Research Overview

Piyush Kumar

1. Optimization

2. Computational Geometry

3. Computer Graphics

4. Pattern Recognition and Machine Learning / Biometrics

5. Robotics

Research Interests

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

Covering Problems : An Example

1. Cover a given point set:

1. With k-shapes (k < 5)

Optimization

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.

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

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

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.

Cache Oblivious/Ext Memory/Parallel Delaunay

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.

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.

Thanks for your attention

Questions?