Image Processing for Physical Data Xuanxuan Su May 31, 2002

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

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

Momentum Image Momentum POLARIZATION AXIS

Real Space Correlation Images Correlation Approach Real Space Correlation Images AVERAGE IMAGE CORRELATION IMAGE POLARIZATION AXIS 1 24 - 15o (= Dj) Angle Sectors 30 - 0.66 eV (= DE) Energy Sectors

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

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

Applied Technologies Clustering Correlation Sampling

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

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

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

Correlation Coefficients A measure of linear association The formula

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

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

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

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

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