1. CSC 381/481 Quarter: Fall 03/04 Daniela Stan Raicu
Homepage:
School of CTI, DePaul University
12/3/2018
Daniela Stan - CSC381/481

2. Outline Chapter 3: Image Enhancement in the Spatial Domain
Introduction (Section 3.1)
Enhancement by point processing (Section 3.2):
Image negatives
Log transformations
Power-law transformations
Piecewise-linear transformations
Histogram Processing (Section 3.3)
Final Projects discussion
12/3/2018
Daniela Stan - CSC381/481

3. Introduction
Image Enhancement procedures are techniques used to achieve a subjective improvement in image “quality” for a specific application (problem-oriented).
Typical applications:
noise removal
geometric correction
smoothing
sharpening
edge enhancement or extraction.
Usually ad hoc procedures.
Image Enhancement:
in the Spatial Domain (pixel operators)
the Frequency Domain (frequency filtering).
12/3/2018
Daniela Stan - CSC381/481

4. Spatial Domain Methods
Procedures that operate directly on the aggregate/neighborhood of pixels composing an image
A neighborhood about (x,y) is defined by using a square (or rectangular) subimage area centered at (x,y).
12/3/2018
Daniela Stan - CSC381/481

5. Spatial Domain Methods
When the neighborhood is 1 x 1 then g depends only on the value of f at (x,y) and T becomes a gray-level transformation (also called an intensity or mapping) function:
s=T(r)
r,s: gray levels of f(x,y) and g(x,y) at any point (x,y)
r denotes the pixel intensity before processing
s denotes the pixel intensity after processing.
These intensity transformations are also called point processing techniques.
12/3/2018
Daniela Stan - CSC381/481

6. Enhancement by Point Processing
The following methods are based only on the intensity of single pixels.
Image negatives
Log transformations
Power-law transformations
Piecewise-Linear Transformation Functions:
Contrast stretching
Gray-level slicing
Bit-plane slicing
12/3/2018
Daniela Stan - CSC381/481

7. Image Enhancement in the
Spatial Domain
Linear: Negative, Identity
Logarithmic: Log, Inverse Log
Power-Law: nth power, nth root
12/3/2018
Daniela Stan - CSC381/481

8. [0,L-1] the range of gray levels
Image Negatives
Are obtained by using the transformation function s=T(r).
Function T reverses the order from black to white so that the intensity of the output image decreases as the intensity of the input increases.
[0,L-1] the range of gray levels
S= L-1-r
12/3/2018
Daniela Stan - CSC381/481

9. Image Enhancement in the
Spatial Domain
Medical applications: much easier to analyze the breast tissue in the
negative image
12/3/2018
Daniela Stan - CSC381/481

10. Log Transformations s = c log(1+r) c: constant, r >=0
Compresses the dynamic range of images with large variations in pixel values
12/3/2018
Daniela Stan - CSC381/481

11. Piecewise-Linear Transformation Functions: Contrast Stretching
To increase the dynamic range of the gray levels in the image being processed.
12/3/2018
Daniela Stan - CSC381/481

12. Contrast Stretching
The locations of (r1,s1) and (r2,s2) control the shape of the transformation function.
If r1= s1 and r2= s2 the transformation is a linear function and produces no changes.
If r1=r2, s1=0 and s2=L-1, the transformation becomes a thresholding function that creates a binary image.
12/3/2018
Daniela Stan - CSC381/481

13. Image Enhancement in the
Spatial Domain
Contrast Stretching
Thresholding
12/3/2018
Daniela Stan - CSC381/481

14. Contrast Stretching More on function shapes:
Intermediate values of (r1,s1) and (r2,s2) produce various degrees of spread in the gray levels of the output image, thus affecting its contrast.
Generally, r1≤r2 and s1≤s2 is assumed.
12/3/2018
Daniela Stan - CSC381/481

15. Image Enhancement in the
Spatial Domain
Low contrast
image
High contrast
image
12/3/2018
Daniela Stan - CSC381/481

16. Spatial Domain Methods
Mask processing or filtering: when the values of f in a predefined neighborhood of (x,y) determine the value of g at (x,y).
Through the use of masks (or kernels, templates, or windows, or filters).
More in the next lecture when we discuss about Basics of Spatial filtering (Section 3.5)
12/3/2018
Daniela Stan - CSC381/481

17. Example of the use of a mask
Step 1: Move the window to the first location where we want to
compute the average value and then select only pixels
inside the window.
Step 2: Compute
the average value 4 6 7 1 9 2 5 3 4 1 9 2 3 7
Sub image p
Step 3: Place the
result at the pixel
in the output image
Original image
4.3
Step 4: Move the
window to the next
location and go to Step 2
Output image
12/3/2018
Daniela Stan - CSC381/481

18. Histogram Processing
The histogram of a digital image with gray levels from 0 to L-1 is a discrete function h(rk)=nk, where:
rk is the kth gray level
nk is the # pixels in the image with that gray level
n is the total number of pixels in the image
k = 0, 1, 2, …, L-1
Normalized histogram: p(rk)=nk/n
sum of all components = 1
To visualize the histogram of a digital image, we plot pr(rk)
versus rk
12/3/2018
Daniela Stan - CSC381/481

19. Image Enhancement in the
Spatial Domain
The shape of the histogram
of an image does provide
useful info about the
possibility for contrast
enhancement.
12/3/2018
Daniela Stan - CSC381/481

20. Types of Histogram Processing
Histogram equalization
Histogram matching (specification)
Local enhancement
12/3/2018
Daniela Stan - CSC381/481

21. Histogram Equalization
As mentioned above, for gray levels that take on discrete values, we deal with probabilities:
pr(rk)=nk/n, k=0,1,.., L-1
The plot of pr(rk) versus rk is called a histogram and the technique used for obtaining a uniform histogram is known as histogram equalization (or histogram linearization).
12/3/2018
Daniela Stan - CSC381/481

22. Histogram Equalization (HE)
The technique used for obtaining a uniform histogram
is known as histogram equalization (or histogram linearization).
where pr(rk)=nk/n, k=0,1,.., L-1
Histogram equalization(HE) results are similar to contrast stretching but offer the advantage of full automation, since HE automatically determines a transformation function to produce a new image with a uniform histogram.
12/3/2018
Daniela Stan - CSC381/481

23. 12/3/2018
Daniela Stan - CSC381/481

24. Local Enhancement
When it is necessary to enhance details over smaller areas, then we need to devise transformation functions based on the gray-level distribution in the neighborhood of every pixel
The procedure is:
1. Define a square (or rectangular) neighborhood and move the center of this area from pixel to pixel.
2. At each location, the histogram of the points in the neighborhood is computed and either a histogram equalization or histogram specification transformation function is obtained.
3. This function is finally used to map the gray level of the pixel centered in the neighborhood. The center is then moved to an adjacent pixel location and the procedure is repeated.
12/3/2018
Daniela Stan - CSC381/481