Digital Image Processing: A Remote Sensing Perspective
FW5560
Lecture 9
Image Enhancement and Image Transformations
Types of enhancement include:
Reduction
Magnification
Pseudocolor
Spectral Profiles
Contrast Stretching
Integer Image Reduction
Is based on the file coordinates, not
geographic or project coordinates.
Function is a stepwise progression and is
always a factor of 2.
Represents a loss of information
Can be reduction for display purposes or
can be a spatial resolution degradation
Integer Image Magnification
Is based on the file coordinates, not
geographic or project coordinates.
Function is a stepwise progression and
is always a factor of 2.
Represents a duplication of information
Generally only used for display
purposes
Pseudocolor or Density Slicingassigning colors to a gray scale image (1 band) to improve the visual
appearance and interpretability.
21-24 shades of gray vs. thousands of shades of color
Commonly used with thermal imagery
Spectral Profile
Based on linear transects.
Provides a graphic
representation of the
digital values.
Contrast Enhancement
Min-Max
Contrast
Stretch
+1 Standard
Deviation
Contrast
Stretch
Linear Contrast Enhancement:
Minimum- Maximum Contrast Stretch
 BVin  mink
BVout  
 maxk  mink

quantk

where:
- BVin is the original input brightness value
- quantk is the radiometric resolution
- mink is the minimum value in the image,
- maxk is the maximum value in the image, and
- BVout is the output brightness value
Non-linear Contrast Stretching
Piecewise Stretch
 BVin  mink
BVout  
 maxk  mink

quantk

Histogram Equalization
evaluates the individual brightness values in a band of imagery and
assigns approximately an equal number of pixels to each of the userspecified output gray-scale classes
applies the greatest contrast enhancement to the most populated range
of brightness values in the image.
reduces the contrast in the very light or dark parts of the image
associated with the tails of a normally distributed histogram.
Histogram Equalization
Transformation Function, ki for each
individual brightness value
For each brightness value level BVi in the quantk
range of 0 to 7 of the original histogram, a new
cumulative frequency value ki is calculated:
ki 
quant k

i 0
f BVi 
n
where the summation counts the frequency of pixels
in the image with brightness values equal to or less
than BVi, and n is the total number of pixels in the
entire scene (4,096 in this example).
Statistics of How a a 64 x 64 Hypothetical Image with
Brightness Values from 0 to 7 is Histogram Equalized
Gaussian Stretch
Fitting the histogram to a normal or Gaussian histogram
Image Transformations
Operation that re-expresses the information content of an image
Desired result of transformation- generate an image the may well
have properties that make it more suited to a particular purpose
than the original data
Commonly used transformationsArithmetic operations
Principal Components
Vegetation Indices
Tasselled Cap
Principal Components Analysis (PCA)
transformation of the raw remote sensor data using PCA will result in
new principal component images that may be more interpretable than
the original data.
May also be used to compress the information content of a number of
bands of imagery (e.g., seven Thematic Mapper bands) into just two or
three transformed principal component images.
The ability to reduce the dimensionality (i.e., the number of bands in the
dataset that must be analyzed to produce usable results) from n to two or
three bands is an important economic consideration
The spatial relationship between the first two principal components:
(a) Scatter-plot of data points collected from two remotely bands labeled
X1 and X2 with the means of the distribution labeled µ1 and µ2.
(b) A new coordinate system is created by shifting the axes to an X
system. The values for the new data points are found by the relationship
X1 = X1 – µ1 and X2 = X2 – µ2. This is a Translation
(c) The X axis system is then rotated about its origin (µ1, µ2) so that PC1
is projected through the semi-major axis of the distribution of points and
the variance of PC1 is a maximum. PC2 must be perpendicular to PC1 or
orthogonal. The PC axes are the principal components of this twodimensional data . This is a Rotation
The n  n covariance matrix, Cov, of the n-dimensional remote sensing
data set to be transformed is computed. Use of the covariance matrix
results in an unstandardized PCA, whereas use of the correlation matrix
results in a standardized PCA.