research overview piyush kumar. 1.optimization 2.computational geometry 3.computer graphics...
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Research Overview
Piyush Kumar
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1. Optimization
2. Computational Geometry
3. Computer Graphics
4. Pattern Recognition and Machine Learning / Biometrics
5. Robotics
Research Interests
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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
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Covering Problems : An Example
1. Cover a given point set:
1. With k-shapes (k < 5)
Optimization
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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.
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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
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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
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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.
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Cache Oblivious/Ext Memory/Parallel Delaunay
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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.
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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.
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Thanks for your attention
Questions?