1. Chap2 Image enhancement (Spatial domain)

2. Preprocessing Why we need image enhancement? Un-necessary noises
Defects caused by image acquisition
Uneven illumination: non-uniform
Lens: blurring object or background
Motion : blurring
Distortion: geometric distortion caused by lens
registration

3. Image Enhancement in the
Chapter 2
Image Enhancement in the
Spatial Domain
2.1 Background
Specific application—problem oriented
Trial and error is necessary
Spatial domain will be denoted by the expression g(x,y)=T[f(x,y)]
The simplest form of T: s=T(r)
Contrast stretching: (Fig. 3.2 (a))
Thresholding function: binary image (Fig. 3.2)
Masks (filters, kernels, templates, windows)
Enhancement : mask processing or filtering
2.2 Some gray level transformations
Three basic types of functions used for image enhancement
Linear
logarithmic
Power-law

4. Is obtained by using the negative transformation s=L-1-r
2.2.1 Image negatives
Is obtained by using the negative transformation s=L-1-r
Produces the equivalent of a photographic negative
Suited for enhancing white or gray detail embedded in dark regions of an image
2.2.2 Log transformations
The general form of the log transformation : s=clog(1+r)
Expand the values of dark pixels while compressing the high-level values
Compress the dynamic range of images with large variations
2.2.3 Power-law transformation
The basic form:
Gamma correction
CRT device have an intensity-to-voltage response that is a power function
Produce images that are darker than intended
Is important if displaying an image accurately on a computer screen

5. Image Enhancement in the
Chapter 3
Image Enhancement in the
Spatial Domain

6. Image Enhancement in the
Chapter 3
Image Enhancement in the
Spatial Domain

7. Image Enhancement in the
Chapter 2
Image Enhancement in the
Spatial Domain

8. Image Enhancement in the
Chapter 2
Image Enhancement in the
Spatial Domain

9. Image Enhancement in the
Chapter 2
Image Enhancement in the
Spatial Domain

10. Image Enhancement in the
Chapter 2
Image Enhancement in the
Spatial Domain

11. 2.2.4 Piecewise-linear transformation functions
Low r: wash-out in the background (Fig r=0.3)
High r: enhance a wash-out appearance (Fig. 3.9 r=0.5 areas are too dark)
2.2.4 Piecewise-linear transformation functions
Advantage: the form of piecewise functions can be arbitrary complex over the previous functions
Disadvantage: require considerably more user input
Contrast stretching
One of the simplest piecewise function
Increase the dynamic range of the gray levels in the image
A typical transformation: control the shape of the transformation
r1=r2 s1=0 and s2=L-1
Gray level slicing
Highlight a specific range of gray levels
Display a high value for all gray levels in the range of interest and a low value for all other gray levels : produce a binary image

12. Continue
Brighten the desired range of gray levels, but preserves the background and gray level tonalities (Fig. 3.11)
The higher order bits (especially the top four) contain the majority of the visually significant data

13. Image Enhancement in the
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Image Enhancement in the
Spatial Domain

14. Image Enhancement in the
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Image Enhancement in the
Spatial Domain

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Image Enhancement in the
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16. Image Enhancement in the
Chapter 2
Image Enhancement in the
Spatial Domain

17. 2.3 Histogram processing 2.3.1 Histogram equalization
Histogram of a digital image with the gray levels in the range[0, L-1]
Low contrast: a narrow histogram, a dull, wash-out gray look
High contrast : cover a broader range of the gray scale and the distribution of pixels is not too far uniform, with very few vertical lines being much higher than the others
A great deal of details and high dynamic range
2.3.1 Histogram equalization
Histogram of S=T (r) 0 r1
produce a level s for every pixel value in the original image, the transformation satisfies the following conditions:
(1) T(r) is single-valued and monotonically increasing in the interval
0 r 1; and
(2) 0 T ( r )  1 for 0 r 1
r=T-1(s) 0 s 1

18. Image Enhancement in the
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Image Enhancement in the
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19. Image Enhancement in the
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Image Enhancement in the
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20. 3.4 Enhancement using arithmetic/logic operations
Image subtraction —g(x,y)=f(x,y)-h(x,y)
Masking
is referred to as ROI (region of interest) processing
Isolate an area for processing
Arithmetic operations
Addition:
Subtraction:
Multiplication: used to implement gray-level rather than binary
Division:
Logic operations
And: used for masking (Fig. 3.27)
Or:used for masking
Not operation: negative transformation
Also are used in conjunction with morphological operations

