Introduction to Multivariate Image Analysis (MIA) · PDF fileMATLAB for Chemometricians Chemometrics I -- PCA Chemometrics II -- Regression and PLS Clustering and Classification Advanced
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Table of Contents
• Intro to 3-way arrays and simple visualizations and
size/shape analyses
• Practical Multivariate Image Analysis (MIA)
• Principal Component Analysis (PCA)
• SIMCA
• Multivariate Curve Resolution (MCR)
• Partial Least Squares Discriminant Analysis (PLSDA)
2
Eigenvector University
Our week long series of courses each spring
• May 10-15, 2015 Seattle, Washington, USA
• 6 full days and 3 evenings
• 15 hands-on courses
• 8 instructors (Eigenvector staff + Rasmus Bro)
• User poster session and group meeting
EigenU Europe
• Oct 5-8, 2015 Hillerød, DENMARK
• 4 full days
• 7 hands-on courses
Training
We offer standard and custom courses on a range of chemometric and
application topics:
Chemometrics Without Equations Series
Chemometrics Without Equations
Advanced Chemometrics Without Equations
Basic Chemometrics Series
Linear Algebra for Chemometricians
MATLAB for Chemometricians
Chemometrics I -- PCA
Chemometrics II -- Regression and PLS
Clustering and Classification
Advanced and Specialty Topics
Advanced Preprocessing
Applied Multiway Analysis
Multivariate Statistical Process Control for PAT
Calibration Model Maintenance
Calibration Transfer and Instrument Standardization
Chemometrics in Mass Spectrometry
Chemometrics in Metabolomics
Classical Least Squares (CLS) Methods
Common Mistakes in Chemometrics
Correlation Spectroscopy
Design of Experiments for QbD
Getting PLS_Toolbox/Solo Models Online
Hierarchical and Optimized Models
Implementing Chemometrics in PAT
Introduction to Multivariate Image Analysis
Modeling Fluorescence EEM Data
MSPC-Multivariate Statistical Process Control
Multi-block, Multi-set, and Data Fusion Methods
Multivariate Curve Resolution
Non-linear Methods for Calibration and Classification
PLS_Toolbox Beyond the Interfaces
Robust Methods
Variable Selection
Bring Your Own Data (BYOD)
And we're always adding more…
Resources
• Hyperspectral Image Analysis, eds. P. Geladi and H. Grahn, Wiley (2007), ISBN 978-0-470-01086-0
• Chemometrics, M.A. Sharaf, D.L. Illman and B.R. Kowalski, Wiley-Interscience (1986) ISBN 0-471-83106-9
• Multivariate Analysis, K.V. Mardia, J.I. Kent and J.M. Bibby, Academic Press, (1979) ISBN 0-12-471252-2
• Multivariate Calibration, H. Martens and T. Næs, John Wiley & Sons Ltd. (1989) ISBN 0-471-90979-3
• Chemometrics: a textbook, D.L. Massart et al., Elsevier (1988) ISBN 0-444-42660-4
• Chemometrics: A Practical Guide, K.R. Beebe, R.J. Pell, M.B. Seasholtz, Wiley (1998) ISBN 0-471-12451-6
• Multivariate Data Analysis In Practice, Kim H. Esbensen, CAMO ASA (2000), ISBN 82-993330-2-4
• A user-friendly guide to Multivariate Calibration and Classification, T. Næs, T. Isaksson, T. Fearn, T. Davies, NIR Publications(2002), ISBN 0-9528666-2-5
• Journal of Chemometrics
• IEEE Trans. on Geosci. and Remote Sensing
• Chemometrics and Intelligent Laboratory Systems
• Analytical Chemistry
• Analytica Chemica Acta
• Applied Spectroscopy
• Critical Reviews in Analytical Chemistry
• Journal of Process Control
• Computers in Chemical Engineering
• Technometrics
• ....
