Image Display & Enhancement

Lecture 2

Prepared by R. Lathrop 10/99

updated 1/03

Readings:

ERDAS Field Guide 5th ed

Chap 4; Ch 5:137-153;

App A Math Topics: 459-469

Digital Images

• Digital Number (DN) or Brightness Value (BV) - the tonal gray scale expressed as a number, typically 8-bit number (0-255)

• Dimensionality - determined by the number of data layers (bands)

• Measurement Vector of a pixel - is the set of data file values for one pixel in all n bands

Digital Image

0

255

8 bit DN

Multiple spatially co-registered bands, can be displayed singly in B&W or in color composite

Band 1

Band 2

Band 3

Image Notation

• i = row (or line) in the image

• j = column

• k, l = bands of imagery

• Bvijk = BV in row i, column j of band k

• n = total # of pixels in an array

Rows = i = 4

Columns = j = 5

Calculating disk space

[ ( (x * y * b) * n) ] x 1.4 = output file size

where:

y = rows

x = columns

b = number of bytes per pixel

n = number of bands

1.4 adds 30% for pyramid layers and 10% for other info

Digital Image Storage Formats

• Band sequential (BSQ) - each band contained in a separate file

• Band interleaved by line (BIL) - each record in the file contains a scan line (row) of data for one band, with successive bands recorded as successive lines

• Band Interleaved by Pixel (BIP)

Image Display

Computer Display Monitor has 3 color planes: R, G, B

that can display DN’s or BV’s with values between 0-255

3 layers of data can be viewed simultaneously:

1 layer in Red plane

1 layer in Green plane

1 layer in Blue plane

Image Display: RGB color compositing

Red band DN

Blue band DN

Red band DN = 0

Blue band DN = 200

Green band DN

Green band DN = 90

Blue-green pixel (0, 90, 200 RGB)

Landsat MSS bands 4 and 5

GREEN RED

Landsat MSS bands 6 and 7

INFRARED 2INFRARED 1

Note: water absorbs IR energy-no return=black

• combining bands creates a false color composite

• red=vegetation• light blue=urban• black=water

• pink=agriculture

Rutgers

Manhattan

PhiladelphiaPine barrensChesapeake BayDelaware River

MSS color composite

Primary Colors

Red Green

Blue

Subtractive Primary Colors

Yellow (R+G)

absence of blue

Cyan (G+B)

absence of red

Magenta (R+B)

absence of green

Color Additive Process: the way a computer display works

R G

B

M

Y

CW

Black background

Y C

M

R

G

BB

Color Subtractive Process: the way paint pigment works

White background

Additive Color Processcolor R G B

white 255 255 255

black 0 0 0

grey 100 100 100

red 255 0 0

yellow 255 255 0

cyan 0 255 255

magenta 255 0 255

orange 255 100 0

dark blue 0 0 100

Summarizing data distributions

• Frequency distributions - method of describing or summarizing large volumes of data by grouping them into a limited number of classes or categories

• Histograms - graphical representation of a frequency distribution in the form of a bar chart

Summarizing Data Distributions: Histograms

0 255Digital Number

# of pixels

Measures of Central Location

• Mean - simple arithmetic average, the sum of all observations divided by the number of observations

• Median - the middle number in a data set, midway in the frequency distribution

• Mode - the value that occurs with the greatest frequency, the peak in a histogram

Measures of Central Location

0 255Digital Number

# of pixels

Mode

Mean

Median

Measures of Dispersion

• Range - the difference between the largest and smallest value

• Variance - the average of the squared deviations between the data values and the mean

• Standard Deviation - the square root of the variance, in the units of data measurement

Measures of Dispersion: Range

0 255

Digital Number

# of pixels

Min = 60 Max = 200

Example: Range = (max - min) = 200 - 60 = 140

Image Restoration and Enhancement

Image spectral enhancement

0 255Digital Number

# of pixels

Min = 0 Max = 255

Image display devices typically operate over a range of 256 gray levels. Ideally the image data ranges over this full extent.

Image spectral enhancementHowever, sensor data in a single band rarely extend over this entire range, resulting in a loss of contrast. The objective of spectral enhancement is to determine a transformation function to improve the brightness, contrast and color balance and thereby enhance image interpretability.

No data No data

0 255

Digital Number

# of pixels

Min = 50 Max = 200

Image spectral enhancement: lookup tables

• Image file values are read into the image processor display memory. These values are then manipulated for display by specifying the contents of the 256 element color look-up-table (LUT). By changing the LUT, the user can easily change the output display without changing the original file DN values.

Data FileGreen band DN = 100

LUTGreen band DN = 190

Enhanced Green pixel

Display DN = 190

Input LUT Output

Image spectral enhancement: Lookup tables

• Since the same transformation function is used for all the pixels in the image, it is calculated for all possible DN before processing the image. The resulting values of DN are stored in a lookup table (LUT).

• All possible values are computed only once - computationally efficient.

• Each pixel’s DN is then used to index the LUT to find the appropriate DN’ in the output image

LUT Input-Output relationship: ideal

00

255

255

Output

DN

Input DN

Input = 127

Output = 127

From ERDAS Imagine Field Guide 5th Ed.

1-to-1 transformation function

Transformation function

00

255

255

Output

DN

Input DN

The steeper the transformation line -> the greater the contrast stretch

Image spectral enhancement: NO contrast stretch

0 255

60 108 158

Image spectral enhancement: Min-max linear contrast stretch

0 255

60 108 158

125

Linear transformation function

The steeper the transformation line -> the greater the contrast stretch

00

255

255

Output

DN

Input DN

Input min = 60

Output min = 0

Input max = 158

Output max = 255

Image spectral enhancement: Min-max linear contrast stretching• Linear stretch: uniform expansion , with all

values, including rarely occurring values, weighted equally

• DN’ = [(DN - MIN)/(MAX - MIN)] x 255

• Example: DN = 108DN’ = [(108 - 60) / (158 - 60)] x 255

= [48 / 98] x 255 = .49 x 255 = 125

Example from Lillesand & Kiefer, 2nd ed

Image spectral enhancement: Std. Dev. linear contrast stretching• If data histogram near normal, then 95% of

the data is within +- 2 std dev from the mean, 2.5% in each tail

0 255

Image spectral enhancement: Histogram stretching

• Histogram stretch: image values are assigned to the display LUT on the basis of their frequency of occurrence

greatest contrast near modeleast contrast in histogram tails

0 255

108 158

38

60

Example from Lillesand & Kiefer, 2nd ed

Histogram stretching

00

255

255

Output

DN

Input DN

Input min = 60

Output min = 0

Input max = 158

Output max = 255

Nonlinear function in tails of distribution

Image spectral enhancement: Contrast stretching

• Special stretch: display range can be assigned to any particular user-defined range of image values

Example from Lillesand & Kiefer, 2nd ed

0 255

15860 92

Special piecewise stretching

00

255

255

Output

DN

Input DN

Different sections of the input data stretched to different extents;

I.e. different pieces of the transformation function line with different slopes

Simple Image Segmentation• Simplifying the image into 2 classes based on

thresholding a single image band, so that additional processing can be applied to each class independently

• < DN threshold = Class 1• >= DN threshold = Class 2• Example: gray level thresholding of NIR band used

to segment image into land vs. water binary mask

+