image display & enhancement lecture 2 prepared by r. lathrop 10/99 updated 1/03 readings: erdas...
TRANSCRIPT
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
Analog-to-digital conversion process
A-to-D conversion transforms continuous analog signal to discrete numerical (digital) representation by sampling that signal at a specified frequency
Discrete sampled value
Continuous analog signal
Radiance, L
dt Adapted from Lillesand & Kiefer
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)
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
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 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
Covariance & Correlation Matrices
• Provide a useful summary of data relationships
• High variance suggests a higher information content for that band
• High correlation suggests a substantial amount of redundancy
• Low correlation suggests that each band provides information not found in the other
Covariance Matrix
Covariance matrix 1 2 3 4 5 6 7
1 232.3 139.1 237.2 -35.3 191.9 42.0 182.62 139.1 89.9 153.4 -4.6 142.1 24.1 122.03 237.2 153.4 273.1 -26.9 249.1 46.4 219.44 -35.3 -4.6 -26.9 341.1 216.1 -38.1 25.35 191.9 142.1 249.1 216.0 555.2 33.5 305.36 42.0 24.1 46.4 -38.1 33.5 31.22 40.67 182.6 122.0 219.4 25.3 305.3 40.6 227.6
Diagonals represent band variances. Example, variance for Band 3 = 273.1Off-diagonals represent covariances. Example, covariance of Band 1 and 4 = -35.3; same as covariance of Band 4 and 1. Negative covariance: as one band increases, the other decreases.
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)
• 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
Subtractive Primary Colors
Yellow (R+G)
absence of blue
Cyan (G+B)
absence of red
Magenta (R+B)
absence of green
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
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
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
Adaptive Filtering
• Image stretching represents a global operator – i.e. applies the stretch equally across the entire scene and doesn’t take into account local differences in image brightness or other characteristics. Not always the best approach.
• Adaptive filters work by adapting the stretch to a smaller region of interest, usually the area within a moving window.
Multisensor fusion
• Various techniques have been developed to merge low spatial resolution (but high spectral resolution) with high spatial resolution (but low spectral resolution, e.g., panchromatic) imagery example: TM and ETM+ PAN
• Multisensor fusion will become more common as the new high spatial resolution PAN imagery becomes more widely available
One meter Pan-sharpened Multispectral IKONOS imagery (simulated)
Tennis courts in Washington Park, Denver, CO
Quickbird image example: Barnegat Bay, NJ 10/18/2004
Panchromatic: 0.61-1m
Multispectral (color): 2.5-4 m
Pixel size for this merged Pan-Multi image is 0.7 m
Example: IHS Color-space transform
• RGB to IHS: transform fro Red-Green-Blue color space to Intensity-Hue-Saturation
• Low and high resolution images are co-registered and resampled to same GRC
• 3 bands of the multispectral image converted to IHS space then PAN band substituted for the Intensity component, then back-transformed into RGB color space
• A disadvantage is that only 3 bands may be transformed simultaneously
Intensity, Hue & Saturation color coordinate system
Saturation
Hue
Intensity
0
255
0255
redgreen
blue
255,0
Example: PCA Spectral domain fusion
• Low and high resolution images are co-registered and resampled to same GRC
• PCA of multispectral image• Substitution of PAN image for 1st PC, often the
“brightness component”, then backtransform to image space
• This technique can be used for any number of bands
• Generally a good compromise between limited spectral distortion and visually attractiveness
Example: High Pass Filter (HPF) method
• Capture high frequency information from the high spatial resolution panchromatic image using some form of high pass filter
• This high frequency information then added into the low spatial resolution multi-spectral imagery
• Often produces less distortion to the original spectral characteristics of the imagery but also less visually attractive
Example: Brovey Transform fusion
For each spectral band i
[DNBi / (DNB1 + DNB2 + DNB3)] x (DN high res. Image)
Brovey transform was developed to increase contrast in the low and high tails of the image histogram for visual interpretation- doesn’t preserve the original scene radiometry.
Other methods: Multiplicative
Spherical Coordinates
Wavelets
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
+