1. Image Enhancement Band Ratio Linear Contrast Enhancement
Geography KHU Jinmu Choi
Band Ratio
Linear Contrast Enhancement
Spatial Filtering
Histogram Equalization
Principle Component Analysis

2. Band Ratioing
where:
BVi,j,k is the original input brightness value in band k
BVi,j,l is the original input brightness value in band l
BVi,j,ratio is the ratio output brightness value
Ratio values within the range 1/255 to 1 are assigned values between 1 and 128 by the function:
Ratio values from 1 to 255 are assigned values within the range 128 to 255 by the function:
(source: Jensen, 2011)

3. Linear Contrast Enhancement: Minimum- Maximum Contrast Stretch
(source: Jensen, 2011)
where:
- BVin is the original input brightness value
- quantk is the range of the brightness values that can be
displayed on the CRT (e.g., 255),
mink is the minimum value in the image,
maxk is the maximum value in the image, and
BVout is the output brightness value
All other original brightness values between 5 and 104 are linearly distributed between 0 and 255.

4. Min-Max Contrast Stretch +1 Standard Deviation Contrast Stretch
(source: Jensen, 2011)

5. Spatial Filtering to Enhance Low- and High-Frequency Detail and Edges
A characteristics of remotely sensed images is a parameter called spatial frequency, defined as the number of changes in brightness value per unit distance for any particular part of an image.
Spatial frequency may be enhanced or subdued using two different approaches:
- Spatial convolution filtering based primarily on the use of convolution masks, and
- Fourier analysis which mathematically separates an image into its spatial frequency components.

6. Spatial Convolution Filtering
A linear spatial filter is a filter for which the brightness value (BVi,j,out) at location i,j in the output image is a function of some weighted average (linear combination) of brightness values located in a particular spatial pattern around the i,j location in the input image.
The process of evaluating the weighted neighboring pixel values is called two-dimensional convolution filtering.
The size of the neighborhood convolution mask or kernel (n) is usually 3 x 3, 5 x 5, 7 x 7, 9 x 9, etc.

7. Spatial Convolution Filtering
We will constrain our discussion to 3 x 3 convolution masks with nine coefficients, ci, defined:
c1 c2 c3
Mask template = c4 c5 c6
c7 c8 c9 1
The coefficients, c1, in the mask are multiplied by the following individual brightness values (BVi) in the input image:
c1 x BV c2 x BV c3 x BV3
Mask template = c4 x BV c5 x BV c6 x BV c7 x BV c8 x BV c9 x BV9
The primary input pixel under investigation at any one time is BV5 = BVi,j

8. Spatial Convolution Filtering: Low Frequency Filter1
(source: Jensen, 2011)

9. Spatial Convolution Filtering
A median filter has certain advantages when compared with weighted convolution filters, including: 1) it does not shift boundaries, and 2) the minimal degradation to edges allows the median filter to be applied repeatedly which allows fine detail to be erased and large regions to take on the same brightness value (often called posterization).
Minimum or Maximum Filters: Operating on one pixel at a time, these filters examine the brightness values of adjacent pixels in a user-specified radius (e.g., 3 x 3 pixels) and replace the brightness value of the current pixel with the minimum or maximum brightness value encountered, respectively.

10. Spatial Convolution Filtering: High Frequency Filter
High-pass filtering is applied to imagery to remove the slowly varying components and enhance the high-frequency local variations. One high-frequency filter (HFF5,out) is computed by subtracting the output of the low-frequency filter (LFF5,out) from twice the value of the original central pixel value, BV5:

11. Spatial Convolution Filtering: Edge Enhancement
Edge enhancement delineates edges and makes the shapes and details comprising the image more conspicuous and perhaps easier to analyze. Edges may be enhanced using either linear or nonlinear edge enhancement techniques.
The result of the subtraction can be either negative or possible, therefore a constant, K (usually 127) is added to make all values positive and centered between 0 and 255

12. Compass Gradient Masks
Spatial Convolution Filtering 1 -1
Linear Edge Enhancement - Embossing
Emboss East
Emboss NW 1 -2 -1
Compass Gradient Masks
(source: Jensen, 2011)
North
Northeast
East

13. Sobel Operator 1 2 -1 -2 -1 1 -2 2 X = Y = 1 4 7 8 2 6 9 3 order-1 -2 -1 1 -2 2
X =
Y =
(source: Jensen, 2011)

14. 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 (e.g., 32, 64, and 256).
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.

15. Statistics for a 64 x 64 Hypothetical Image
with Brightness Values from 0 to 7
(source: Jensen, 2011)
4096 total

16. Statistics of How a a 64 x 64 Hypothetical Image with
Brightness Values from 0 to 7 is Histogram Equalized
(source: Jensen, 2011)

17. Principal Components Analysis
Transformation of the raw remote sensor data using PCA can result in new principal component images that may be more interpretable than the original data.
to compress the information content of a number of bands
(source: Jensen, 2011)

18. Charleston, SC Thematic Mapper scene statistics used in the principal components analysis (PCA)
(source: Jensen, 2011)

19. Statistics Used in the Principal Components Analysis
(source: Jensen, 2011)
where EVT is the transpose of the eigenvector matrix, EV, and E is a diagonal covariance matrix whose elements, li,i, called Eigenvalues, are the variances of the pth principal components, where p = 1 to n components.

20. Eigenvalues Computed for the Covariance Matrix7
p = 1 7
p = 1
(source: Jensen, 2011)

21. Eigenvectors (ap) (Factor Scores) Computed for the Covariance Matrix
(source: Jensen, 2011)

22. Correlation, Rk,p, Between Band k and Each Principal Component p
where:
ak,p = eigenvector for band k and component p
lp = pth eigenvalue
Vark = variance of band k in the original
covariance matrix
(source: Jensen, 2011)

23. original remote sensor data for pixel 1,1
It is possible to compute a new value for pixel 1,1 (it has 7 bands) in principal component number 1 using the following equation:
original remote sensor data for pixel 1,1
where akp = eigenvectors, BVi,j,k = brightness value in band k for the pixel at row i, column j, and n = number of bands.
(source: Jensen, 2011)

24. Kauth-Thomas “Tasseled Cap” Transformation
(source: Jensen, 2011)

25. Next Lab: Exercise: Image Enhancement
Lecture: Supervised Classification
Source:
Jensen and Jensen, 2011, Introductory Digital Image Processing, 4th ed, Prentice Hall.