principle component analysis (pca)

7/31/2019 Principle Component Analysis (PCA)

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Principle Component Analysis(PCA)

A mechanism used to make the

analysis of remote sensing datasimpler.


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PCA reduces the dimensionality of the data

keeping the (what we hope) is the

most significant parts of the data simultaneously filters out noise

It is a way of identifying patterns in

data, and expressing the data in such away as to highlight their similarities anddifferences


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PCA contd.hyperspace graphing is not available

to visualize data

the 3 first principle components makea powerful tool for identifying patternsin the data

This is can be seen as a tool for imagecompression with no loss of information


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History Early image processing systems were

limited in their processing capacity it

was important to reduce the number ofcalculations required to process animage.

Currently, useful as tool to explore thevariability of an image

Also used in facial recognition software


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How it works The data, though clumped around

several central points in that

hyperspace, will generally tend towardsone direction.

If one were to draw a solid line that

best describes that direction, then thatline is the first principle component(PC).


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Eigenvectors and Eigenvalues Each eigenvector represents a principle

component.

The first Principle Component is defined asthe eigenvector with the highestcorresponding eigenvalue.

The individual eigenvalues indicate thevariance they capture - the higher the value,the more variance they have captured.


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Any variation that is not captured by

that first PC is captured by subsequentorthogonal eigenvectors.

When the data is plotted in this manner

they are said to be plotted in PrincipleComponent-space(PC-space)


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Data means WHAT? The first PC represents the greatest

variability in the data

so?

How does the interpreter convertvariability into information?


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Image Registration and

Rectification Removing spatial errors in an image

Systematic errors

(skew)

Curvature of the earth

General instrument correction e.g. scan

line overlap


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Projection and Random errors In order to get RS data into a format

compatible with the GIS, a projection

needs to be specified (the alternative is to do an image

based GIS that ignores real world

coordinates)


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Ground Control Points (GCPs) Use GCPs that are well distributed

across the image

Features visible on the image thatcorrespond to known locations on theground (or on a map)

GCP1- XY (UTM?)

GCP1-row/column


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Affine Coordinate Transformation X=a0+a1X+a2Y

Y = b0+b1X+b2Y

Where x and y are the row/ columnlocations

And X,Y are the ground coordinates an and bn are transformation

parameters


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Page 2 (of 3)of the affinecoordinatetransformationexample in

Jensen 1986


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Bilinear Interpolation Weighted average of the four nearest

pixels (2 left-right and 2 up-down)

weighted average of a 2X2 kernel


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Cubic Convolution or Cubic spline Cubic spline of 16 closest neighbors

a weighted average of from a 4X4

kernel


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How well do they work? Every manipulation of a grid changes

the data in every grid cell

The accuracy of the original data ? The accuracy of the new cells ?

Loss of information ?

The only real test of accuracy is howaccurately INFORMATION is supplied bythe image.


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Image Filtering Noise removal

Smoothing

Edge enhancement

Most image enhancement operationswork the same way

A moving window


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The kernel or window The factors in the moving window are

specified based on the desired result

The 3X3 array moves across the imageand converts the value of the centerpixel based on the operations specified

by the surrounding pixels


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A high pass filter or kernel

Di ti l Ed E h t


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Directional Edge Enhancementexamples

principle component analysis (pca)

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