Generating Raster DEM from Mass Points via TIN Streaming Jack Snoeyink UNC Chapel Hill Jonathan Shewchuk UC Berkeley Tim Thirion UNC Chapel Hill Martin Isenburg UC Berkeley Yuanxin Liu UNC Chapel Hill raster DEM LIDAR points

Generating DEMs from LIDAR LIDAR points raster DEM resampling interpolatingtriangulating temporary TIN i j

Billions of Points courtesy of billion points 11 GB Neuse-River Basin Elevation map Contour map

Streaming TIN output output final DEM to disk DEM Generation via TIN Streaming small buffer in main memory Streaming Computation of Delaunay Triangulation read points from disk Immediate Rasterization of Streaming TIN store elevation rasters to temporary files (grouped by rows)

Example Result 500,141,313 Points 11 GB ( binary, xyz, doubles )  on a household laptop with two harddisks  50,394 × 30,500 DEM 3 GB ( binary, BIL, 16 bit, 20 ft ) raster DEM LIDAR points  in 67 minutes   64 MB of main memory   270 MB temporary disk space 

Related Work

break data into (overlapping) tiles popular GIS packages – ArcGIS 9.1 ( limit: ~ 25 million points, 1 GB ) – QTModeller 4 ( limit: ~ 50 million points, 1 GB ) – GRASS ( limit: ~ 25 million points, 1 GB ) Rasterizing Billions of Points [ Agarwal et al. ‘06 ]

Inverse Distance Weighting ( IDW ) Natural Neighbors Kriging Splines TIN – linear – quintic … Interpolation Methods

External Memory Quadtree rearrange points on disk into quadtree From Point Cloud to Grid DEM: A Scalable Approach [ Agarwal et al. ‘06 ] process cell – find its neighbors – interpolate all ( i,j ) – write rasters to temporary file sort temporary file on ( i,j ) & write DEM

reorganize computations … not points Our Approach: TIN Streaming – compute TIN in places where all points have already arrived – raster, output & deallocate – keep parts that miss neighbors enhance points with spatial finalization

reorganize computations … not points Our Approach: TIN Streaming enhance points with spatial finalization – compute TIN in places where all points have already arrived – raster, output & deallocate – keep parts that miss neighbors

reorganize computations … not points Our Approach: TIN Streaming – compute TIN in places where all points have already arrived – raster, output & deallocate – keep parts that miss neighbors enhance points with spatial finalization

Delaunay Triangulation a triangulation in which every triangle has an empty circumscribing circle standard algorithm for TIN construction good properties for interpolating points

locate triangle enclosing the point Incremental Point Insertion find and remove all triangles with non- empty circumcircles triangulate by connecting new point [ Lawson ’77 ] [ Bowyer ’81 ] [ Watson ’81 ]

Spatial Finalization Tags inject tags into the point stream that inform when grid cells are free of future points finalized region future points only arrive in these cells use tags to certify triangles as being part of the final triangulation and output them

Streaming TIN Generation output to diskinput from disk small buffer in main memory triangulate point stream seamlessly output completed parts & reuse memory finalization tags small buffer in main memory another small buffer finalization tags Streaming Computation of Delaunay Triangulations [ Isenburg et al. ‘06 ] output (pipe) streaming TIN to rasterizer

input (pipe) streaming TIN from triangulator Rasterization of Streaming TIN input from disk yet another small buffer output final DEM to disk points from single UTM time zone triangles with long edges are killed output to a single row-ordered DEM

Streaming Rasterization Pipeline spfinalize -i points.raw -ospb | spdelaunay –ispb –osmb -ospb | tin2iso –ismb –o dem.bil

The Finalizer (spfinalize)

Spatial Finalization of Points  compute bounding box

Spatial Finalization of Points  compute bounding box  create finalization grid – count number of points per cell

Spatial Finalization of Points  compute bounding box  create finalization grid – count number of points per cell  output finalized points – buffer per grid cell – if full, output points in one randomized chunk followed by finalization tag

