Displaying Hyperspectral Images on RGB Displays

Report
Displaying
Hyperspectral Images
on RGB Displays
Victoria Kogan
November 2012
This presentation was prepared for
a seminar on hyperspectral images,
Computer Science Department,
University of Haifa, Israel
Agenda
Introduction
Comprehensive Representation
Algorithms
1BT Based Band Selection
Principal Components Analysis (PCA)
Spectral Weighting Envelopes
Misc
Data Scaling and Effective Gammut
Adapting to Data SNR
Projections with Additional Info
Introduction
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Hyperspectral and multispectral images may
contain hundreds of image bands.
Much analysis of hyperspectral imagery is
performed by software packages
The data should be presented in a comprehensive
way for human users so they will be able to make
decisions
The dimensionality of the image bands must be
reduced to three bands (or less) to display on a
standard tristimulus display.
Comprehensive Representation (1)
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Summarization: Accurately
summarizes all or some of
the original data based on the
need.
Consistency: Recognition
across images in terms of
color.
Natural palette: Creating a
natural palette of colors,
producing preattentive colors
when appropriate but not
creating noninformative
distractions
Computational ease: Real
time usage or interactivity
Comprehensive Representation (2)

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Appropriate pre-attentive features: The visualization
minimizes pre-attentive features of the image that
distract the viewer without reason.
Generalizability: The visualization method workswith N
bands, for a wide range of values of N, and where N
could vary for spectral zooming, or for a change of
instrument.
Edge representation: Edges in the original
hyperspectral image are represented faithfully in the
visualization.
Comprehensive Representation (3)
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Equal-energy white point: A data vector with the
same value for each component appears gray. At the
extremes, a value of zero for all components maps to
black, and the maximum value for all components
maps to the white point of the display.
Equal luma rendering: An equal brightness is one
way to specify that all data components are given
equal emphasis in the display
1BT Based Band Selection

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Method uses the one-bit transform of hyperspectral
image bands to select three suitable bands for RGB
display.
1BT method was initially used for motion detection
1BT obtains well structured hyperspectral image bands
suitable for the color display of available information
Low complexity, very suitable for hardware
implementation
Applying 1BT

A 17×17 sized multi band-pass
filter kernel is defined by

Apply the kernel above to each hyperspectral band
Compare the result against the original image band
using

where IF(i,j) is the filtered form of the image frame
I(i,j).
Measure of Band Characteristics

The spatial bit transitions in 1BTs (changes from 1 to
0, and vice-versa) are counted and the total number of
transitions in horizontal and vertical directions of each
band is used as a measure of structure.
Obtaining Well-Structured Bands
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Image bands are regarded to be wellstructured
and retained if their A(l) values are below a
local threshold T(l) (moving average)
The local thresholding approach ensures that
more informative bands in local neighborhoods
are selected, discarding less informative bands.
The threshold can be defined by T(l) = a×t(l)
where a is a constant used as threshold
weighting factor to allow flexibility in the number
of retained bands.
Selecting Three Bands for Color
Display
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The three image bands that are the least alike are
selected.
Initially the two least similar bands are selected. The
two bands that give that highest total EX-OR result will
have the largest difference and are selected as the
two least similar well-structured image bands.
The third band is selected as the band which is again
least alike to the already selected two bands. For this
purpose the total sum of the EX-OR results of the
remaining bands with the first and second selected
bands are added up, and the band giving the largest
sum is selected.
Principal Component Analysis
(PCA)

The PCA employs the statistic properties of
hyperspectral bands to examine band dependency
or correlation
PCA – Data Processing
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See Rita Osadchy’s slides on PCA here
An image pixel vector for the PCA algorithm is
calculated as:
Principal Components Analysis
(PCA)
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For an N-band hyperspectral image, the first three principal
components are the three N-dimensional, orthonormal
basis vectors that capture the most data variance; spatial
information is not used.
The N-band image pixels are linearly projected onto these
three N-dimensional basis vectors to create three image
bands. The three bands can be mapped to RGB, HSV, etc.
for display
PCA - Pros
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A standard method for
reducing the
dimensionality
Materials with similar
spectral characteristics
are presented in similar
hues, and basic
classification and
clustering decisions can
be made by the
observer
PCA - Cons
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Very saturated regions.
The PCA bands correspond to
the maximum data variance, but
mapping those three bands to
R,G, and B does not necessarily
yield maximum human visual
discriminability.
Colors ‘pop-out’ and draw
attention. Since PCA maps
colors without a fixed semantic
meaning, bright saturated color
regions can be distracting.
High computational complexity.
Spectral Weighting Envelopes

Consider an original N-band image, where λn [i, j]
denotes the value of the nth hyperspectral of the ith row
and jth column pixel, where n = 1, . . . , N. Let rn, gn, and
bn for n = 1, . . . , N be weights on the nth spectral band.
Then the proposed visualizations are linear integrations
of the form:
Spectral Weighting Envelopes
R, G, and B to be fixed linear integrations
of the original hyperspectral image
weighted by three different spectral
envelopes.
 Focus on useful fixed spectral envelopes
in order to satisfy the consistency goal
for representing hyperspectral images

