006 Fig6 To row Original image and obtained normals o surace and the segment rom the Gauss ma; Middle row Two views o the reconstructed surace 6 ; Fig7 To row Original image and obtained normals o surace and the segment rom the Gauss ma; Middle row Two views o the reconstructed surace 7 ;

9 9 Fig8 Results o the Bichsel and Pentland algorithm 8 Bichsel Pentland 4 Green Edwin Hancock Antonio Robles-Kell

10 0 Journal o Sotware Vol7 Sulement ovember 006 Reerences [] Boissonnat JD Cazals F Smooth surace reconstruction via natural neighbour interolation o distance unctions In ACM Proc o the XVIth Annl Sm in Com Geom Hong Kong 000 [] Deverna F Comuting dierential roerties o -D shaes rom stereoscoic images without -D model RR-04 Sohia Antiolis 994 [] Feldmar J Aache Registration o Smooth Suraces Using Dierential Proerties Berlin Sringer-Verlag 994 [4] Worthington P Hancock E Histogram-Based object recognition using shae rom shading In Proc o the IEEE Con CVPR [5] Yuen P et al Curvature and torsion eature etraction rom -D meshes and multile scales IEEE ProcVis Image Signal Process [6] Kamberov G Kamberova G Recovering suraces rom the restoring orce In ECCV 00 LCS [7] Kimia BB Kimmel R Siddii K Bruckstein AM Shae rom shading Level set roagation and viscosit solutions International Journal o Comuter Vision [8] Metaas D Terzoulos D Dnamic D models with local and global deormations Deormable sueruadrics IEEE PAMI [9] Sara R Bajcs R Fish-Scales Reresenting uzz maniolds In Proc o the Int l Con on Comuter Vision Bomba arosa Publishing House998 [0] Horn BKP Brooks MJ The variational aroach to shae rom shading CVGIP [] Horn BKP Brooks MJ Height and gradient rom shading Int l Journal o Comuter Vision [] Kimmel R Bruckstein AM Tracking level sets b level sets A method or solving the shae rom shading roblem Comuter Vision and Image Understanding [] Frankot RT Chellaa R A method o enorcing integrabilit in shae rom shading algorithms IEEE Trans on Pattern Analsis and Machine Intelligence [4] Leclecrc YG Bobick AF The direct comutation o height rom shading In Proc o the Comuter Vision and Pattern Recognition [5] Tsai PS Shah M Shae rom shading using linear aroimation Image and Vision Comuting [6] Bichsel M Pentland AP A simle algorithm or shae rom shading In Proc o the Comuter Vision and Pattern Recognition [7] Worthington PL Hancock ER ew constraints on data-closeness and needle ma consistenc or shae-rom shading IEEE Trans on Pattern Analsis and Machine Intelligence 999 [8] Forsth DA Ponce J Comuter Vision A Modern Aroach ew York Pearson Education 004 [9] Zhang R Tsai PS Crer JE Shah M Shae rom shading A surver IEEE Trans on Pattern Analsis and Machine Intelligence [0] Sommereld A Mechanics o deormable bodies In Lectures in Theoretical Phsics Vol ew York Academic Press [] Rookwood AP Winget J Tree-Dimensional object reconstruction rom two dimensional images Comuter-Aided Design

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