3D Photography Applications Obtaining 3D shape (and sometimes color) of real-world objects • Determine whether manufactured parts are within tolerances • Plan surgery on computer model, visualize in real time • Quality control during building Based on slides from Szymon Rusinkiewicz and Roberto Scopigno Sculpture Scanning Graphics Research • Availability of complex • The Pietà Project datasets drives research IBM Research (you wouldn’t believe how the poor bunny has been treated…) • The Digital Michelangelo Project Stanford University • The Great Buddha Project University of Tokyo Why Scan Sculptures? Why Scan Sculptures? • Interesting geometry • Challenging • Introduce scanning to new – High detail, large areas disciplines – Large data sets – Art: studying working techniques – Field conditions – Art history – Pushing hardware, software technology – Cultural heritage preservation – Archeology • But not too challenging • High-visibility projects – Simple topology – Possible to scan most of surface 1 1
Issues Addressed The Digital Michelangelo Project • Resolution • Coverage – Theoretical: limits of scanning technologies – Practical: physical access, time • Type of data – High-res 3D data vs. coarse 3D + normal maps – Influenced by eventual application • Intellectual Property Goals Why Capture Chisel Marks? • Scan 10 sculptures by Michelangelo • High-resolution (“quarter-millimeter”) geometry ? ? • Side projects: architectural scanning ugnetto ugnetto ugnetto (Accademia and Medici chapel), scanning fragments of Forma Urbis Romae Atlas Atlas Why Capture Chisel Marks? Scanner Design 4 motorized axes 4 motorized axes 2 mm 2 mm Day (Medici Chapel) Day (Medici Chapel) laser, range camera, laser, range camera, white light, and color camera white light, and color camera 2 2
Scanning a Large Object • Uncalibrated motions • Calibrated motions – vertical translation – pitch (yellow) – rolling the gantry – pan (blue) Single Scan of St. Matthew – horizontal translation (orange) – remounting the scan head 1 mm 1 mm 1 mm Statistics About the Scan of David Head of Michelangelo’s David • 480 individually aimed scans • 0.3 mm sample spacing • 2 billion polygons • 7,000 color images • 32 gigabytes • 30 nights of scanning • 22 people Photograph Photograph 1.0 mm computer model 1.0 mm computer model Side project: Forma Urbis Romae Fragment The Forma Urbis Romae side face 3 3
IBM’s Pietà Project • Michelangelo’s “Florentine Pietà” • Late work (1550s) • Partially destroyed by Michelangelo, recreated by his student • Currently in the Museo dell’Opera del Duomo in Florence Results The Great Buddha Project • Great Buddha of Kamakura • Original made of wood, completed 1243 • Covered in bronze and gold leaf, 1267 • Approx. 15 m tall • Goal: preservation of cultural heritage 3D Scanning The 3D scanning pipeline • 3D Scanning : The acquisition of a – Acquisition planning single range map is only – Acquisition of multiple range maps an intermediate single – Range maps Editing step of the overall acquisition session – Registration of range maps – Merge of range maps – Mesh Editing – Geometry simplification – Capturing appearance – Archival and data conversion 4 4
NP-hard problem � find good heuristics & approximate solutions Acquisition Planning Acquisition Planning Definition of the optimal acquisition patchwork : • Given: scanner & object characteristics • Obtain an optimal & complete coverage (all object surface covered): – Minimal number of scans – Sufficient inter-scan overlap (registration) – Where each scan should be: • shot from a view direction nearly orthogonal to the surface • physically feasible (consider potential collisions with the object/environment, self-occlusions) Selecting the set of views is not easy • NP-hard problem � find good heuristics & approximate solutions Registration and Merging Registration • Independent scans are defined in coordinate spaces which depend on the spatial locations of the scanning unit and the object at acquisition time. They have to be registered (roto- translation) to lie in the same space First: Register all range maps • Standard approach: Second: Merge in a single 1. initial manual placement triangulated surface with no 2. Iterative Closest Point redundancy (ICP) [Besl92,CheMed92] Manuel Pairwise Registration Pairwise Registration • An approximation to the Mode 1) The user distance between range manually places a scans is: range map over – another (interactive E = S || T qi – pi ||2 manipulation) • where the qi are samples from scan Q and the pi are the corresponding points of Mode 2) Selection scan P . of multiple pairs of matching points 5 5
