1. Research Overview Piyush Kumar

2. 1.Optimization 2.Computational Geometry 3.Computer Graphics 4.Pattern Recognition and Machine Learning / Biometrics 5.Robotics Research Interests

3. Covering Problems 1.Cover a given point set: 1.With k-shapes (k < 5) 2.With smallest ball 3.With smallest 1-ellipsoid 2.Cover a set of balls/ellipsoids 1.With smallest ball/ellipsoid Optimization

4. Covering Problems : An Example 1.Cover a given point set: 1.With k-shapes (k < 5) Optimization

5. Covering Problems: Motivation Clustering for various applications 1.3D Terrain Covers/ Surveillance 2.Automatic Surface estimation 3.Antenna/Other placement problems. 4.Operations Research 5.Signal/Image Processing. 6.Bio-Metrics / Bio-Informatics 7.Compression.

6. Computational Geometry: Surface Estimation 1.LIDAR / Laser Range scanner Data Problems 1.How to do surface estimation 2.How to handle massive data sizes 3.How to make sense of the data

7. Surface estimation problems 1.Other problems 1.How to handle noise 2.How to use SMP machines for fast processing 3.How to do processing online/dynamically

8. Triangulations Compute Delaunay Triangulations in 2D for massive data sets 1.External Memory 2.Parallel 3.Cache-Oblivious (In Theory) 4.Practical Variant Joint work with E. Ramos. (UIUC) Courtesy D. Eppstein Acknowledgements:  Cobalt: Altix at UIUC (1024p) (NCSA, UIUC)  Gestalt: 4P Opteron at CAVIS.

9. Cache Oblivious/Ext Memory/Parallel Delaunay

10. Biometrics 1.Recognition using hand outlines 2.One of the cheapest biometric solutions 3.Current Work: How to use 3D range scans of faces to do face detection from images.

11. Other Problems 1.Detection of soil type using robot motion 2.Swarm robots (Covering type problems) 3.Cache oblivious and cache aware algorithms 4.Machine learning/Clustering. 5.Face recognition from 3d range scans.

12. Thanks for your attention Questions?