Post on 05-Apr-2018
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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