Spatial Finalization of Points  compute bounding box  create finalization grid – count number of points per cell  output finalized points – buffer per grid cell – if full, output points in one randomized chunk followed by finalization tag

Spatial Finalization of Points  compute bounding box  create finalization grid – count number of points per cell  output finalized points – buffer per grid cell – if full, output points in one randomized chunk followed by finalization tag

Spatial Finalization of Points  compute bounding box  create finalization grid – count number of points per cell  output finalized points – buffer per grid cell – if full, output points in one randomized chunk followed by finalization tag

Spatial Finalization of Points  compute bounding box  create finalization grid – count number of points per cell  output finalized points – buffer per grid cell – if full, output points in one randomized chunk followed by finalization tag

Spatial Finalization of Points  compute bounding box  create finalization grid – count number of points per cell  output finalized points – buffer per grid cell – if full, output points in one randomized chunk followed by finalization tag

Spatial Finalization of Points  compute bounding box  create finalization grid – count number of points per cell  output finalized points – buffer per grid cell – if full, output points in one randomized chunk followed by finalization tag

Spatial Finalization of Points  compute bounding box  create finalization grid – count number of points per cell  output finalized points – buffer per grid cell – if full, output points in one randomized chunk followed by finalization tag

Exploit the Existing Coherence raw point stream finalized point stream document with finalization tags enhance by releasing chunks of points  benefits of global sort, but cheaper

Exploit the Existing Coherence document with finalization tags enhance by releasing chunks of points  benefits of global sort, but cheaper raw point stream finalized point stream

Unfinalized Region as Quadtree as tags finalize cell after cell, maintain remaining cells in adaptive quadtree  used for efficient overlap tests by the triangulator finalization tags

The Triangulator (spdelaunay)

Modified Incremental Delaunay insert points when reading a finalization tag – find certified triangles – output them to disk or pipe – deallocate data structure

Modified Incremental Delaunay insert points when reading a finalization tag – find certified triangles – output them to disk or pipe – deallocate data structure

Modified Incremental Delaunay insert points when reading a finalization tag – find certified triangles – output them to disk or pipe – deallocate data structure

The Rasterizer (tin2dem)

write raster directly into final DEM on disk write raster to temporary files on disk ( use small buffer, compress when writing buffer ) Rasterizing the Streaming TIN

Results

Neuse- River Basin

Pipeline Details for the 20 ft DEM 6 min 5 MB 512 x 512 grid 10 MB 60,388 triangles 19 MB 444 million rasters 43 min 35 MB 2,249,268 points 270 MB 239 files 8 min 46 MB 128 rows per file

53 hours – 3.4 GHz desktop – 10,000 RPM disks – scratch space: quadtree: ~ 8 GB rasters: ~ 2.5 GB Comparison to ( 20 ft ) [ Agarwal et al. ‘06 ] 67 minutes – 2.1 GHz laptop – 5,400 RPM disks – scratch space: compressed rasters: 270 MB 86 % of CPU time for expensive RST – remaining 7.5 hours constructing quadtree: 1.1 hours finding cell neighbors: 5.6 hours

Demos & Discussion

Demos streaming generation of DEM extraction of elevation contours

final DEM Streaming DEM Rasterization raw points

avoid temporary query structure on disk – data-driven, no gathering of neighbors Main Features order of magnitude faster than method that uses external memory no global sort – don’t fight the data, use existing coherence interleave input & computation & output – 100% CPU usage while interpolating

other interpolation methods – natural neighbors – inverse distance weighting Future Work breaklines / barriers ( e.g. rivers, roads ) – use Constraint Delaunay Triangulation stream other tasks – thinning of points – compression of raw LIDAR data ( useful? ) – hydrological enforcement ( streamable? )

Acknowledgements data – Kevin Yi, Duke support – NSF grants "Collaborative Research: Fundamentals and Algorithms for Streaming Meshes." – NGA award HM – Alfred P. Sloan Research Fellowship

Thank You executables, video, slides, paper, and soon also source code: