1. Digital Image Processing
Session 3
Dr. Ghassabi Tehran shomal University Spring 2015

2. Outline Introduction Digital Image Fundamentals
Intensity Transformations and Spatial Filtering
Filtering in the Frequency Domain
Image Restoration and Reconstruction
Color Image Processing
Wavelets and Multi resolution Processing
Image Compression
Morphological Operation
Object representation
Object recognition

3. Outline Chapter 3 Background
Some Basic Intensity Transformation Functions
Histogram Processing
Fundamentals of Spatial Filtering
Smoothing Spatial Filters
Sharpening Spatial Filters
Combining Spatial Enhancement Tools

4. Methods Image Enhancement Spatial Domain: Frequency Domain: Linear
Nonlinear
Frequency Domain:
پردازش در حوزه مکانی و در حوزه تبدیل. اولی مبتنی بر دستکاری مستقیم پیکسلها هست. دومی شامل تبدیل تصویر و پردازش و تبدیل معکوس هست.
ارتقا فرایند بهبود تصویر برای کاربرد خاص
Process an image so that the result will be more suitable than the original image for a specific application.
The suitableness is up to each application.
A method which is quite useful for enhancing an image may not necessarily be the best approach for enhancing another image
Spatial Domain : (image plane)
Techniques are based on direct manipulation of pixels in an image
Frequency Domain :
Techniques are based on modifying the Fourier transform of an image
There are some enhancement techniques based on various combinations of methods from these two categories

5. IE in Spatial Domain S=T(r)
Neighborhood of a point (x,y) can be defined by using a square/rectangular (common used) or circular sub image area centered at (x,y)
The center of the sub image is moved from pixel to pixel starting at the top of the corner
فیلتر کردن مکانی: مثال: محاسبه میانگین در همسایگی سه در سه اطراف هر پیکسل و تکرار این عمل برای هر سطر
Gray-level transformation function
S=T(r)
where r is the gray level of f(x,y) and s is the gray level of g(x,y) at any point (x,y)

6. Transformation For 11 neighborhood:
Contrast Enhancement/Stretching/Point process
For w w neighborhood:
Filtering/Mask/Kernel/Window/Template Processing
تابعی که در آن مقدار پیکسل r به پیکسل S نگاشت میشود.
در تابع اول تصویری با کنتراست بالاتر تولید می شود. که سطوح شدت پایین تر از m را تیره تر و سطوح شدت بالاتر از m را روشن تر خواهد نمود.
نگاشت دوم تصویر باینری ایجاد میکنه.

7. Transformation Functions
IE in Spatial Domain
Input gray level, r
Output gray level, s
Negative
Log
nth root
Identity
nth power
Inverse Log
Some Basic Intensity
Transformation Functions
Image Negatives:
An image with gray level in the range [0, L-1] where L = 2n ; n = 1, 2…
Negative transformation :
s = L – 1 –r
Reversing the intensity levels of an image.
Suitable for enhancing white or gray detail embedded in dark regions of an image, especially when the black area dominant in size

8. Image Negatives: Image Negatives
برای ارتقای تصویری که ناحیه های سیاه در آن زیاد باشد یا بخش سفیدی در بخش خاکستری قرار داشته باشد.

9. y
Image Negatives
y=L-x L L x

10. Log Transformation
بازه نازکی از مقادیر پایین شدت در تصویر ورودی را به بازه وسیع تری از سطوح خروجی تبدیل می نماید. درباره مقادیر بالاتر سطوح ورودی عکس آن درست است. از این تبدیل برای بسط مقادید پیکسلهای تاریک در یک تصویر و فشرده سازی مقادیر سطح بالاتر استقاده خواهیم کرد.
کاربرد: نمایش طیف بعد از تبدیل فوریه
c is a constant and r  0
Log curve maps a narrow range of low gray-level values in the input image into a wider range of output levels.
Used to expand the values of dark pixels in an image while compressing the higher-level values.

11. Log Transformation
Compress the dynamic range of images with large variations in pixel values
Stretch dark region, suppress bright region
From the range 0 – 1.5×106 to the range 0 to 6.2
We can’t see the significant degree of detail as it will be lost in the display.

12. Range Compression L x y
c=100
Y=clog10dd

13. Power-Law(Gamma) Transformations
Power-law transformations:
s=cr or s=c(r+ε)
 <1 maps a narrow range of dark input values into a wider range of output values, while  >1 maps a narrow range of bright input values into a wider range of output values
 : gamma, gamma correction
مقادیر مختلف S بر حسب r برای گاماهای مختلف ترسیم شده است.
برای گامای کمتر از یک مثل تابع لگاریتم هست. برای گامای یک مثل تابع همانی هست.

