1. Image Processing for Physical Data
Xuanxuan Su
May 31, 2002

2. Outline Background System Implementation Evaluation
Physical experimental image data
Pre-processing method
Correlation computing
System Implementation
Evaluation

3. Image & Time-of-Flight Spectrometer
Time-Resolved Images
128 x 128 Pixels
730 Hz Digital Acquisition
500,000 – 1,000,000 Frames
Mass-Resolved
Energies & Angular Distributions
Time-Resolved Waveforms
Digital Scope Acquisition
Mass-Resolved
Energies Distributions

4. Momentum Image
Momentum
POLARIZATION
AXIS

5. Real Space Correlation Images
Correlation Approach
Real Space Correlation Images
AVERAGE IMAGE
CORRELATION IMAGE
POLARIZATION
AXIS 1
o (= Dj) Angle Sectors eV (= DE) Energy Sectors

6. Image Data For each experiment 500,000 ~ 1,000,000 frames
8G ~ 16G uncompressed data
5M ~ 150M compressed data
Pixels are sparse

7. Challenge Previous work Low accuracy Computational resource is limited
Data compression
Correlation of sectors
Low accuracy
Computational resource is limited
Large data set can’t fit in memory
More than 3 hours for 600 sectors correlation

8. Applied Technologies
Clustering
Correlation
Sampling

9. Clustering Pre-processing method
Represent a cluster of points by their centroid
Can be used to achieve data compression 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

10. K-Means Clustering Algorithm Simply and fast
Randomly choose k cluster centers
Assign each data to the closest cluster center
Recompute the cluster centers using the current cluster member until a stop criteria is met
Simply and fast
Sensitive to initial seed selection

11. Incremental Clustering
Algorithm:
Assign the first data item to a cluster
For next data item, either assign it to one existing cluster or a new cluster
Repeat step 2 until all the data items are clustered
Advantage
Small space requirement
Non-iterative

12. Correlation Coefficients
A measure of linear association
The formula

13. Sampling Calculate correlation Estimate the accuracy of approximation
Image sampling
Problem: the number of samples that have a good estimation of correlation
Estimate the accuracy of approximation
Useful for evaluation
Pixels sampling

14. System Implementation
Pre-processing
Incremental clustering method Spotlize
Pre-define the radius of clusters

15. System Implementation (con’t)
Progressive Correlation Computing
Pyramidal grids
Algorithm
Compute the correlation in a low resolution, find the most correlated grids
Divide the corresponding grids into smaller grids
Repeat step 1 & 2 until a stop criteria is met
Increase accuracy
have to multi-scan data set

16. Evaluation Run time Accuracy of correlation
Spotlized images vs. original images
Choose sample pixels

17. Future Work Avoid multi-scan data set
Find a number of sampling images so that the data can fit in memory and have high accuracy
Investigate other association measure methods