5
Univariate Image• Grey scale
• each pixel is an number defining an
intensity level e.g.,
• integer (0 to 255) unsigned 8-bit
• integer (0 to 4095)
• double (floating point)
100 200 300
100
200
300
400
500
600
y-pixels
x-p
ixel
s MxxMy pixels
provides spatial
information
6
100 200 300
100
200
300
400
500
600
Multivariate Image (3 Variables)
• Red/Green/Blue (RGB) (e.g. JPEG)
• each layer defines color intensity level
• much more information-rich
7
Image Analysis
• Many methods have been developed to examine
the spatial structure w/in an image
• the methods recognize spatial patterns within an image
• based on the light / dark contrast and continuity of regions
• edge detection, image sharpening, wavelets
• particle size distributions, machine vision, medical
applications, security, …
• MIA has been traditionally applied to the spectral
dimension first followed by spatial analysis
• some methods that examine both are appearing
8
Multivariate Image (4-10 Variables)
• Measure at several wavelengths (e.g., Landstat)
bluegreen
redNIR
SWIR-1SWIR-2
thermal
How should we display
a seven variable image?
9
Multivariate Image (4-10 Variables)
• Choose 3 of 7 (Landstat)Montana (blue/SWIR-1/thermal)
100 200 300 400 500
50
100
150
200
250
300
350
400
450
500
100 200 300 400 500
50
100
150
200
250
300
350
400
450
500
Paris (NIR/blue/SWIR-1)*
*contrast enhanced
10
Hyperspectral Image (>10 Variables)
• Spectrum at each pixel
• could be 100-1000s of variables
• often floating point double 10-100s Mbytes
y ν
x
800 900 1000 1100 1200 1300 1400 1500 16000
0.5
1
1.5
Wavelength (nm)
Ab
sorb
ance
each pixel is a spectrum
each voxel is a channel
in the spectrumPixels � Spatial Information
Spectral � Chemical Information
11
File Formats
Inherent Image Formats
• Cameca Ion-Tof BIF/BIF6 Image (BIF,BIF6)
• ENVI Image Format (HDR)
• Lispix Raw Formatted Image (RAW)
• Multi-layer TIFF files (TIFF)
• Physical Electronics RAW Image (RAW)
• Image standard (JPG, TIFF, GIF, BMP, PNG)
Non-Image Formats (add image context after load)
• Text (e.g. CSV)
• Thermo-Galactic SPC (binary)
12
Memory Considerations
• 512 x 512 pixels and 2048 variables
= 536 Million data points
= 4.3 GB memory (double precision)
BEFORE preprocessing!
• Larger images require 64-bit computers with 4GB
or more of memory
13
Multivariate Images
• Data array of dimension three (or more)
• where the first two dimensions are spatial and
• the last dimension(s) is a function of another variable
(e.g, spectroscopy).
• Chemical system(s) of interest include
• microscopic, medical, machine vision, process
monitoring crystallization, stand-off and remote
sensing, …
• vapors, liquids, solids (or combination)
• visible, infra-red, Raman, mass spectroscopy, …
14
Displaying a Multivariate Image (4-10 Variables)
• How to choose the 3 variables?
• In which order should they be displayed?
• Doesn’t choosing ignore potential information in
the remaining variables?
• How could information be extract from the image?
• What happens when we go to more variables? ...
• …. Factor-based techniques
• use the correlation structure to enhance S/N
• really good for hyperspectral
15
Matlab-Based Stand-Alone
PLS_Toolbox SoloModeling & Analysis:
MIA_Toolbox Solo+MIAImage Analysis:
Model_Exporter Solo+Model_ExporterModel Export:
Solo_PredictorModel Application:
� Matlab-Based products provide access to all Graphical User Interfaces (GUIs)
plus command-line scripting and programming functionality
� Stand-Alone products provide access to same GUIs plus basic script operations
without needing Matlab
EVRI Product Outline
Matlab-Based Stand-Alone
PLS_Toolbox SoloModeling & Analysis:
MIA_Toolbox Solo+MIAImage Analysis:
Model_Exporter Solo+Model_ExporterModel Export:
Solo_PredictorModel Application:
Exporting of models is for use in high-frequency or low-resource applications such
as hand-held instruments
Solo_Predictor supports all model types, preprocessing, calibration transfer, and
many other PLS_Toolbox/Solo features
EVRI Product Outline
Map of Eigenvector Software
18
Workspace Browser(Starting Point)
Trend Tool(Visualization)
Plot Controls &
DataSet Editor
Image
ManagerAnalysis(Modeling)
PLS_Toolbox and MIA_Toolbox (in Matlab)
Solo+MIA (Stand-alone)
Particle Analysis
Texture Analysis
Simple Image Analysis Tools
• TrendTool – Univariate Data Investigation
• Analyze multivariate data using simple univariate