Iterative Closet Point (ICP) [Besl+92] Registration, many more issues Pairwise Sequential vs. Global [Pulli99] • If the correspondences are known a priori, Using Color in registration [Bernardini00] then there is a closed form solution for T . However, the correspondences are not known in advance. • Iterative closest point (ICP) [Besl+92] – Start from an approximate registration – Repeat • Identify corresponding points (minimal distance) • Compute and apply the optimal rigid motion T Image by F. Bernardini – Until registration error E is small So far… Consolidation • Mainly engineering problems, Desirable properties for surface reconstruction: planning, scanning and – No restriction on topological type registration. – Representation of range uncertainty • Now, once registered, all scans – Utilization of all range data (integrate over overlapped regions) have to be fused in a single, – Incremental and order independent updating continuous, hole-free mesh – Time and space efficiency • In other words – surface – Robustness (to noise) reconstruction… – Ability to fill holes in the reconstruction • Or, surface consolidation Filling Holes [Sharf+04] Filling Holes [Sharf+04] Holes… Smooth Interpolation Intelligent… 6 6
Methods that construct triangle meshes directly : Methods that construct implicit functions: Reconstruction from point clouds From range maps • Local Delaunay triangulations [Boissonat84] • Alpha shapes [Edelsbrunner+92] • Signed distances to nearest surface [Hilton+96] • Crust algorithm [Amenta+98] • Signed distances to sensor + space carving [Curless+96] • Delaunay-based sculpturing [Attene+00] • Marching Intersections [Rocchini+00] • Ball Pivoting [Bernardini+99] • Localized Delaunay [Gopi+00] From point clouds Reconstruction from range maps • Voxel-based signed distance functions [Hoppe+92] • Point Set Surfaces [Levin, Alexa, Flieshman+ 01] • Radial Basis Functions [Carr+01] • Re-triangulation in projection plane [Soucy+92] • Partition of Unity [Ohtake+03] • Zippering in 3D [Turk+94] Range images Single Laser Range Image • Converting a range image into a range surface is easy. • Use a tessellation threshold A single scan is a grid: Connect adjacent samples when z-difference is small. So, what’s the problem? Zippering [Turk+94] • Redundancy removal and zippering scan, register, and apply some zippering? Image by Brian Curless, Sig’2000 Course Notes 7 7
Sampling quality and reconstruction issues Sampling quality and reconstruction issues Interpolating? Ideal Sampling Or noisy sampling? Uneven Sampling or holes? Sampling quality and reconstruction issues Sampling quality and reconstruction issues Solid Object with small features? Solid Object with thin section? Sampling quality and reconstruction issues Methods that construct implicit functions: From range maps Smooth or Sharp features? • Signed distances to nearest surface [Hilton+96] • Signed distances to sensor + space carving [Curless+96] • Marching Intersections [Rocchini+00] From point clouds • Voxel-based signed distance functions [Hoppe+92] • Point Set Surfaces [Levin, Alexa, Flieshman+ 01] • Radial Basis Functions [Carr+01] • Partition of Unity [Ohtake+03] 8 8
Implicit Surface Representation Distance Field Represented as a function f(x,y,z) = 0 • Define an implicit function D(p) = distance to the surface at point p Volumetric representation > 0 outside the surface One important implicit function is the distance < 0 inside the surface function = 0 on the surface Use interpolation to compute distance at an arbitrary point Distance Field Marching Cube Tangent plane and signed distance estimation Results of Three Phases[Hoppe92] • Compute n i that minimizes ( ) ∑ − ⋅ p x n j i i p j Points Phase 1 Phase 2 Where ( ) p ∈ Nbhd x j i Phase 3 Assume that if points are close then normals are nearly parallel 9 9
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