14. Power-Law(Gamma) Transformations
Gamma Correction:
Power-law transformations:
s=cr or s=c(r+ε)
 <1 maps a narrow range of dark input values into a wider range of output values, while  >1 maps a narrow range of bright input values into a wider range of output values
 : gamma, gamma correction

15. Power-Law(Gamma) Transformations
(a) a magnetic resonance image(MRI) of an upper thoracic human spine with a fracture dislocation and spinal cord impingement
The picture is predominately dark
An expansion of gray levels are desirable  needs  < 1
(b) result after power-law transformation with  = 0.6, c=1
(c) transformation with  = (best result)
با کاهش گاما جزییات بیشتری قابل مشاهده است ولی در نقطه ای که تصویر از آن جا روشن تر میشود ، مخصوصا در پس زمینه تصویر کنتراست شروع به کاهش میکند.
(d) transformation with  = 0.3 (under acceptable level)
Effect of decreasing Gamma:
When the  is reduced too much, the image begins to reduce contrast to the point where the image started to have very slight “wash-out” look, specially in the background

16. Power-Law(Gamma) Transformations (Effect of decreasing gamma)
تصویری که وجود دارد ظاهری روشن دارد که نیاز به فشردگی سطوح شدت داریم. پس نیاز به گامای بزرگتر از یک داریم
a) image has a washed-out appearance, it needs a compression of gray levels needs  > 1
(b) result after power-law transformation with  = 3.0 (suitable)
(c) transformation with  = 4.0 (suitable)
(d) transformation with  = 5.0 (high contrast, the image has areas that are too dark, some detail is lost)

17. Power-Law(Gamma) Transformations (Effect of decreasing gamma)
Another medical image

18. Piecewise-Linear Transformation Functions
Contrast Stretching
Contrast slicing
Bite-Plane slicing
Advantage:
The form of piecewise functions can be arbitrarily complex.
A Practical Implementation of some important transformations can be formulated only as piecewise functions.
Disadvantage:
Their specification requires considerably more user input.

19. Contrast Stretching y yb ya x a b L بازه سطوح شدت را افزایش میدهد.a b L
بازه سطوح شدت را افزایش میدهد.
کنتراست پایین: روشنایی ضعیف، عدم وچود بازه پویا در حسگر تصویر برداری، تنظیم نادرست لنز در تصویر برداری

20. Contrast stretching
Original
C. S.
THR.

21. Contrast Stretching

22. Clipping y x a b L

23. Gray-level Slicing برجسته کردن بازه خاصی از شدت
2 تا تابع هست. کلا بخش مورد نظر را روشن میکند و بقیه را صفر میکند. در حالت بعدی فقط بخش مورد نظر را روشن میکند و به بقیه دست نمیزند.
Highlighting a specific range of gray levels in an image
Display a high value of all gray levels in the range of interest and a low value for all other gray levels
(a) transformation highlights range [A,B] of gray level and reduces all others to a constant level
(b) transformation highlights range [A,B] but preserves all other levels

24. Gray-level Slicing
بخش بندی سطح شدت

25. Gray-level Slicing

26. Gray-level Slicing

27. Gray-level Slicing

28. Bit-plane Slicing
Highlighting the contribution made to total image appearance by specific bits
Suppose each pixel is represented by 8 bits
Higher-order bits contain the majority of the visually significant data
Useful for analyzing the relative importance played by each bit of the image
برجسته کردن با بیتها به جای استفاده از سطوح شدت.
4 صفحه بالا دارای اطلاعات ارزشمندی هستند.

29. Bit-plane Slicing

30. Bit-plane Slicing
The (binary) image for bit-plane 7 can be obtained by processing the input image with a thresholding gray-level transformation.
Map all levels between 0 and 127 to 0
Map all levels between 129 and 255 to 255

31. Bit-plane Slicing - Fractal Image

32. Bit-plane Slicing - Fractal Image

33. Bit-plane Slicing
کاربرد بخش بندی صفحه بیتی

34. Enhancement based on statistical Properties: Local, Global
Histogram Processing
Enhancement based on statistical Properties: Local, Global
Histogram Definition
h(rk)=nk
Where rk is the kth gray level and nk is the number of pixels in the image having gray level rk
Normalized histogram:
P(rk)=nk/n
Histogram of an image represents the relative frequency of occurrence of various gray levels in the image
So far, we have discussed various forms of f(x) that leads to different enhancement results
The natural question is: How to select an appropriate f(x) for an arbitrary image?
One systematic solution is based on the histogram information of an image.

35. Histogram Visual Meaning: Dark Bright Low Contrast High Contrast
Histogram Examples
Histogram Visual Meaning:
Dark
Bright
Low Contrast
High Contrast
Dark Image: Components of histogram are concentrated on the low side of the gray scale.
Bright Image: Components of histogram are concentrated on the high side of the gray scale
Low-contrast: Histogram is narrow and centered toward the middle of the gray scale
High-contrast: Histogram covers broad range of the gray scale and the distribution of pixels is not too far from uniform, with very few vertical lines being much higher than the others

36. Histogram Example

37. Histogram Example

38. Histogram Modification
Histogram Stretching
Histogram Shrink
Histogram Sliding
پردازش هیستوگرام

39. Histogram Stretching

40. Histogram Stretching

41. Histogram Stretching

42. Histogram Shrinking

43. Histogram Shrinking

44. Histogram Sliding