Digital Image Processing, 2nd ed. Digital Image Processing, 2nd ed. The principal objective of enhancement

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1 Chapter 3 Image Enhancement in the Spatial Domain The principal objective of enhancement to process an image so that the result is more suitable than the original image for a specific application. Enhancement methods Spatial Domain (in this chapter) based on direct manipulation of pixels in an image Frequency Domain (in chapter 4) based on modifying the Fourier transform of an image The viewer is the ultimate judge of how well of a particular method works. Chapter 3 Image Enhancement in the Spatial Domain 3.1 Background 3.2 Some basic gray level transformations 3.3 Histogram processing 3.4 Enhancement using arithmetic/logic operations 3.5 Basics of spatial filtering 3.6 Smoothing spatial filters 3.7 Sharpening spatial filters 3.8 Combining spatial enhancement methods

2 3.1 Background Spatial domain methods operate directly on image pixels ( x, y) T[ f ( x, y) ] (3.1-1) g = T operates only for one pixel s = T (r) (3.1-2) Mapping Contrast Stretching Thresholding Binary Image 3.1 Background

3 3.1 Background T operates with neighboring pixels Mask (filter, kernel, template, window) 3.1 Background Mask m = m m m m m m m m T [ f ( x, y) ] = f ( x 1, y 1) m00 + f ( x 1, y) m01 + f ( x 1, y + 1) m f ( x, y 1) m10 + f ( x, y) m11 + f ( x, y + 1) m12 + f ( x + 1, y 1) m20 + f ( x + 1, y) m21 + f ( x + 1, y + 1) m

4 3.1 Background Original Image 1 9 Mask = Processed Image 3.2 Some basic gray level transformations

5 3.2 Some basic gray level transformations Image Negative s = ( L 1) r (3.2-1) 3.2 Some basic gray level transformations Original Image Processed Image

6 3.2 Some basic gray level transformations Log Transformation s = c log + r ( 1 ) (3.2-2) 3.2 Some basic gray level transformations Log Transformation Original Image Processed Image

7 3.2 Some basic gray level transformations Power-Law Transformation γ s = cr (3.2-3) 3.2 Some basic gray level transformations Power-Law Transformation

8 3.2 Some basic gray level transformations Power-Law Transformation 3.2 Some basic gray level transformations Power-Law Transformation

9 3.2 Some basic gray level transformations Piecewise-Linear Transformation Functions Contrast Stretching 3.2 Some basic gray level transformations Piecewise-Linear Transformation Functions Original Image Processed Image

10 3.2 Some basic gray level transformations Piecewise-Linear Transformation Functions Gray-level slicing 3.2 Some basic gray level transformations Piecewise-Linear Transformation Functions Original Image Processed Image

11 3.2 Some basic gray level transformations Piecewise-Linear Transformation Functions Bit-plane slicing 3.2 Some basic gray level transformations Piecewise-Linear Transformation Functions

12 3.3 Histogram Processing h ( r k ) = nk 3.3 Histogram Processing

13 3.3 Histogram Processing Histogram Equalization Conditions: (a) T(r) is single valued and monotonically increasing (b) 0 T(r) 1 for 0 r Histogram Processing Histogram Equalization PDFs( ) of r and s Transformation Function s = T () r 0 r 1 (3.3-1) Inverse function 1 r = T () s 0 s 1 (3.3-2) p r ( r) dr p () s p () r (3.3-3) r s s = r s s r ds

14 3.3 Histogram Processing Histogram Equalization If s is the Cumulative Density Function (CDF) of p r 3.3 Histogram Processing Histogram Equalization p dr () s pr () r ds s = p s (s) is a uniform PDF Because p s (s) is 1 for any p r (r)

15 Discrete Version 3.3 Histogram Processing Histogram Equalization r k = k, n k r k 0 sk Histogram Processing Histogram Equalization Histogram Equalization to produce an output image that has a uniform histogram procedures Histogram CDF( )T() T()

16

17 3.3 Histogram Processing Histogram Matching (Specification) Development of the method r z T( ): r -> s G( ): z->s