21. Image Enhancement in the
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Image Enhancement in the
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22. 2.4.1 Image subtraction
The difference between two images f(x,y) and h(x,y) is expressed as g(x,y)=f(x,y)-h(x,y)
Enhance the difference part of two images
Contrast stretching transformation—useful for evaluating the effect of setting to zero the lower-order planes (Fig. 3.28(d))
Mask mode radiography (Fig 3.29)
Sort of scaling : solve image values outside form the range 0 to 255 (-255 to 255)
(1) Add 255 to every pixel and divide by 2: fast and simple to implement, but the full rang of the display may not be used
(2) more accuracy and full coverage of the 8-it range
The values of the minimum difference is obtained and its negative added to all the pixels in the difference image
All the pixels in the image are scaled to [0,255] by multiplying 255/Max
2.4.2 Image averaging
g(x,y)=f(x,y)+(x,y) (assume every pair of coordinates (x,y) the noise is uncorrelated and has zero average value)

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Image Enhancement in the
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25. Reduce the noise content by adding a set of noise images {gi(x,y)}
An image is formed by averaging K different noisy images
As k increases, the variability of the pixel values at each location (x,y) decreases
The image gi(x,y) must be registered in order to avoid the introduction of blurring
Use integrating capabilities of CCD or similar sensors for noise reduction by observing the same scene over long periods of time
3.5 Basics of spatial filtering
Sub-image: (filter, mask, kernel, template or window)
Frequency domain:
Spatial domain
Linear spatial filtering: is give by a sum of products of the filter coefficients R=
In general, linear filtering of an image with a filter mask of size MxN is given by g(x,y)
Convolving a mask with an image by pixel-by-pixel basis

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Image Enhancement in the
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Image Enhancement in the
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30. 2.6 Smoothing spatial filters
Used for blurring and for noise reduction
Blurring is used for removal of detail and bridging of small gaps in lines or curves
2.6.1 Smoothing linear filters
Averaging filter (low pass filter)
Replace the value of every pixel by the average of the gray levels in the neighborhood by the filter mask
Reduce sharp transition (such as random noise)
Blur edges
The average of the gray levels in the 3x3 neighborhoods
Averaging with limited data validity
only to pixels in the original image in a pre-defined interval of invalid data
Only if the computed brightness change of a pixel is in some pre-defined interval

31. Arithmetic mean Harmonic mean Geometric mean
Averaging according to inverse gradient
=Averaging using a rotation mask
2.6.2 Order Statistics filters (rank filters)
Nonlinear spatial filter based on ordering (ranking)
Median filter
Remove impulse noises (salt and pepper noises)
Represent 50 percent of a ranked set
Large clusters are affected considerably less
Min filter
Max filter--useful in finding the brightest points
Non-linear mean filter
Arithmetic mean
Harmonic mean
Geometric mean

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35. 3.7 Sharpening spatial filter Highlight fine detail or enhance detail
Enhance detail that has been blurred
Application ranging from electronic printing and medical imaging to industrial inspection
Can be accomplished by digital differentiation
3.7.1 Foundation
Sharpening filter based on first- and second-order derivatives
Definition for first derivatives
Must be zero in flat segment
Muse be nonzero at the onset of a gray level step or ramp
Must be nonzero along ramps
Def. of first derivate:
Produce “thick” edges
Has a strong response to gray-level step

36. Must be zero in flat areas
Definition for second derivatives: is better suited than the first-derivative for image enhancement
Must be zero in flat areas
Muse be nonzero at the onset and end of a gray level step or ramp
Must be zero along ramps of constant slope
Def. Of a second order derivate:
Produces finer edges
Enhance fine detail much more than a first order derivate for example: a thin line
The stronger response at an isolated point
Has a transition form positive back to negative
Produces a double response to a gray-level step
Highlight the fundamental similarities and differences between first- and second- order derivatives (Fig. 3.38)

37. Image Enhancement in the
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Image Enhancement in the
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Image Enhancement in the
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41. Image Enhancement in the
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Image Enhancement in the
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42. Robert operator Sobel operator Prewitt operator
Approximate the magnitude of the gradient by using absolute values
Lost isotropic feature property
Vertical and horizontal edges preserve the isotropic properties only for multiples of 90
Mask of odd sizes
Robert operator
Robert Ross-gradient operators
An approximation using absolute values (3.7-18)
Sobel operator
Use a weight value of 2 to achieve some smoothing by giving more importance to the center point
Constant or slowly varying shades are eliminated
Prewitt operator