Stretched CMF Basis
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CIE 1964 color matching functions transformed to the
sRGB color space normalized and stretched across the
available wavelengths
Stretched CMF Basis - Discussion
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The middle data
components are more
emphasized than those at
the end in terms of
luminance and saturation
The change of hue across
the spectrum is uneven
Can lead to colors that are
outside of the sRGB
gamut, such as negative
sRGB values.
Stretched CMF Basis Example
PCA Example
•
•
The legend for monochromatic spectra is
calculated basing on a specific image
Display mapping: (P1, P2, P3) → (R, G, B).
Envelopes Based on Linear
Functions
Envelopes based on piecewise linear functions
provide more even hue changes as the spectrum
varies, particularly at the extremes of the spectral
range
Unwrapped Cosine Basis
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Strong changes in luma across the data
components
The hue of the basis colors does not change at a
constant rate over the data components
Constant-Luma Disc Basis Cons
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Colors are equally saturated, but only a few hues (cyans
and reds) are fully saturated, while greens and purples
are undersaturated at this luma value.
Interpretability is decreased because the endpoint colors
are nearly identical.
Constant-Luma Border Basis
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Maintaining a balance between the equal chromatic
differences and the best use of the sRGB gamut
Data points with the maximum value for each
component are rendered as offwhite
This basis has similar strengths as the constant-luma
disc, but has distinct endpoint colors.
Data Scaling and Effective Gamut

In order to fit the available gamut, it is necessary to
rescale the input data in a consistent way. A raw data
vector z is normalized as follows to create the
normalized vector x that is then linearly projected:

If the data is Kronecker data points, then it may be
desirable to scale the input data to be larger by
decreasing k.
Adapting Bases to Data SNR
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In many applications the lowest SNR bands are
thrown out as they contain little usable signal
Instead, reweight a basis, adjusting the luminance and
the chrominance changes to increase monotonically
with SNR.
Start with a basis that yields equal luminance and
equal local chromatic differences, such as the
constant-luma border basis.
Given original basis functions r, g, and b, the
reweighted basis functions for each component are
given by Ar, Ag, and Ab, where A is a reweighting
matrix formed from the SNR values for each
component.
Constructing a Reweighting
Matrix
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The following constraints are used to construct A.
1. The sum of the ith row of A is equal to the SNR of the ith
component.
2. The sum of each column of A is 1.
3. All values in A are nonnegative.
4. All the nonzero values of A are arranged on a
nonbacktracking path from the top left to bottom right.
The matrix A is built from the SNR vector row by row. For each
row, begin at the leftmost column of A which does not yet sum to
one, and add to it until the column sums to one or until the row
sum is equal to the SNR for that component. If the SNR for that
row is not exhausted but the column sums to one, then add to
the next element in that row.
The result is an SNR-optimized basis with the same total sum for
the RGB channels, but which has greater brightness and greater
chromatic differences for components with high SNR.
SNR Adaptation Examples
Color Projections With More
Info.
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Combine a color projection of a hyperspectral image
with probabilistic information about the class of
material for each pix
pc - the probability that a hyperspectral vector x is in
material class c
Generate an overlay color m for the hyperspectral
pixel x that is x’s expected color given the probabilistic
class memberships
For each pixel x, combine its overlay color m with the
pixel’s color projection color s, to create a final display
color for each pixel f, where
Probabilistic Overlay Method
Example
References
Design Goals and Solutions for Display of
Hyperspectral Images
Nathaniel P. Jacobson, and Maya R. Gupta
IEEE Trans. On Geoscience and Remote Sensing, Vol
43(11), 2005
http://idl.ee.washington.edu/publications/grspaperJaco
bsonGupta.pdf
Display of Hyperspectral Imagery by Spectral
Weighting Envelopes,
Nathaniel P. Jacobson and Maya R. Gupta,
Proceedings of the IEEE Intl. Conf. on Image
Processing, pp. 622-625,2005.
http://idl.ee.washington.edu/publications/icip05Jacobso
nGupta.pdf
Linear Fusion of Image Sets for Display
Nathaniel P. Jacobson, Maya R. Gupta and Jeffrey
Cole
IEEE Trans. On Geoscience and Remote Sensing, Vol
45(10), 2007
http://www.umbc.edu/rssipl/people/jwang/citation_4.pdf
Color Display for Hyperspectral Imagery
Qian Du, Shangshu Cai and Robert J. Moorhead,
IEEE Trans. On Geoscience and Remote Sensing, Vol
46(6), 2008
http://www.ece.msstate.edu/~du/TGRS-VIS2.pdf
A Low-Complexity Approach for Color Display of
Hyperspectral Remote-Sensing Images Using
OneBit Transform Based Band Selection
Begüm Demir, Anıl Çelebi, and Sarp Ertürk
http://kulis.kocaeli.edu.tr/pub/tgrs08_hsidisplay.pdf
Dimensionality Reduction for Useful Display of
Hyperspectral Images
J. Cole
http://jeffcole.org/academics/image_display/image_dis
play.pdf

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