18 Discrete Version 3.3 Histogram Processing Histogram Matching (Specification) 3.3 Histogram Processing Histogram Matching (Specification)

19 3.3 Histogram Processing Histogram Matching (Specification) Implementation 1. Histogram 2. (3.3-13) s k 3. (3.3-14) pz(z) G 4. (3.3-17) z k r k s k s k z k Comparison between histogram equalization and histogram matching

20

21 3.3 Histogram Processing Local Enhancement : histogram 2.2. histogram equalization/matching 3.3 Histogram Processing Use of histogram statistice for image enhancement N-Norm mean value 2-Norm Standard Deviation S x,y

22 3.3 Histogram Processing Use of histogram statistice for image enhancement 3.3 Histogram Processing Block Size = 3x3 Use of histogram statistice for image enhancement

23 3.3 Histogram Processing Use of histogram statistice for image enhancement E=4.0, k 0 =0.4, k 1 =0.02, k 2 = Enhancement using Arithmetic/Logic Operations performed on a pixel by pixel basis between two or more images Logic Operations AND OR NOT Arithmetic Operations Substraction Averaging

24 3.4 Enhancement using Arithmetic/Logic Operations 3.4 Enhancement using Arithmetic/Logic Operations Image Substraction

25 3.4 Enhancement using Arithmetic/Logic Operations 3.4 Enhancement using Arithmetic/Logic Operations

26 3.4 Enhancement using Arithmetic/Logic Operations - Image averaging 3.4 Enhancement using Arithmetic/Logic Operations - Image averaging

27 3.5 Basics of spatial filtering Mask filter, kernel, templete, window 3.5 Basics of spatial filtering Mask filter, kernel, templete, window converlution mask/kernel

28 3.6 Smoothing Spatial Filter Smoothing filters are used for blurring noise reduction 3.6 Smoothing Spatial Filter Smoothing linear filters Smoothing linear filters also called averaging filter lowpass filter Smoothing Linear Filters

29 3.6 Smoothing Spatial Filter Smoothing Linear Filters Mask 3.6 Smoothing Spatial Filter Smoothing Linear Filters

30 3.6 Smoothing Spatial Filter Order-Statistics Filters Non-linear filters Median filter example unsorted (60,20,15,23,35,47,78,53,65) sorted (15,20,23,35,47 47,53,60,65,78) the median is 47 Max filter Min filter 3.6 Smoothing Spatial Filter Order-Statistics Filters

31 3.7 Sharpening Spatial Filters Sharpening Spatial filters are used to highlight fine detail enhance detail that has been blurred 3.7 Sharpening Spatial Filters First-order derivative Foundation Second-order derivative

32 3.7 Sharpening Spatial Filters Foundation 3.7 Sharpening Spatial Filters Use of second Derivatives for enhancement The Laplacian Development of the method

33 3.7 Sharpening Spatial Filters Use of second Derivatives for enhancement Filters 3.7 Sharpening Spatial Filters Use of second Derivatives for enhancement

34 3.7 Sharpening Spatial Filters Use of second Derivatives for enhancement Simplification 3.7 Sharpening Spatial Filters Use of second Derivatives for enhancement

35 3.7 Sharpening Spatial Filters Use of second Derivatives for enhancement Unsharp masking and high-boost filtering 3.7 Sharpening Spatial Filters Use of second Derivatives for enhancement

36 3.7 Sharpening Spatial Filters Use of second Derivatives for enhancement 3.7 Sharpening Spatial Filters Use of First Derivatives for enhancement The Gradient ( ( )

37 3.7 Sharpening Spatial Filters Use of First Derivatives for enhancement for 3 x 3 masks (b) and (c) are refered as Roberts cross-gradient Operators (d) and (e) are called Sobel Operators 3.7 Sharpening Spatial Filters Use of First Derivatives for enhancement

38 3.7 Sharpening Spatial Filters Use of First Derivatives for enhancement 3.7 Sharpening Spatial Filters Use of First Derivatives for enhancement

39 3.8 Combining Spatial Enhancement Methods 3.8 Combining Spatial Enhancement Methods

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