COMP37111 Advanced Computer Graphics 4: Model Acquisition - 2 - - PDF document
COMP37111 Toby Howard COMP37111 Advanced Computer Graphics 4: Model Acquisition - 2 toby.howard@manchester.ac.uk 1 Surface fitting using triangulation The raw range data is triangulated , to form an approximate surface We need
toby.howard@manchester.ac.uk
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§ We need a tolerance, so unrelated distant points are not connected § This leads to holes, but holes can be filled (see later)
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§ The raw range data is triangulated, to form an approximate surface
This point is too far away to join in
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§ We can guess a simple algorithm to triangulate this: § But what about this point set (more likely):
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0.001565 26.307560 151.121063 91.730026 106.553444 43.791836 9.408923 135.772949 135.859283 186.938583 76.700417 103.883278 166.193069 6.914422 10.692327 105.940041 134.229874 1.539637 76.683128 13.368447 83.497200 137.354538 117.795326 186.087296 169.233383 105.385757 18.392979 130.783798 83.199867 140.238113 182.064163 152.439606 52.490597 9.492903 147.216385 65.646843 126.527718 151.282089 198.207474 73.067734 49.407776 196.510056 144.532089 150.671173 130.303711 14.537176 126.326942 176.941437 54.541992 87.282280 153.298950 95.546356 47.554886 54.981369 71.852997 33.301441 97.303474 179.531250 181.841629 12.112865 180.930618 100.904587 103.258392 63.806587 197.328430 98.795334 53.228905 18.146580 189.552856 14.749815 100.141418 76.828430 55.416359 182.763489 105.949471 92.889168 188.195984 10.016797 152.302856 154.040909 165.563461 25.073074 3.173540 137.691055 173.649429 125.908684 147.244904 145.082397 199.891586 177.714447 46.638973 61.264366 70.203049 102.654739 118.222717 169.196304 82.416153 168.302124 53.863453 83.078918 107.460800 93.583473
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a Delaunay edge a Delaunay edge NOT a Delaunay edge: it’s impossible to draw a circle passing through edge AB which doesn’t enclose any other vertices
A B
§ Following the definition of a Delaunay edge, a triangle T is called a Delaunay triangle IFF its circumcircle does not enclose any
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§ Create a big dummy triangle that surrounds the entire point set. Mark all Pi as “not done”. Then:
find a triangle T which encloses it.
as a vertex.
see if it is Delaunay. If it is, OK. If it isn’t, swap edges around (the fiddly bit, details ignored) until it is.
§ Efficiency of algorithm is crucial for huge datasets
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T1 T Pi T T2 T3 T1 T2 T3
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… compared to some random triangulations:
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§ In many cases we have too much data § Space complexity § Time complexity § Difficult to render in real-time § So we simplify the mesh by removing vertices, but preserving shape § Many methods have been developed, still ongoing field of research § The following example uses “Quadratic Edge Collapse” – see “Surface Simplification Using Quadratic Error Metrics, http://www1.cs.columbia.edu/~cs4162/html05s/garland97.pdf (the paper itself is not examinable).
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§ We collapse edges between P1 and P2 into a single point and adjust triangulation § We select candidate points based on an estimation of error – for example || P2-P1 ||, but many different approaches used to quantify error
P1 P2
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P1 P2
§ P1 and P2 are removed and replaced by their mid-point M § The two green triangles will be removed § Edges which previously connected to P1 or P2 will be moved to M (and duplicates removed)
M
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M
§ The resulting mesh retains its convex hull § Changes are localised within the mesh § The key to the success of the method is the computation of a suitable error metric for vertices, for choosing which to collapse
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Example of Simplification Triangles = 25000
FOR YOU TO DO These simplification examples were produced using Meshlab (meshlab.sourceforge.net) Download it and try some simplification experiments with its sample objects
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Example of Simplification Triangles = 12000
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Example of Simplification Triangles = 6000
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Example of Simplification Triangles = 3000
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Example of Simplification Triangles = 500
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Raw range data Approximated surface
29 www.impactstudiostv.com
30 http://www.impactstudiostv.com
31 graphics.stanford.edu/papers/volrange/
§ Most models self-occlude… § … so no single range image can capture a model § Parts of the captured model will be missing § We need to take multiple range images and combine them… how? § Basic approach: § Sets of range data are registered § Data is filtered § Attempt to estimate a new “ideal” surface that is “closest” to as many range points as possible § Remesh “ideal” surface into triangles § Paper: “Zippered Polygon Meshes from Range Images” (required reading, examinable)
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§ Stanford University, from 1999 and ongoing
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graphics.stanford.edu/projects/mich/
§ Scan depth resolution = 0.1mm § Scan sample resolution = 0.29mm
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ScanView: graphics.stanford.edu/software/scanview
FOR YOU TO DO: download Scanview and try it
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Client Local interaction with free low-res model Secure server Computes high-res rendering on demand Client requests high-res rendering, sending parameters Server returns high-res rendering as a texture internet internet
§ A different method for dealing with holes caused by occlusions is “volumetric diffusion” § http://graphics.stanford.edu/papers/holefill-3dpvt02
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Photograph of original Acquired model: 1mm resolution, 4m polygons
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§ Complex objects require multiple scans which must be aligned and connected § Occlusions cause holes which must be “intelligently” filled § Data sets are huge § Polygon soup or structured model?
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