Meshless wavelets and their application to terrain modeling

1. Meshless wavelets and their application to terrain modeling A DARPA GEO* project Jack Snoeyink, Leonard McMillan, Marc Pollefeys, Wei Wang (UNC-CH) Charles Chui, Wenjie He (UMSL)

2. Schedule 9:00 PIs He, Wang, McMillan, Snoeyink discuss priorities and projects Aim: a clear idea of who is producing what demos 10:30 Joined by students for brainstorming on projects Aim: get the students on board, and have some fun doing research rather than spending all our time on politics and administrivia. 12:00 break for dept meeting; students to take Wenjie for lunch 2:00 - 3:00 PIs meet with Charles joining on the phone (11am his time) Aim: any clarification of how the mathematical development can integrate with development of prototypes & demos 3:15-3:30 Wenjie departs for 5:30 flight.

3. GEO* history Jan 2000 Randolph Franklin joins NSF, negotiates with DARPA program directors Doug Cochran & Carey Schwartz GIS projects May 2001 NSF CARGO announced ($3M DARPA, $4M NSF) Sep 2001 DARPA consultant Yehuda Avniel contacts us about possible GEO* program www.darpa.mil/dso/future/geo/index.htm Oct 2001 Yehuda visits triangle team (Arge, Edelsbrunner, Harer, Agarwal, Snoeyink, Band, Mitasova, …) http://www.cs.unc.edu/Research/compgeom/DARPA_slides/ Jan 2002 White paper on LIDAR & Morse theory sent to Yehuda Mar 2002 Pitch by Yehuda to DARPA; more detail requested Apr 2002 DARPA directorate ceases work on GEO*; puts only 250K into CARGO Oct 2002 Doug Cochran contacts triangle team; nothing happens Mar 2003 Visit by Doug Cochran leads to participation in protein design project… Apr 2004 Renewed call for GEO* with PD Carey Schwartz http://www.darpa.mil/baa/baa04-12mod2.htm Apr 2004 UNC-UMSL team formed, & white paper submitted May 2004 Invitation to submit proposal on streaming meshes Jun 2004 Meshless wavelet proposal submitted Nov 2004 Approval for GEO* program; NGA administering Feb 2005 Anticipated beginning of funding Mar 2005 Anticipated kickoff workshop

4. What is GEOSPATIAL REPRESENTATION AND ANALYSIS (GEO*)? From www.darpa.mil/baa/baa04-12mod2.htm • Emphasizes the development of math and algorithms that enable parsimonious representations coupled to end user applications : image to DEM, targeting, route planning, and motion mobility simulations. • Digital terrain is a geometric surface modeled to specified precision and accuracy. Need to support applications with variable spatial resolution and spatial accuracy from a single common database, conflating and deflating as new data is obtained. • Schemes to compress the data, including lossless and lossy compression, are desirable provided they preserve the utility of the underlying data for calculating gradients used in visibility calculations, motion mobility models, route planning, and radar placements. • A common primitive : registration of imagery obtained from a sensor to the underlying digital elevation model and the direct construction of a digital elevation model from in theater imaging sensors. Sensor geometry Incompletely known, and methods may not be invariant to the spatial quantization of the image. The effect of errors must be quantified.

5. GEO*’s stated objectives • New representations for surface and geodetic data that support conflation and deflation (100X improvement in storage relative to JPEG no additional loss of precision in an end user application. Must support lossy compression that simultaneously preserves height and gradient); • Local vs. global representations of geodetic data : reduction of 100x relative to spherical harmonic expansions; • New mathematical methods with analysis tools for automated registration of images to images that enable image stabilization, frame integration, passive moving target indication, and three dimensional model building with appropriate metrics and accuracy. The associated analysis should provide quantified errors. New mathematical methods with analysis tools for automated registration of images to digital point position databases. • New representations for rapid storage retrieval that enable techniques that would allow Retrieval by Image in the absence of text annotation where one of the images has been subjected to a perspective or projective transform as well as contrast or illumination changes. • New representations for rapid search and retrieval of lines of iso-height that are compatible with multi-resolution methods and require only a single pass through the stored database. (All of the above at 60 Hz with images that are 512 x 512 with 12 bits/pixel or 0.3 meter post spacing for DEM);

6. Other players Carey’s email went to: • Level Set Systems (Stan Osher) terrain compression • Dr. Lenny Rudin, co-founder (with Stan Osher) & CEO of Cognitech • Randolph Franklin, RPI EE (White paper was, “Geologically correct terrain data structures”) • Ron Devore, approx theory, S. Carolina • Gary Hewer, Navy appl. mathematician • manj@mayachitra.com?

7. What did we say we would do? We propose • a new compact representation for geospatial data that is optimized for specific geometric and image queries. • ``meshless'' bivariate wavelets defined over scattered point sets allows a flexible description since the point set can be specified without connectivity and each point's influence is local, while still supporting the multiscale analysis afforded by wavelets. Objectives • complete the theory of bivariate meshless wavelets • point/knot selection algorithms optimized for specific geometric tasks and data queries • demonstration implementation the advantages of our modeling approach.

8. Four phases • mathematics of meshless wavelets and finding key points for applications to include compression, registration, route planning, and visibility. • developing prototypes for these applications on top of the meshless wavelets and key points representations, • Option to develop one or more applications in detail, • Option for additional focused efforts by the PIs to transition technology to an industrial or military partner.

9. Questions to address • What problems? • What demos? • What data? • Who will deliver what?

10. What problems?

11. What data? • Likely to be a problem • Larry Band’s group in Geography • USGS grids • UNC data library