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 Slicing

appearance and interpretability.

assigning colors to a gray scale image (1 band) to improve the visual 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

BV

out

  

BV

in

max

k

 min  min

k k

 

quant

k

where:

- BV in

is the original input brightness value

- quant k

is the radiometric resolution

min max k BV out k

is the minimum value in the image, is the maximum value in the image, and is the output brightness value

Non-linear Contrast Stretching Piecewise Stretch

BV

out

  

BV

in

max 

k

 min min

k k

 

quant

k

Histogram Equalization

evaluates the individual brightness values in a band of imagery and

assigns approximately an equal number of pixels to each of the user specified 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,

k i

for each individual brightness value For each brightness value level

BV i

in the

quant k

range of 0 to 7 of the original histogram, a new cumulative frequency value

k i

is calculated:

k

i



quant k i

  0

f

 

i

n

where the summation counts the frequency of pixels in the image with brightness values equal to or less than

BV i

, 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 transformations Arithmetic 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

X

1 and

X

2 with the means of the distribution labeled

µ

1 and

µ

2 .

(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

X

1  =

X

1 –

µ

1 and

X

2  =

X

2 –

µ

2 . This is a Translation  (c) The

X

 axis system is then rotated about its origin (

µ

1 ,

µ

2 ) so that

PC

1 is projected through the semi-major axis of the distribution of points and the variance of

PC

1 is a maximum.

PC

2 must be perpendicular to

PC

1 or orthogonal. The

PC

axes are the principal components of this two dimensional 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

.